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B.A. (Hons) Economics-II Year Paper – IV MICRO QUESTION BANK SHIVAJI COLLEGE House Examination-2009-10 1. Answer any three parts. All parts carry equal Marks A. Professor goodheart always give two midterm in his microeconomics class. He only use the higher of the two score that a student gets on the midterms when he calculates the curse grade. (a) Nancy learner wants to maximize her grade in this course. Lets x1 be her score on the first midterm and x2 be the her score on the second midterm. Draw her indifference curve and find out Which combination of scores would nancy prefer, x1 = 20 and x2 = 70 or x1 = 60 and x2 = 60 (b) Does the nancy have convex preferences over these combination. B. Vanna Gogie likes to have large parties. She also have strong preferences for having exactly as many men as women at her parties. in facts vanna’s preferences among parties can be represented by the utility function Ux, y min 2x y, 2y x where x is the number of women and y is the number of the men at the party. (a) Draw indifference curve along which vanna’s utility is 10. (b) Suppose that there is 9 men and 10 woman at Vanna’s party. Would Vanna think it was a better party or worse if 5 more men came to her party. C. Jim’s utility function is Ux, y xy . Jerry’s utility function is Ux, y 1000 xy 2000 . Tammy’s utility function is Ux, y xy 1 - xy . Marjoe’s utility function is Ux, y x y 1000 . Pat’s utility function Ux, y .5xy - 10000 . Billy’s utility function is Ux, y x/y . F Francis’s utility function is Ux, y xy . (a) Who has the same preferences as Jim? (b) Who had the same indifference curve as jim? (c) Explain why the answers to a and b differ. D. Billy has a von Neumann- Morgenstern utility function U c c1/2 If Billy is not injured this season, he will receive an income of 25 million dollars. If he is injured, his income will be only $10,000. The probability that he will be injured is. 1 and the probability Bliss Point Studies Ravinder N. Jha 9891555578 1 9811343411 B.A. (Hons) Economics-II Year Paper – IV that he will not be injured is 9. Find out his expected utility (11 marks) 2. Dudley’s utility function is U(C (12 R) 2 , where R is the amount of leisure he has per day. He has 16 hours a day to divide between work and leisure. He has an income of $20 a day from nonlabour sources. The price of consumption goods is $1 per unit. (a) If Dudley can work hours a day as he likes but gets zero wages for his labour, how many hours of leisure will he choose? (b) Of If Dudley work can work as many hours a day as he wishes for a wage rate of $10 an hour, how many hours he will choose to work. (c) If Dudley’s nonlabour income decreased to $5 a day, how many hours would he choose to work. 3. Mr. O.B Kandle will only live for two periods. In periods. In the first period s he will earn $50000. In the second period he will retire and live on his saving. His utility function is Uc1 c 2 c1 c 2 , where c1 is consumption in period 1 and c 2 is consumption in period 2. He can borrow and lend at the interest rate = 10. (a) If the interest rate rises, will his consumption increase, decrease, or stay the same? (b) Would an increase in the interest rate make him consume more or less in the second period? (c) If Mr. Kandle’s income is zero in period 1 and $55000 in period 2, would an increase in the interest r rate make him consume more less, or the same amount in period 1? 4. A firm has two variable factors and a production function f x1, x 2 2x1 4x2 Draw production isoquants corresponding to an output of 3 and to an output of 4. (a) If the price of the output good is 4, the price of factor 1 is 2, and the price of factor 2 is 3, find the production maximizing amount of factor 1, the Production maximizing amount of factor 2, and the production maximizing output. 5. Consider an industry with the following structure. There are 50 firms that behave in a competitive manner and have identical cost functions given by cy y 2 /2 . There is one monopolist that has 0 marginal costs. The demand curve for the product is given by Dp 1000 50p Bliss Point Studies Ravinder N. Jha 9891555578 2 9811343411 B.A. (Hons) Economics-II Year Paper – IV (a) What is th.e supply curve of one of the competitive firms? The total supply from the competitive sector at price p is S(p) (b) If the monopolist sets a price p, the amount that it can sell is Dm(p) = (c) The monopolist’s production-maximizing output is Ym = What is the monopolist’s production-maximizing price? (d) How much output will the competitive sector provide at this price? What will be the total amount of output sold in this industry? 6. Suppose that the market demand curve for bean sprouts is given by P = 2080-2Q; where P is the price and Q is total industry output. Suppose that the industry has two firms, a Stackleberg leader, and a follower. Each firm has a constant marginal cost of $80 per unit of output. What will be the equilibrium output by the two firms. HALF-YEARLY EXAMINATION 2010 1. Answer any three questions. All question is carry marks. (a) How can a black market in food stamps be explained? (b) Do you agree with the following statement A student preparing for an examination should not study after reaching diminishing returns. Explain. (c) Explain the concept of maximin strategy. (d) If preferences are not convex, is it possible that substitution effect is non negative? (e) Explain the difference between increasing returns to scale and economies of scale. 2. (a) What does an Engel curve for an inferior good look like? (b) Can both goods in a two commodity world be inferior? Explain (c) Given U = min x1 , x 2 , obtain MU xl and depict it graphically as function of x 1 (d) Given convex preferences, can it be the case that a consumer specializes in the consumption of only one of the two goods? 3. (a) A self employed plumber is endowed with 168 hours per week and no non labor income. Current wage rate is RS 10/- per hour. (i) Write down and draw his budget equation (ii) His optimal choice of work is 40 hours per week. He is offered Rs.20/- per hour by an MNC to work for longer hours. Bliss Point Studies Ravinder N. Jha 9891555578 3 9811343411 B.A. (Hons) Economics-II Year Paper – IV But he still chooses to work only for 40 hours. Do you think that the plumber’s behavior is rational? Explain graphically. (iii) What alternative remuneration scheme would you suggest to the MNC to induce the plumber to work for longer hours? Explain graphically. (b) If leisure is an inferior good, what can you say about the slope of labour supply curve? Varian 4. (a) John’s utility function (u) for income (I) is given as UI I 2 for I 10 I 101/2 100 for I 10 (i) Draw John’s utility function. (ii) He is offered the following choice: Income of zero with a chance 0.25 and income of Rs. 14/- with chance 0.75. Or, a certain income of Rs.10/. Will he accept this bet? Why? (iii) He is offered a choice of income zero with chance 0.25 and income Rs 4/- with chance 0.75. Or a certain income of Rs. 3/-. Will he accept the bet? Why? What is his certainty equivalent? (b) Is satisfaction of WARP a sufficient condition for an optimizing consumer? 5. (a) Explain Stackleberg’s model of model duopolistic completion. (b) Let the following be a model of two part tariff under monopoly. If there are only two consumers in the market with the following demand curves respectively: Q1 14 2P1 Q2 10 2P2 MC = Rs. 4/- and the firm follows the rule of marginal cost pricing. (i) If the monopolist is able to keep the two markets separate, what rental and usage fee would he charge for each consumer? (ii) If a common two part tariff had to be changed, what would be the rental and csage fee? (iii) Compare the total profits of the firm an both (i) and (ii) above. 6. (a) In a democratic society why do most political parties tend profess moderate ideologies rather than extreme radical ideologies? Use the correct game theoretic model to explain your answer. Bliss Point Studies Ravinder N. Jha 9891555578 4 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) You are given the following pay off matrix: Firm B Enter Don’t Enter Low Price 3, -1 3, 1 Firm A High Price 4,5 6,3 (i) Does each firm have a dominant strategy? What is it? (ii) Why is the entry-deterrent threat by firm A to lower price not credible to firm B? (iii) What could firm A do to make its threat credible without building excess capacity? SATYAWATI COLLEGE (EVENING) MID-TERM EXAMINATION 2009-10 1. Answer any four parts: (i) If preferences are quasilinear what will the indifference curve be like? Write the equation for such an indifference curve. (ii) What does the inverse demand function measure? What will be the form of inverse demand function for good 1 in the case of perfect complements? (iii) If leisure is an inferior good, what can you say about the slope of the labour supply curve? (iv) A consumer’s endowment is w1 , w 2 4,4 , The prices are p1 , p 2 3,4 and the consumer is presently consuming (4, 4). Now the prices change to p1 , p 2 3,6 . Could the consumer be better off under these new prices? (v) A consumer, initially a lender, remains a lender after a decline in interest rate. Is he better off or worse off? If he becomes a borrower is he better off or worse off? (vi) Amita runs a biscuit factory that uses labour, L, and capital, K as inputs. If she hires L workers on a given day and K units of capital, she can manufacture FL, K L K biscuits. Does this technology 1/2 imply increasing, decreasing or constant returns to scale? 2. (a) Suppose that Amisha and Sanjay have two production plants for producing mango juice. They have a total of 850 crates of mangoes and the marginal product of mangoes in plant 1 is MP1M 1000 M1 and in plant 2 is MP 2 M 1200 2M 2 . What is the best assignment of mangoes between the two plants? Bliss Point Studies Ravinder N. Jha 9891555578 5 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) Many resort hotels remain open in the off season, even though they appear to be losing money. Why do they do so? 3. (a) The market demand function for wheat is Q d 21 4P , and the supply function is Qs 5P 6 , both quantities measured in crores of bushels per year. What are the aggregate surplus, consumer surplus, and producer surplus at the competitive market equilibrium? (b) Clearly bring out the welfare effects of monopoly pricing with the help of a diagram. 4. (a) Explain the monopoly pricing strategy known as a two-part tariff. To maximize its profit using a two-part tariff, a perfectly discrimination monopolist needs to set the per-unit charge equal to its marginal cost . (b) Atul and Richa play a simple one-stage game where each chooses either 1 or 2. If they both choose 1, Atul pays Richa Re.1. If they both choose 2, Atul pays Richa Rs.2.If they choose different numbers, Richa pays Atul Re.1. Draw a table showing the two players’ strategies and payoffs. Are any strategies dominant, weakly dominated, or dominated? Indicate each players best responses. Is there a Nash equilibrium? 5. (a) In each of following cases, calculate the interest earned on bank deposit after the specified number of years, given the specified initial deposit and the rate of interest – (i) Rs.300 deposited at 8% interest for 10 years, (ii) Rs. 4000 deposited at 5% for 30 years. (b) Calculate the present discounted value (PDV) of a 5-year bond with an annual coupon payment of Rs.200, and a principle payment at maturity of Rs.5000, at an interest rate of 5%. HOUSE EXAMINATION-2009-10 1. Attempt any three parts, all carry equal marks: (a) Radhika’s utility function is given by Ux, y max x,2y (i) Draw Radhila’s indifference curve for U = 4. (ii) If price of x is 1, the price of y is 2 and her income is 8, what bundle does Radhila choose in this situation? (b) Amit’s preferences are represented by the utility function Ux1, x 2 x1 x 2 . The prices of x 1 and x 2 are p1 and p 2 . Derive the income offer curve and Engel curve for goods x 1 and x 2 for Amit. Bliss Point Studies Ravinder N. Jha 9891555578 6 9811343411 B.A. (Hons) Economics-II Year Paper – IV (c) Firm A’s production function is given by Qa = L1/4 .K3/4 while form B’s production function is given by Qb L K . (i) Does the law of diminishing MPL hold for these production functions? (ii) Indicate whether these production functions have IRS, DRS, or CRS. (iii) Calculate MRTS LK for both the production functions. (d) Using slutsky equation show the effect of wage increase on supply of labor when (i) leisure is a normal good (ii) leisure is an inferior good. (e) Explain the difference between a strictly dominant strategy and an iterated strictly dominant strategy equilibrium. 2. (a) Fly- by- night Airlines and Going – going- gone Airways are considering whether to switch from their current standard fare schedule or implement a frequent – flyer program. The table below summarizes the monthly profits in thousands of dollars from alternative pricing strategies; Going- going- Gone Standard Frequent flyer Standard (250,275) (210,350) Fly- by- night (325,190) (200,150) Frequent Flyer (i) If larger payoffs are preferred, does either air corner have a dominant strategy? Explain. (ii) Determine the pure strategy Nash equilibrium for this game. (iii) What is the strategy profile for this game of both air carriers adopt a maximum decision rule? (b) What does it mean to be risk averse and risk loving? Assuming that a person is risk show the risk premium and certainty equivalent for a risky consumption bundle. 3. (a) Rohan has a small garden where he raises carrot and potatoes. He consumes some of these vegetables, and sells some in the market. His utility function is given by U(C,P) = min. {C, P}.His endowment of carrot and potatoes in 30 and 10 respectively and the price of each vegetable is Rs. 5. (i) What are Rohan’s net demands? (ii) Suppose now that the price of potatoes rises to Rs. 15 from Rs. 5. Calculate the change in demand due to substitution effect, ordinary income effect and endowment effect. Bliss Point Studies Ravinder N. Jha 9891555578 7 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) Show using isoquants and iso-cost lines that SRAC would normally be greater than the LRAC. Under what conditions would they be same? 4. (a) Suppose that the demand equations for the product of two profit maximizing firms in a duopoly industry are: Q1 50 5P1 2.5P 2 Q 2 20 2.5P 2 5P1 The firm’s total cost functions are: TC1 25 Q1 TC 2 50 Q 2 Suppose that these firms are Bertrand competitors. (i) What is the Bertrand –Nash equilibrium for this game? (ii) If the firm’s cooperate and agree to maximize profits, what is the equilibrium price they will charge? (b) Explain briefly the kinked demand curve model of oligopoly. What are its limitations? 5. (a) Show using indifference curve analysis that ‘lumsum’ subsidy makes the consumer better off compared to an ‘excise’ subsidy which costs the government the same amount. (b) A movie monopolist sells to college students and other adults. The demand function for students is Qs 800 100P and the d demand function for other adults is Qa 1600 100P . Marginal d cost is $2 per ticket. What prices will the monopolist set when she can discriminate between the college students and other adults? Also calculate the monopolist’s profit at equilibrium. 6. (a) Reena loves to consume two goods, grapefruits and almonds. The slope of an indifference curve through any point where she has a mare grapefruits than almonds is -2 while the slope of an indifference curve through any point where she has fewer grapefruits than almonds is -1/2. (i) Draw indifference curve for Reena through bundle (10A, 10G). (ii) Does Reena have strictly convex preferences? Explain. (iii)If price of almonds is Rs. 2, price of grapefruits is Rs. 2 and Reena’s income is Rs. 40, determine Reena’s equilibrium. (b) How long run total cost curve is related to the concept of the expansion path? Is there any relationship between LRTC and SRTC curves? Explain. Bliss Point Studies Ravinder N. Jha 9891555578 8 9811343411 B.A. (Hons) Economics-II Year Paper – IV Sanchi Bhatia Janki Devi Memorial College Home Examination 2009–10 1. (i) What is the present value of $100 one year from now if the interest rate is 10%? What is the present value if the interest rate is 5%. (ii) Can the long run total cost curve of a firm be a positively sloped straight line through the origin? What does it imply? What shapes will the long run average cost & long run marginal cost take in this case? Can the short run average cost be ‘U’ shaped? (iii) Why taking a monotonic transformation of a utility function does not change the marginal rate of substitution? (iv) Can an indifference curve cross itself? Give reason for your answer. Why indifference curve is always convex to the origin? If good 1 is a ‘neutral”, what is its MRS for good 2? (v) Distinguish b/w returns to scale and economies of scale. Is it possible to have constant return to scale & economies of scale together? 2. (i) If the same person acts as a risk avoider (Purchase fire insurance) and also acts as a risk seeker (gambles), can one explain such seemingly contradictory behaviour? (ii) Given that the demand for electricity is higher during same periods than at other times and that it is non-storable i.e., it must be generated when it is needed, how would consumer welfare be affected if different prices are charged for the service at these different times rather than charging a constant price in both periods? Why? 3. (i) How resources are allocated under monopoly and monopolistic competition market? Explain the short run and long run equilibrium under monopoly market? (ii) What is price discrimination. Explain the degrees of price discrimination? In what condition monopoly power will be higher? 4. (i) In a Production process is it possible to have decreasing marginal product in an input and yet increasing returns to scale? Explain the main Properties of technology? Why marginal rate of technical substitution is always diminishes? (ii) Why price and output is indeterminate under oligopoly market? Can you explain how output is determinated by Cournot model? Bliss Point Studies Ravinder N. Jha 9891555578 9 9811343411 B.A. (Hons) Economics-II Year Paper – IV 5. (i) A consumer, who is initially a lender, remains a lender even after a decline in interest rates. Is this consumer better off or worse off after the change in he better off or worse off? Show with the help of a diagram? (ii) How Revealed Preference theory is differ from Indifference Curve Analysis? Distinguish b/w Hicksion & Slutsky’s Substitution effect. 6. (i) For what kind of preferences will the consumer be just as well- off facing a quantity tax as an income tax? Show the income offer curve & Engel Curve in case of quasilinear preferences & Homothetic Preferences. (ii) Under Cournot’s Model market demand curve as p = 20 – q where q is the total production of two firms 1 and 2. Determine (a) Reaction Curves of the two firms assuming that both firms are producing under zero cost of production. (b) Equilibrium level of output for both the firms & equilibrium market price. In the place of Q. 4(a), Do the following question: 4. (a) Demand for light bulbs can be characterized by Q = 100 – P, where Q is in millions of boxes of lights sold and P is the price per box. There are two producers of lights, Surya Roshini and Osram. They have identical cost functions: 1 Ci 10Qi Qi2 2 Q QSR Q 0 (i) If the manager of each firm plays cournot, find the equilibrium values of QSR , Q 0 and P? (ii) Suppose Surya’s manager guesses correctly that Osram is playing Cournot, so he then plays Stackelberg. What are the equilibrium values of QSR , Q 0 and P? (iii) If the managers of the two companies collude, what are the equilibrium values of QSR , Q 0 and P? Home Examination 2009-10 1. Attempt any three parts. All parts carry equal marks. (a) Show that if a consumer spends all his income on two goods then the weighted average of the income elasticities of demand of the two goods in unity. Bliss Point Studies Ravinder N. Jha 9891555578 10 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) A consumer has the utility function given by U = y + log x. What can you say about demand for good x when money income changes? (c) Why does the minimum point of the AVC curve lie to the left of the minimum point of the ATC curve? (d) Why does the minimum point of the AVC curve lie to the left of the minimum point of the ATC curve? (e) Suppose MRS between goods x and y increases (in absolute value) as good x is substituted for good y. What would the tangency between budget line and indifference curve indicate? What would be the most preferred consumption choice? 2. (a) Consider the pricing of first-classes and coach airline tickets on a route where the airlines has a monopoly in air travel. Marginal cost is constant at Rs. 100. The demand for first-class tickets is P = 1000 – 5Q, while the demand for coach tickets is P = 500 – Q. (i) What are the profit-maximizing prices and quantities for first-class tickets and coach tickets? (ii) What is the demand elasticity for each market segment at the profit-maximizing prices you found in part (i)? (b) Suppose there are two types of consumers (in equal numbers) but the firm must charge the same price to everyone. The “high demand” consumers have the demand curve given by QH 130 P and the “low demand” consumers have the demand curve Q L 100 P . Marginal cost is constant at Rs. 10. Calculate profits for the firm if it sets a two-part tariff with usage fee equal to Rs. 10 and rental fee equal to consumer surplus for the “low demand” consumers at that price. Then calculate profits if usage fee is equal to Rs. 15 and entry fee is equal to consumer surplus for the “low demand” consumers at that price. Which pricing strategy is more profitable? 3. (a) Why is the firm’s demand curve flatter than the total market demand curve in monopolistic competition? A monopolistically competitive firm earns zero profit in the long run but still it has monopoly power. Explain. (b) Using the Rule of Thumb for Pricing, explain how a zero cost firm will determine its profit-maximizing price and output. Show it using a diagram also. (c) The Best Bakery sells a popular type of sandwich roll. It spends 4 percent of sales revenue on advertising. It sells its rolls for Rs. 0.35 when each roll has a marginal cost of Rs. 0.25. If the firm Bliss Point Studies Ravinder N. Jha 9891555578 11 9811343411 B.A. (Hons) Economics-II Year Paper – IV is maximizing profits, what is its advertising elasticity of demand? 4. (a) The kinked demand curve model describes price rigidity under oligopoly. Explain how it works and what is the limitation of this model? (b) The following is the pay-off matrix of two firms A and B in a pricing game: Firm B Low Price High Price Low Price 2, 2 5, 1 Firm A High Price 1, 5 3, 3 (i) Does there exist a dominant strategy for each firm? (ii) Determine the pure strategy Nash equilibrium in this game? 5. (a) A consumer’s utility function is given by U(x, y) = min (2x, y). Suppose that the price of good x is Rs. 1 per unit, price of good y is Rs. 0.75 per unit and income is Rs. 20. How many units of x and y will the consumer demand in this situation? Derive the demand function for good y. (b) A consumer has an income of Rs. 2000 this year and he expects an income of Rs. 1100 next year. He can borrow and lend at an interest rate of 10%. Consumption goods cost Rs. 1 per unit this year and there is no inflation. He has the utility function UC1 , C 2 C1C 2 . Calculate the following : (i) The present value and future value of endowment (ii) Optimal choice of present and future consumption 6. (a) State the Weak Axiom Revealed Preference. When prices are p1 , p 2 1, 2 a consumer demands x1 , x 2 1, 2 and when prices are q1 , q 2 2, 1 the consumer demands y1 , y 2 2, 1 . Does this behaviour satisfy WARP? (b) Study the impact on the labour supply when: (i) higher overall wages are offered (ii) higher overtime wages are offered Bliss Point Studies Ravinder N. Jha 9891555578 12 9811343411 B.A. (Hons) Economics-II Year Paper – IV House Examination 1. (a) Give a critique of the colonial monetary policy of the Indian Government and discuss it in the context of the Great Depression experienced by India. (b) “The guarantee system of financing the Indian railways was inherently unjust and inefficient.” Comment. (c) What were the constituents of the “Drain”? Discuss how the persistent export surplus maintained by India was necessary for the financing of the ‘Drain’. (d) Write short notes on any one : (a) commercialization of agriculture in colonial India (b) trends in foreign trade after the first world war (c) Rural indebtedness in colonial India 2. What factors were responsible for the Great Divide in the population history of the Indian subcontinent? 3. Analyze the changes in the composition and direction of foreign trade of India especially between 1850 and the First World War. 4. Would you agree that underneath the overall picture of a stagnant occupational structure in colonial India, certain forces of change can be observed? Discuss with special reference to the manufacturing sector and some states which were exceptions to the general trend. 5. Discuss the ‘Famine Codes’ and examine how far they were successful in combating the horror of famines. 6. Did the development of Railways become an engine of growth for the Indian subcontinent during colonial rule? Discuss. ST. STEPAHN QUESTION 2009-10 1. (a) Show that if the weak preference relationship is transitive, the indifference relationship is also transitive. Is the converse true? (b) What is the weak axiom of revealed preference? Use WARP to prove that the Slutsky compensated demand curve is downward sloping. 2. (a) A consumer has the utility U(x, y) = ln x + ln y. For a given y, find the offer curve of the consumer as p x and p y vary. (b) Prove that starting from a position of no risk; any risk averse individual will buy a positive fraction of a gamble with positive expected value. Bliss Point Studies Ravinder N. Jha 9891555578 13 9811343411 B.A. (Hons) Economics-II Year Paper – IV 3. (a) Discuss the impact of a decrease in the rate of interest on the saving decision and the utility level of an individual. (b) Explain the concepts of risk sharing, hedging and diversification in choices involving risky prospects. 4. (a) What do you mean by the cost function of a firm? Show that profit maximization implies cost minimization. Is the converse true? (b) Define the following (i) Increasing returns to scale. (ii) Convexity, additivity and divisibility axioms in production technology (iii) Efficiency in production (c) Derive the profit maximization conditions of a monopolist. Show that such a firm (with increasing cost function) Will never choose a price at which the market demand is inelastic. LADY SHRI RAM COLLEGE FOR WOMEN QUESTION 2009-10 1. (a) When prices are (4, 6), Ram chooses the bundle (6, 6) and when prices are (6, 3) he chooses bundle (10, 0). Is this behaviour consistent with WARP? (b) Draw and discuss the shape of the budget line if a consumer can consume x each month at a subsidy of s per unit upto 100 units, and then pays the normal price P upto 300 units, but thereafter pays a per unit tax t on all consumption beyond 300 units. (c) Explain the concepts of economies of scale and economies of scope with examples. (d) Miss X says that given any two drinks she always prefers the one that is sweeter and colder. Is this preference relation complete? Is it transitive? (e) A firm is employing 100 hours of labour(L) and 50 bags of cement(K) to produce 500 blocks. Labour costs Rs. 40 per hour and cement Rs. 120 per bags for the quantities employed MPL 3, MPK 2 . Can the firm produce the same output at a lower total cost. Explain using a diagram. 2. Consider the market for a particular good. There are two types of customers: those of type I are low demand customers, each with a demand function fo the form P 10 Q1 , and those of type 2, who are high demand customers, each with a demand function of the form Bliss Point Studies Ravinder N. Jha 9891555578 14 9811343411 B.A. (Hons) Economics-II Year Paper – IV P 210 Q 2 . The firm producing the product is a monopolist in this market and has a cost function CQ 4Q 2 where Q Q1 Q 2 . (a) Suppose the firm is unable to prevent the customers from selling the good to one another, so that monopolist cannot charge different customers different prices. What prices per unit will the monopolist charge to maximize its total profit and what will be the equilibrium quantities to be supplied to the two groups in equilibrium? (b) Suppose the firm realizes that by asking for IDs it can identify the types of the customers. It can thus charge different per unit prices to the two groups, if it is optimal to do so. Find the profit maximizing prices to be charged to the two groups. (c) Do you agree with the assertion that a lump sum tax is superior to a quantity tax that gives the same revenue to the government? 3. (a) A consumer, who is initially a lender, remains a lender even after a decline in interest rates. Is this consumer better off or worse off after the change in interest rates? If the consumer becomes a borrower, after the change is he better off or worse off? (b) DAULAT RAM COLLEGE HOUSE EXAMINATION (JAN 2009) 1. Answer any 4 Parts from the following: (a) U X1 X 2 , the in difference curve passes through a point (9, 12). Find two other points on the same indifference curve. What is the slope at point (9, 12). (b) Is the tangency between an indifference curve and budget line a necessary and sufficient condition for consumer’s equilibrium? Give reasons (c) U X1 8X 2 X1 X1X 2 X 2 , P1 10, P2 5 and money income is 95. 2 2 Find equilibrium values of X1 and X 2 consumed. (d) Income stream given by a project is as follows – 110 after one year, -121 after two years and 66.5 thereafter indefinitely into Bliss Point Studies Ravinder N. Jha 9891555578 15 9811343411 B.A. (Hons) Economics-II Year Paper – IV the future. If rate of interest is 10% should the project be undertaken. (e) The cost function for a good x is given as C 30 8x 4x 2 x 3 . Write down TFC, TVC, AVC, AFC and MC. What will the shut down price? (f) Explain how advertising affects the profits of the firm. What is the condition for equilibrium amount of advertising and the advertising sales ratio? 2. The government decides to subsidize first 20 units of food and tax the remaining amounts consumed, consider a family who is neither better off nor worse off with this scheme. Show that the amount of tax it pays cannot exceed the amount of subsidy it receives. (Hints : There is a net subsidy) 3. Production function is given by X L3/4 K1/4 . Does law of diminishing marginal productivity hold. If labour increases, will marginal productivity of capital increase or decrease. If PL 10 and PK 20 how much K & L should be used to maximize profits. Will this proportion change if X increase? 4. The market demand equation is given as P 100 .5Q . There are two firm I & II with cost functions C1 5q, C II .5 Q 2 respectively. Find the II reaction function of the two diabolists, Their respective output, total output and the price. 5. Given the following model of “Two Part Tariff” under monopoly. Let there be two consumers with demand functions Q1 14 2P1 and Q2 10 2P2 . Marginal cost = 4. Assume the firms follows the rule of marginal cost pricing. (a) If two markets are separate, what rental fee and usage fee would the monopolist charge from each group? (b) If one had a common “Two Part Tariff” What would be ‘rental fee’ and ‘usage fee’? (c) Is it possible to increase profits by charging a different price. 6. Suppose two computer companies A & B are planning to invest in a company. Each from can be develop a High Quantity system or a low quality system. The resulting profits to each company are given as follows: B High Low High 50, 40 60, 45 A Bliss Point Studies Ravinder N. Jha 9891555578 16 9811343411 B.A. (Hons) Economics-II Year Paper – IV Low 55, 55 15, 20 (a) If both times make, their decisions simultaneously & follow the “Maximin” (b) In case A gets to move first, then which strategy it will adopt what will B do? (c) In case B gets to move first will the outcome change. (d) What should the first mover do so that it can continue to remain a leader and earn more profits? SRI GURU GOBIND SINGH COLLEGE OF COMMERCE HOME EXAMINATION 2008-09 1. Answer any three parts (11 marks) (a) Mrs X likes bread but doesn’t care whether she consumes biscuits or not; that is eating biscuit leads to no change in the level of happiness. Draw an IDC to represent the above preferences. (b) Calculate AVC when AP of Labour is 10 and wages is Rs. 40. (c) A firm has the total cost function C(Y) = 500 + 5Y. What are the equations of its AFC, AVC & MC. (d) Why are Iso-cost lines straight lines? 2. A consumer consumes only two goods x and y. The utility function is U x y . What is the relation between the two goods? Does the 2 relation change if U x y ? Why? 3. Assume that a consumer who consumes only two goods & has MRS given as MRS MU A /MU B B/A . If his money income is PA Rs 5, PB Rs 10 . What quantities of the two goods will he consume? 4. (a) Suppose a firm hires 100 units of both L & K, and its output is 1000 units and MRTS LK is 2. If the firm hires one more worker & wants output to remain at 1000, how many units of k must it lay off? (b) A product can be produced using either input Labour or Capital & the firms present output position indicates MPK 3, PK Rs 1, MPL 6, PL Rs 4. Is the firm employing cost- minimizing combinations of inputs? If not what should the firm do? Bliss Point Studies Ravinder N. Jha 9891555578 17 9811343411 B.A. (Hons) Economics-II Year Paper – IV 5. (a) What is a firm’s Expansion Path? Under what conditions would it be a straight line? (b) Explain the backward bending Labour supply Curve in terms of Slutsky’s equation. KAMALA NEHRU COLLEGE 1. Attempt all the parts. (a) Explain the relationship between two goods if U 5/2 * x1 2/5 * x 2? (b) If a consumer views a unit of consumption in period 1 as a perfect substitute (one for one) for a unit of consumption in period 2 and if the real interest rate is positive, the consumer will (i) consume only in period1. (ii) consume only in period 2. (iii) consume equal amounts in each period. Which of the above option is true? Give reasons (c) How is Rawlsian welfare function different from Benthemite welfare function? (d) What is the difference between the long run equilibrium of a perfectly competitive firm and that of a monopolistically competitive firm? (e) What happens to a firm’s marginal product of labour curve if the rental price of capital falls and capital is complementary to labour? Also, what happens if capital is a substitute for labour? 2. (a) Show the Slutsky decomposition when the consumer buys two goods, both good 1 and good 2 are normal, and suddenly stores offer “buy one get one free” for good 2. (b) When the government levies a tax on one good, and then reimburses the tax revenue in lump-sum to the consumers, then nothing happens to the consumed bundle, because the consumer is facing the same budget constraint and the same preferences. True or False? Explain your answer. (c) Marginal rate of substitution for indifference curves is equal to the marginal utility for the corresponding utility function. True or false? Explain your answer. (d) What is the present value of a perpetuity that has a coupon of Rs. 1500 per year and the yield to maturity is 2.5%? If the yield to maturity doubles, what will happen to its price? Bliss Point Studies Ravinder N. Jha 9891555578 18 9811343411 B.A. (Hons) Economics-II Year Paper – IV (d) What is the present value of a perpetuity that has a coupon of Rs. 1500 per year and the yield to maturity is 2.5%? If the yield to maturity doubles, what will happen to its price? 3. (a) How is production possibilities frontier related to the production contract curve? (b) Suppose that A’s production possibility frontier is X 2 Y 2 50 and representative A’s utility function is UX, Y X 2/3 Y1/3 . If A trades with other countries at fixed world prices PX PY 1 , what should A produce and consume? (c) Prove “The monopoly allocation is Pareto inefficient”. 4. (a) Suppose the production function for widgets is given by q kl 0.8k 2 0.2l 2 Where q represents the annual quantity of widgets produced, k represents annual capital input and l represents annual labor input. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point? Does the widget production function exhibit constant, increasing or decreasing returns to scale? (b) Is agricultural industry perfectly competitive? Use economic rationale to explain why or why not? (c) Distinguish between return to scale and economics of scale. Is it possible to have constant return to scale and economies of scale together? 5. (a) Determine whether the consumer with the following choices is rational or not: Px x Py y (i) State I 1 15 1 5 (ii) State II 2 12 3 13/3 (iii) State III 3 9 1.5 14/3 (b) Explain how curvature of the expected utility function describes the consumer’s attitude towards risk. SRI VENKATESWARA COLLEGE MID TERM EXAMINATION 2006-07 Bliss Point Studies Ravinder N. Jha 9891555578 19 9811343411 B.A. (Hons) Economics-II Year Paper – IV 1. Vishnu likes strong coffee the stronger the better but he can’t distinguish differences smaller than one teaspoon per six cup pot. He is offered cup A using 14 teaspoons of coffee (per pot). Cup B using 14.75 teaspoon and cup C using 15.5 teaspoon. For each of the following expressions. Determine whether it is true or false (a) A ~ B (b) B C (c) C A Is this relation transitive? Sita likes chocolates and ice cream but after 10 slices of chocolates, she gets tired of chocolates and eating more makes her less happy. She always prefers more ice cream to less (a) If however she is made to eat everything put on her plate, what will her indifference curves look like? (b) If she is allowed to leave any thing she doesn’t want on her plate. What would her indifference curve look like? (c) When price are (4.6). Ram chooses the bundle (6.6) and when prices are (6.3) he chooses bundle (10.0). Is his behavior consistent with WARP? (d) State whether true or false and explain your answer on the basis of YE and SE. If both current and future consumption are normal goods, an increase in rate of interest will necessarily make a save (i) Save more (ii) Consume more in the second period. 2. S.V.C has Rs. 60000 to spend on computers and other stuff. The U.G.C wants to encourage computer literacy in colleges and the following two plans were proposed : (i) Plan A gives a grant of Rs. 10000 to each college, that the college is free to spend as it wishes. (ii) Plan B is a matching grant. For every rupee spent on computers, the U.G.C gives the college Re 0.50. (a) Write the budget equation and draw the budget line in each case. (b) If S.V.C. has preferences that can be represented by the utility function UC, X C.X 2 . What will be the amount spent on computers under each plan? 3. Shyam’s demand function for good x is XPs, Py, m 2m/5Px . His income is Rs. 1000. Px = Rs. 5 and Py = Rs. 20. (a) If Px falls to Rs. 4, by how much does his demand change? Bliss Point Studies Ravinder N. Jha 9891555578 20 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) If his income changes at the same time so that he could exactly afford his old commodity bundle. What would his new income be? What would be his equilibrium bundle at this new set of prices? (c) What is S.E and Y.E? 4. Ganga has Rs. 50000 to invest in a mutual fund. The expected return on mutual fund A is 15% and an mutual fund B is 10%. Should Ganga pick mutual fund A or B? 5. Sukanya is shopping and sees an attractive shirt. However, the price of Rs. 800 is more than she is willing to pay. A few weeks later, she finds the same shirt on sale for Rs. 400 and buys it. When her friend offers Rs. 800 for the shirt she refuses to sell it. Explain Sukanya’s behavior. 6. (a) Distinguish between third degree price discrimination inter- temporal price discrimination and peak load price (b) If Hero Honda has the following demand for its motorbikes : P = 20000 – Q. The downstream division’s cost of assembling motorbikes is Ca(Q) = 8000Q The upstream division cost of producing engines is Ce(Qe) = 2Qe squared If there is not outside market for the engines, how many engines and motorbikes should the firm produce? What should be the transfer price for engines? HOUSE EXAMINATION 2008-09 1. Attempt any three parts, all carry equal marks: (a) Veena consumes two goods, peanut butter and jelly in the ratio of 3 units of butter per unit of jelly. She has an income of Rs. 30. Price of peanut butter is Re. 1 and that of jelly is Rs. 3: (i) Draw Veena’s indifference curve for U = 30 (ii) How many units of peanut butter and jelly will she demand in equilibrium? (b) Amit’s preferences are represented by the utility function υx1 , x 2 x1x 2 . The prices of x 1 and x 2 are P1 & P2 . Derive the income offer curve and price consumption curve for Amit. Bliss Point Studies Ravinder N. Jha 9891555578 21 9811343411 B.A. (Hons) Economics-II Year Paper – IV (c) Suppose a production function is given by Fk, L KL2 ; the price of K is Rs. 10 and the price of labor Rs. 15. What combination of L and K minimizes the cost of producing any given output. (d) Define and distinguish between dominant strategy equilibrium and Nash equilibrium. (e) What would happen to a lender’s present year consumption and welfare if the rate of interest increases? 2. (a) Consider the following simultaneous game : Player 2 A B Player 1 A ((3, 2) (0, 0) B (0, 0) (2, 3) (i) Does there exist a dominant strategy for each player? (ii) Determine the pure strategy Nash equilibrium in this game. (iii) Find the mixed-strategy Nash equilibrium. (b) Explain graphically the utility function of an individual who is (i) Risk-averse (ii) Risk lover (iii) Risk indifferent. 3. (a) Goldie’s utility function is U C, R C 12 R , where R is the 2 amount of leisiou he has per day. He was 16 hours a day to divide between work and leisure. He has an income of Rs. 20 a day from non-labor sources. The price of consumption goods is Re. 1 per unit. (i) If wage rate is Rs. 10/hour, how many hours of leisure and work will he choose? (ii) If Goldie’s non-labor income decreased to Rs. 5 a day, while wage rate remained at Rs. 10, how many hours would he choose to work? (iii) Suppose that Goldie has to pay an income tax of 20% on all of his income, and suppose that his before tax wage remained at Rs. 10 an hour and his before tax non-labour income was Rs. 20 per day. How many hours would he choose to work? (b) Consider the production function Q 4L1/2 K1/2 . Does this function exhibit constant returns to scale, increasing returns to scale or decreasing returns to scale? Also comment on the shape of long run total cost curve for this production function. 4. (a) In the last three years, an individual exhibited the following consumption behavior: 2005 P1, P2 , P3 1, 3, 10 and x1 , x 2 , x 3 3, 1, 4 Bliss Point Studies Ravinder N. Jha 9891555578 22 9811343411 B.A. (Hons) Economics-II Year Paper – IV 2006 P1, P2 , P3 4, 3, 6 and x1 , x 2 , x 3 2, 5, 3 2007 P1, P2 , P3 1, 1, 5 and x1 , x 2 , x 3 4, 4, 3 In this behavior consistent with WARP? What about SARP? (b) Explain peak-load pricing as a form of price discrimination. How is it different from third degree price discrimination? 5. (a) Consider a duopoly market in which the demand functions for each firm is given by: Firm 1 : Q1 21 2p 1 p 2 Firm 2 : Q 2 21 p1 2 p 2 There are no variable costs for the firms but each incurs a fixed cost of Rs. 10. (i) Find the Bertrand-Nash equilibrium. (ii) If the firm’s cooperate and agree to maximize total profits, what is the equilibrium price they will charge? (b) ‘Long run average cost curve is the envelope of the short run average cost curves.’ Discuss. 6. (a) Nancy has an income of Rs. 2000 this year, and she expects an income of Rs. 1000 next year. She can borrow and lend money at an interest rate of 10% Consumption goods cost Re 1 per unit this year and there is no inflation. Her utility function is UC1 , C2 = C1C2 (i) Find equilibrium levels of C1 and C 2 for Nancy. (ii) Now suppose that the rate at which she can lend increases to 20%, while the rate at which she can borrow remains at 10%. Draw Nancy’s new budget line. (b) Discuss the working and limitations of kinked demand curve model. HOME EXAMINATION 2006-07 1. Answer any four of the following: (a) Price offer curve in case of giffen goods? (b) Slope of the labour supply curve if labour is interior good? (c) Engel curve in case of quasi-linear preferences? (d) Properties of well – behaved preferences (e) Two – part tariff when there are n number of consumes? Bliss Point Studies Ravinder N. Jha 9891555578 23 9811343411 B.A. (Hons) Economics-II Year Paper – IV (f) Distinction between second degree and third degree price discrimination. (g) Prisoner’s Dilemma 2. (a) What do you mean by homothetic preferences? Show that Cobb- Douglas preferences are homothetic in nature. (b) For what kind of preferences will the consumer be equally affected when facing a quantity tax as an income tax? 3. (a) Given interest rate of 10 percent, is it worthwhile to invest in a project in a project of Rs. 1000, if the return is Rs. 300 in years 1, 3, 4 and 7? Explain. (b) What kind of preferences are represented by a utility function of the form ux1 , x 2 x1 x 2 ? Is the utility function vx1, x 2 x1 2x1 x 2 x 2 a monotonic transformation of u x1 , x 2 ? 2 4. (a) Diminishing returns to a single factor of production and constant returns to scale are not inconsistent. Discuss (b) Marginal product of labour in the production is 50 units/hour. 1 The MRTSL.K . What is the marginal product of capital? 4 5. (a) Distinguish between economies of scale and economies of scope. Why can one be present without the other? (b) Suppose the economy takes a downturn, and that labour costs fall by 50 percent and are expected to stay at that level of a long time. Show graphically how this change will affect the firm’s expansion path. 6. (a) Show that outcome of Cournot-Nash equilibrium is much better for firms when compared to that of perfect competition, but not as good as the outcome from collusion. (b) Suppose that two competing firms A and B, produce a homogenous good. Both firms have a marginal cost of Rs. 50. Describe what could happen to output and price in each of the following situations if firms are at (c) Cournot’s equilibrium, and (ii) collusive equilibrium (i) Because firm A must increase wages its MC increases to Rs. 80. (ii) MC of both firms increase (iii) Demand curve shifts to the right Bliss Point Studies Ravinder N. Jha 9891555578 24 9811343411 B.A. (Hons) Economics-II Year Paper – IV PAPER NO. – 4 MICRO ECONOMICS 1. Attempt any four (a) A firm’s production function is f x1 , x 2 x1 2x . Comment upon the shape of isoquant. Does the production function exhibit increasing, decreasing or constant returns to scale? (b) A firm’s production function is given by f x1 , x 2 min x1 , 2x 2 . If the firm faces factor price w 1 , w 2 , what is the cheapest cost of producing q levels of output? (c) A monopolist always operates on the elastic portion of the demand curve. Explain. (d) If the elasticity of demand for the output of a monopolist is 3, in equilibrium (e) Define “homothetic preferences” and give examples. (f) An Individual’s utility function for food (x) and clothing (y) is given as U(x, y) = xy + 10x, where x denotes the amount of food consumed and y the amount of clothing. The price of food is Px, the price for clothing is Py, and his income is I. Answer any three question from 2-6. Each question carries 10 marks. 2. Consider two firms facing the demand curve P = 1000 – Q where Q Q1 Q 2 . The cost function of each firm is identical and given by C1 Q1 4Q1 , where I = Firm1, Firm2. Calculate the outputs, prices, profits of each firm under (a) Cournot Model (b) Stackelberg Model 3. Two major networks, Star Plus and Zee TV, are competing for viewer ratings in 8.00–9.00 p.m and 9.00–10.00 pm slots. Each can choose to put its “bigger” show first or place it second. The combination of decisions leads to the following “ratings points” results: Star Plus Strategy First Second Zee First 15, 15 30, 10 Second 20, 30 18, 18 (a) Find Nash Equlibria assuming that both network make their decisions at the same time. (b) If Zee TV is risk averse and uses a maximin strategy, what will be the resulting equilibrium? Bliss Point Studies Ravinder N. Jha 9891555578 25 9811343411 B.A. (Hons) Economics-II Year Paper – IV (c) What will be the equilibrium if Zee TV makes the selection first? 4. What do the Cournot and Bertrand models have in common? What is different about the two models? 5. What is the difference between intertemporal Price discrimination and third degree price Discrimination? Explain with diagrams. 6. (a) Suppose consumer’s preference for hamburgers and coke can be represented by the utility function U H C , where H measures the number of hamburgers and C the number of cokes. Does the consumer believe that “more is better” for each good? (b) Demonstrate graphically that in the case of a quasi-linear preference, the entire change in demand is due to the substitution effect. SHYAM LAL COLLEGE (EVENING): HOUSE EXAMINATION 2006-07 1. Answer any five parts: (a) A businessman, Mr. X, is considering whether to start a business enterprise in an area of the city where commercial activities are not allowed. The utility from two possible outcomes, the bad outcome (i.e. the authorities come and seal his illegal enterprise) and the good outcome (he is able to run his business unhindered) is given by a von Neumann- Morgenstern utility function. Show that his decision will be affected by (i) credibility of the threat, i.e. the probability of his business being sealed, and, (ii) the degree of risk aversion of Mr. X. (b) A mobile phone functions only when a SIM card is inserted into a compatible mobile handset. Depict the utility function of a consumer, representing consumption of mobile handsets and SIM cards as x and y respectively. Also draw the indifference curve representing this utility function. (c) A second year student of B.A (Hon.) Economics is a movie fan and watches almost every new release on Fridays. In the process, he spends Rs. 300/- of his pocket money every month paying for the tickets. Unfortunately for him, the ticket prices are hiked, forcing him to reduce the number of movies that he could watch in a month. Now he only watches a few select movies starring his favorite actresses. But he still ends up spending Rs. 325/- every month on tickets. What can you infer about his price elasticity of demand for movies? Bliss Point Studies Ravinder N. Jha 9891555578 26 9811343411 B.A. (Hons) Economics-II Year Paper – IV (d) The utility function is given by U x y . Draw the Engel curve for good x. Can x be a Giffen good? Explain your answer. (e) If a consumer always spends 25% of her total income on food, calculate her income elasticity of demand and the price elasticity of demand for food. (f) Distinguish between the concepts of fixed costs and sunk costs with the help of an example. (g) Explain why the monotonic transformation of a von Neumann- Morgenstern utility function, despite representing the same preferences, might not be suitable for analyzing contingent consumption. Which property of a von-Neumann utility function is lost in a monotonic transformation? (h) “A plant is always run below its optional level in the long run.” Is the statement true or false? Answer with reference to two separate cases: (i) When there are only economics of scale. (j) When there are both economics and diseconomies of scale. 2. (a) State Slutsky equation algebraically and explain each term in it. Using the equation answer the following questions: (i) What must be the sign and magnitude of income effect for a download-sloping demand curve? (ii) Show that Marshall’s analysis cannot account for Giffen goods. (b) Define weak axiom of revealed preference. Do the following choices satisfy WARP? Explain your answer. Situation Prices Quantities px py x y I 4 6 6 6 II 6 3 10 0 3. (a) Let there be two individuals A and B with MRS for intertemporal consumption given by A B C C MRSC0 .C1 1 , MRSC0 .C1 1 , A A B B Let the corresponding C0 C0 endowments be (10.100) for A and (50, 20) for B. Find out who would lend and who would borrow and by what amount? What would be the equilibrium rate of interest and intertemporal price ratio? P (b) “ The expression r 0 1 defines the premium on the value of a P1 unit of current consumption in comparison with consumption Bliss Point Studies Ravinder N. Jha 9891555578 27 9811343411 B.A. (Hons) Economics-II Year Paper – IV one year in the future.” Discuss in the context of intertemporal consumptive optimum and lending-borrowing equilibrium. 4. (a) Distinguish between an ordinary and a compensated demand curve. Explain why the slope of a compensated demand curve is unambiguously negative or zero. (b) A well-known movie star said in an interview:”Earlier I had to work really hard to establish myself. Sometimes I even worked 7 days a week for all 12 months a year. However, these days, as I am much more comfortable financially, I have decided to take it easy and enjoy my life. I go on long vacations and usually work only for a few months in a year.” Explain in light of the modified Slutsky equation. Can leisure be considered a Giffen good for her? 5. (a) You are given two income streams: (i) Rs. 50/- per year forever (starting from next year). (ii) Rs. 120/- after one year, Rs.140/- after two years and Rs. 620/- after four years. (b) Distinguish between a risk-lover and a risk-averse consumer. Show that a risk-averse consumer, maximizing a von Neumann- Morgenstern utility function, when offered a fair insurance against a loss, will choose to fully insure. 6. (a) Using the Lagrangian method, show that output maximizing under a given cost constraint leads to identical optimality criterion as cost minimization under a given output constraint. (b) Distinguish between the concept of return to a factor and returns to scale. Is the production function represented by Q 73.87L 0.763K 0.213 characterized by IRS, CRS or DRS? (c) Show that the money rate of interest equals the real rate of interest plus the anticipated rate of inflation. MICRO ECONOMICS 1. (a) A monopolist’s demand curve for labour will be downward sloping even if the marginal physical product of labour is constant. True/false? Why. (b) Suppose that rents are highest in the Cannaught place area of Delhi. Will you agree with the statement that cinema tickets Bliss Point Studies Ravinder N. Jha 9891555578 28 9811343411 B.A. (Hons) Economics-II Year Paper – IV cost more in Cannaught place because of higher rent? Give reason in support of your answer. (c) If MRT x y = 3/2 while MRS x y = 2 for individuals A and B, should the economy produce more of X or more of Y to reach equilibrium of production and exchange simultaneously. (d) Interpret the element of the (1-A)-1 matrix. (e) What is Quasi Rent? Must it always be non-negative? 2. Derive graphically a monopolist’s demand curve for a variable factor when several variable factor are used. If a group of monopolists use this variable factor, derive the market demand curve for the variable factor. 3. (a) Suppose that the labourers face a monopsonistic buyers of labour. Assume that labour is the only variable factor for the monopolist. The supply of labour and the marginal revenue product (MRP) curves are given by the following equations: W = 50 + 5L and MRP = 180 – 3L (Where W is the wage rate and L the quantity of labour). Determine the wage rate and the level of employment when the monopsonist maximizes his profits. What is the wage rate if the labourers from a union and want to maximize their total wages without losing any employment as compared to (i) above? (b) Calculate the market equilibrium value for the following assets. Assume the market rate of interest is 10%. (i) A bond that pays Rs. 100 interest per year for two years and is paid of at Rs. 1000 at the end of two years. (ii) A building that will earn Rs. 100 per year for two years and then will earn Rs. 50 per year indefinitely into the future. 4. (a) A firm wants to reach two types of customers: Households having less than Rs.1lakh or more of family income and those having income of less than Rs.1lakh. The first category twice as much as the second group. One unit of T.V advertisement reaches 2000 families of first group and 8000 families of second group and costs Rs. 20,000 while advertisement in a magazine cost Rs. 12,000 and reaches 6,000 and 3,000 families respectively. No more than 12 advertisements have to be given. The magazine and at least 6 TV advertisements have to be given. The Advertisement budget is Rs. 1, 80, 000. Assume that every contracted family Bliss Point Studies Ravinder N. Jha 9891555578 29 9811343411 B.A. (Hons) Economics-II Year Paper – IV purchases the company product. The firm wants to maximize its sales. Write the above problem as a linear programming problem defining all variables used. Plot the feasible region and fine the optimum solution to the above problem. (b) The following gives the technology matrix for a two sector economy consisting of agriculture and manufacturing industries. Ag Mfg Agr 0.5 0.3 Mfg 0.3 0.2 Lab 0.5 0.33 Find demand for the two industries are 11 and 12 respectively. Write down the 1-0 table for the economy. Calculate total units of labour required. If total labour available is 14; is the solution feasible. 5. (a) Distinguish between transfer earnings and economic rent. What proportion of total income would be economic rent if you have a fully elastic or a fully inelastic supply curve of a factor. (b) Given the industry demand function for labour- QDL = 800 – 15 PL Where Pn is the price of labour in rupees per day. Find the amount of economic rent if the supply function of labour to the industry is – QSL = 50 PL - 500 6. (a) Explain with the help of an Edgeworth box diagram the trading process between two customers when one attempt to behave as a monopolist. (b) Robinson Crusoe has 12 hours per day to catch fish or gather coconuts. He can catch 4 fish per hour or pick 16 coconuts per hour. His utility function is U (F, C)= F.C. where F and C are his daily consumption of fish and coconuts respectively. How many fish will he choose to catch per day and how many coconuts will he pick per day. HOME EXAMINATION 2008 1. What do you mean by the following (answer any four): (a) Concave preferences Bliss Point Studies Ravinder N. Jha 9891555578 30 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) Monotonic transformation (c) Strong Axiom of revealed preference (d) Downward sloping income offer curve (e) Diminishing MRTS (f) Economies of scope (g) Opportunity cost 2. (a) Show that Cobb-douglas preferences are homothetic preferences. (b) Given marked prices p1 , p 2 for the two goods, then at equilibrium everyone will be willing to trade off the two goods in the same way. Prove or refute this statement. 3. (a) ‘Slylsky equation shows that total change in demand, resulting from change in price, is the sum of substitution and income effects. Explain. (b) When prices are p1 , p 2 = (1, 2) a consumer demands x1 , x 2 1, 2 and when prices are q1 , q 2 2, 1 , the consumer demands y1 , y 2 2, 1 . Is this behaviour consistent with the model of maximizing behaviour? 4. (a) The MPL in production is 50 computer chips per hours. The MRTS of labour per hour for hours of machine capital is 1/4 . What is the MPK . (b) With the help of isoquent, show the cost-optimising input use for a level of output. 5. (a) Show the duality between cost and production in the short run. How do we derive Ac and MC curves from short run total cost curve? (b) Show that increasing returns to scale co-exists with diminishing marginal returns. ST. STEPHEN'S COLLEGE (INTERNAL EXAMINATION) JANUARY 2008 1. Attempt any three of the following: All questions carry equal marks. (a) Consider a two-period model in which an Individual has an endowment of income given by m1 , m 2 . Suppose that initially he is a lender in period 1. If the rate of interest falls and his Bliss Point Studies Ravinder N. Jha 9891555578 31 9811343411 B.A. (Hons) Economics-II Year Paper – IV preferences are well-behaved, will he remain a lender? Explain using revealed preference theory. (b) Show that for a fixed-proportions production function, the cost function is linear. (c) Explain why von Neumann-Morgenstern utility function takes an additively separable form. (d) What is excess capacity? With the help of suitable diagrams, show that in the long run firms under monopolistic competition operate with excess capacity at equilibrium. (e) Consider a firm which faces a demand function Q(P, A) where P is the price of the commodity it sells and A is the advertising expenditure. If the firm has some monopoly power in the market, show that the amount firm spends on advertisement is inversely proportional to elasticity of demand. 2. (a) (i) How is the preference approach to consumer behaviour different from the Revealed preference theory? (ii] Suppose a consumer buys 11 units of x and 3 units of y in the first period when the prices are p x 2 and p y 1 in the second period, p x and p y 2 and the consumer buys 10 units of x and 10 units of y. Prove that this set of choices is not consistent with Weak Axiom of revealed preference. (b] Consider a strictly risk-averse, expected utility maximising decision maker who has an initial wealth of w, but runs a risk of a loss of D Rupees. Let the probability of loss p. Suppose he can buy insurance, where one unit of insurance costs q Rupees and pays one rupee if the loss occurs. Let the amount of insurance bought, a, be strictly positive. Show that if insurance is actuarially fair (i.e. q = p), then the individual will insure completely. 3. (a) Consider a utility function ????? (b) Consider a consumer who has a utility function U xy . Price of good x is Rs. 5 and that of good y is Rs. 10. The income of the consumer is Rs. 100. Find the Slutsky substitution and income effects. (c) Consider a Slutsky decomposition of price effect in a two good model where the consumer has certain amount of endowment of both the goods. Suppose both goods are normal and price of good 1 falls. Explain intuitively why the endowment income effect works in the opposite direction of an ordinary income effect. Bliss Point Studies Ravinder N. Jha 9891555578 32 9811343411 B.A. (Hons) Economics-II Year Paper – IV 4. (a) What is the difference between fixed and sunk costs?' Can they be recovered when the firm shuts down? Explain with help of example. (b) It is possible to have decreasing marginal products for all inputs, and yet have increasing returns to scale. True or false? Explain. (c) A firm is producing two commodities : Products X and Y. The total cost (TC) of producing the goods is given by : TC = aX + bY – cXY Where a, b and c are positive constants. Does this total cost function exhibit economies of scope? 5. (a) Explain how peak-load pricing is different from third-degree price discrimination. Are these strategies adopted for the same objectives? (b) Consider the following simultaneous games Player 2 A B A (3, 2) (0, 0) Player 1 B (0, 0) (2, 3) (i) Does there exist a dominant strategy for each player? (ii) Determine the pure strategy Nash equilibrium in this game. (iii) Find the mixed strategy Nash equilibrium. 6. (a) Consider a monopolist who was using a single-price policy in a market with many consumers. If he adopts a two par tariff, what will be the effect on the consumers. (b) Consider a duopoly market in which the demand functions for each firm is given by: Firm 1 : Q1 21 2p 1 p 2 Firm 2 : Q 2 21 p1 2p 2 There are no variable costs for the firms but each incurs a fixed cost of Rs. 10 (i) Find the Berttand-Nash equilibrium (ii) If the firms cooperate and agree to maximize total profits, what is the equilibrium price they will charge? (iii) Show that the collusion outcome is unstable. MID-SESSION EXAMINATION 2007-2008 Bliss Point Studies Ravinder N. Jha 9891555578 33 9811343411 B.A. (Hons) Economics-II Year Paper – IV 1. Do any three parts (a) In a 2 x 2 pure exchange economy with two consumers A and B and two goods X and Y, if A is perfectly discriminating monopolist, will the outcome be efficient? (b) A consumer consumes two goods, 1 and 2 of which good 1 is a neutral good. Draw his indifference curves between good 1 and good 2. What is his Marginal rate of substitution of good 1 for good 2? (c) Explain the Prisoners Dilemna. (d) A borrower is made worse off by an increase in the interest rate. True or False? Explain. (e) For the Cobb-Douglas production function Y 30L1/2 K given PK 10 and PL 5 , what combination of L and K minimizes the cost of producing any given level of output? What combination would be used to produce Y 60 2 ? 2. How is peak load pricing a form of price discrimination? Can it make consumers better off? Give an example. 3. Define Risk Averse. What is the expected utility of an economic agent (with wealth w) from investment of Rs. x, which gives a rate of return r, with probability π and rate of return r2 with probability 1 π , with r1 0 and r2 0 . If such a consumer is risk averse will the optional investment (value of x) be zero? Explain. 4. Explain the determination of price and output in the model of oligopoly where the dominant firm is a quantity leader. 5. Suppose two restaurants, Wonder Burger and Pizza Delite are considering two options, offering a weekend discount to students r not. Their payoffs from these in terms of weekly profits are Wonder Burger Discount Discount Pizza Delite No Discount 1000, 1000 1000, 2000 Discount 2000, 1000 0, 0 Does the game have a dominant strategy equilibrium? What if any, are the Nash equilibria in pure strategies? Find a mixed strategy equilibrium for this game. 6. Consider the following game, where two players A and B can choose from two strategies Big and Little. Their pay offs are as follows: L B B A L 1000, 1000 0, 0 B 0, 0 500, 500 Bliss Point Studies Ravinder N. Jha 9891555578 34 9811343411 B.A. (Hons) Economics-II Year Paper – IV Does this game have a DSE? What are the Nash equilibria in pure strategies? In one Nash equilibrium Pareto superior to the other(s)? SRI GURU GOBIND SINGH COLLEGE OF COMMERCE (UNIVERSITY OF DELHI) Answer any four 1. (a) Well-behaved preferences are monotonic and convex. Explain the statement with a diagram. (b) Which of the following are monotonic transformations? (i) u=2v –17 (ii) u = u3 (iii) u = u + 19 (iv) u = v2 (v) u = 1/v2 (c) Can you explain why taking a monotonic transformation of a utility function does not change the MRS? 2. (a) Show that Perfect Substitutes are an example of homothetic preferences. Derive Price Offer Curve and Demand Curve in case of Perfect substitutes. (b) When Prices are (P1, P2) = (6.5) a consumer demands (X1 X2) = (5, 6), and when Prices are (Q1 Q2) = (5, 6), the consumer demands (Y1 Y2) = (6, 5). Is this behaviour consistent with the model of maximizing behaviour? State WARP and explain how it can be used to check consistent behaviour. 3. (a) What is endowment Income Effect? Explain Price Effect using the same? (b) Suppose a dairy farmer produces 60 Its. of milk a week. The initial price of milk is Rs. 4 per litre and later changes to Rs.3 per litre. Given his demand function X1 10 m/10P 1 , Calculate the Endowment Income effect. 4. (a) Suppose the economy takes a downturn, and that labour costs fall by 50% and are expected to stay at that level for a long time. Show graphically how this change in the relative price of L and K affects the firm's expansion-path. (b) Explain how effluent fees can have an impact on input-choices of a plant. Bliss Point Studies Ravinder N. Jha 9891555578 35 9811343411 B.A. (Hons) Economics-II Year Paper – IV 5. What is the' lowest Price that a monopoly firm practicing perfect first degree price-discrimination charges? What will be its total Output and Consumer Surplus? HANS RAJ COLLEGE MID TERM EXAMINATION 2008 1. Answer any three parts: (i) Draw the price offer curve of an individual who has a cobb- douglas utility function. (ii) Can x = (Py, Y)/Px be a valid demand function? Give reason for your answer. (iii) Assume a quasi-linear utility function. Can you say what would happen to the demand for commodity x if the price of commodity y falls? Assume convex preference. (iv) Define and distinguish between dominant strategy equilibrium and Nash equilibrium. (v) What would happen to a lender’s present year consumption if the rate of interest increases? 2. (i) Ms. Renu has Rs. 1000 to spend on cloth (C) and food (F). The price of the two item is Rs. 50 and Rs. 100 respectively. She only has 100 minutes to devote to shopping and it takes her 10 and 5 minutes respectively to choose each unit of these commodities. Her utility function is given U = FC. (a) Draw her budget line. (b) How much will the consume of two commodities? (ii) What would happen to the saving done by a lender if the rate of interest goes up? 3. (i) When the price of x and y are Rs. 1, individual A buys 6 units of x and 4 units of y, and individual B buys 4 units of x and 6 units of y. The price of x then rises to Rs. 2 and that of y falls to Rs. 0.50. At the same time the income of individual A falls and that of B rises. A now buys 3 units of x and 5 of y and B 8 units of x and 3 of y. (a) Does consumer A violate the weak axiom of revealed preference? (b) Does consumer B? (c) Suppose we aggregate the consumption of A and B. Will this aggregated total satisfy weak axiom of revealed preference? Bliss Point Studies Ravinder N. Jha 9891555578 36 9811343411 B.A. (Hons) Economics-II Year Paper – IV (ii) Work out the relation between real rate of interest, money rate of interest and the rate of inflation. 4. (i) Let firm A be the only producer of shaving blades and firm B is planning to enter as the market is giving good returns. Firm A can either fight him with advertisements or let him come in. The payoff matrix in Rs. Lakhs is given below: Firm A Fight Not fight Not Enter 10, 90 10, 80 Firm B Enter 0, 0 20, 10 (a) Identify Nash equilibrium if it exits. Explain why others are not Nash (b) Suppose Firm A can increase capacity and then fight better and hence can make a profit of Rs. 20 lakhs if it fights when B enters. Write the game in extensive form. Will firm A create this capacity? Explain your answer. (ii) Suppose electricity demand increases sharply for some hours. How can a monopolist take advantage of this using a peak-load pricing? How is it different? How can a regulator ensure that the gains in efficiency go to the consumers? 5. (i) A monopoly sells in two countries, and resales between the countries are impossible. The demand curves in the two countries are: P1 = 100 – Q1 P2 = 120 – 2Q2 (a) The monopolist’s marginal cost is Rs. 30. Solve the equilibrium price in each country. (b) Suppose the monopolist treats both countries as one and wants to charge only one price. What price he should charge. Compare the profit in the two situations. (ii) How good is Price rigidity model in explaining behavior of firms under oligopoly? What are its shortcomings? MID-TERM EXAMINATION – 2008 1. (a) UX1, X2 4 X1 X2 . If X1 9, X 2 10 . Find his total utility. If initially 81 units of X1 and 14 units of X 2 were being consumed how much X 2 an individual is willing to give up to consume 40 more X1 . Bliss Point Studies Ravinder N. Jha 9891555578 37 9811343411 B.A. (Hons) Economics-II Year Paper – IV (b) X L3/4 K1/4 . Does law of DML L hold. If labour increases will marginal product of capital increase or decrease. (c) Cost function for a good x is given as C a bx cx2 dx 3 . Find TFC, AFC, TVC, AVC and MC. What is x when AVC is minimum. (d) Income stream given by a project is a follows – 110 after one year, -121 after two years and +66.5 thereafter indefinitely into the future. If rate of interest is 10% should the project be undertaken. (e) Using slutsky equation show the effect of wage increase on supply of labour. How can one ensure that labour works large hour. (f) What is peak load pricing? Explain using a diagram. 2. When price of gasoline is Rs. 2 per gallon, Herry consumes 1000 gallons per year. The price rises to Rs. 25 and to compensate Harry for the loss he suffers the government gives him a cash transfer of Rs. 500 per year. Will Herry he better-off or worse off as a result of the change. Will he consume the same amount of gasoline as before the change. 3. (a) Differentiate the reasons for a U-shaped SATC and U-shaped LAC curves. If DRF start from the very first unit of output, can the SATC curve have U-shape. (b) Is it possible to have constant LAC curve in this case. 4. Given the market odd equation as P = 50 – 0.5Q MC = 0. Find (a) Competitive equilibrium output, price & profit. (b) Monopoly output, price & profit. (c) Duopoly output, price & profit. (d) (i) Cournot solution assuming homogeneous good (ii) Stackel berg’s solution. Why the price competition is not the best policy with a homogenous good. 5. A firm is deciding to advertise its product, what is the equilibrium amount of advertising that the firm must do. How does advertising effect the output produced. Given P 100 3Q 4JA C 4Q 2 10Q A are equilibrium values the P, Q and A. (Hint : Find II function & differentiate w.r.t Q & A putting each = 0). Bliss Point Studies Ravinder N. Jha 9891555578 38 9811343411 B.A. (Hons) Economics-II Year Paper – IV ***** Bliss Point Studies Ravinder N. Jha 9891555578 39 9811343411