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Midpoint Formula Income Elasticity document sample
PROBLEM SET 5 1) Use the following data for a demand curve: Price Quantity 11 10 10 20 9 30 8 40 7 50 6 60 5 70 4 80 3 90 a) Use the midpoint formula to calculate the elasticity between a price of $10 and $11. b) Use the midpoint formula to calculate the elasticity between a price of $3 and $4. c) Why does the elasticity change along the demand curve? d) At what point is total revenue maximized? What is the elasticity at that point? 2) a) When the price of CDs increased from 20 YTL to 22 YTL, the quantity demanded for CDs decreased from 100 to 87. What is the price elasticity of demand for CDs? Is demand elastic or inelastic? b) You observe a positive relationship between the price your store charges for CDs and the total revenue from CDs. Is the demand for your CDs elastic or inelastic? 3) Compare a market in which supply and demand are very (but not perfectly) inelastic to one in which supply and demand are very (but not perfectly) elastic. Suppose the government decides to impose a price floor $1 above the equilibrium prices in each of these markets. Compare diagrammatically, the surpluses that result. In which market is the surplus larger? 4) Snow spoils the cherry crop. As a result, the prices rises from 4$ to 6$ a box and the quantity demanded decreases from 1000 to 600 boxes a week. Over this price range, a) What is the price elasticity of demand? b) Describe the demand for cherries. 5) If a 12 percent rise in the price of peach juice decreases the quantity of strawberry juice demanded by 22 percent and increases the quantity of apple juice demanded by 14 percent calculate the cross elasticity of demand between peach and strawberry juice. 6) Alex’s income has increased from 3000$ to 5000$. Alex increased his consumption of CD from 4 to 8 a month and decreased his consumption of cakes from 12 to 6 a month. Calculate his income elasticity of demand for a) CDs and b) cakes. 1 7) The following table shows the price and yearly quantity of pencils according to average income. Quantity demanded Quantity demanded Pencil price (average income is $20,000) (average income is $30,000) $4.50 2,400 3,600 $5.50 1,600 2,800 $6.50 800 2,400 $7.50 400 1,800 a) Calculate the price elasticity of demand (using the midpoint method) when the price of pencil rises from $4.50 to $5.50, when average income is $20,000. b) Calculate the income elasticity of demand (using the midpoint method) when average income increases from $20,000 to $30,000, when the price of a pencil is $4.50. 8) Use the given monthly information in the table to answer the questions below. Month Income Demand for Rice Demand for Pasta 1 $400 5 pounds 3 pounds 2 $800 3 pounds 5 pounds 3 $800 5 pounds 3 pounds a) Calculate the income elasticities of demand for rice and pasta and specify the kinds of goods they are in months 1 and 2? b) In Month 3, the price of pasta rose from $2.00 per pound to $3.00 per pound. What is the cross-price elasticity of demand for rice? Are rice and pasta complements or substitutes? 9) The table below gives the demand schedules for good K when the price of good L (PL) is 8 TL and 12 TL. Complete the last column of the table by computing the cross elasticity of demand between goods K and L for each of the three prices of K. Are K and L complements or substitutes PL = 8 TL PL = 12 TL PK QK Q’K Elasticity (η) 8 2,000 4,000 7 4,000 6,000 6 6,000 8,000 10) Suppose that the demand function for good X is: Q = 4/P a) Draw this demand function on P-Q plane. b) Find arc elasticity of demand between P=1 and P=2. c) Find the point elasticity of demand at P=2. d) Find the total revenue and graph it. 2 11) The following table provides information regarding price elasticities, income elasticities and cross elasticities of demand. Commodity Price Income Price change in Cross Elasticity Elasticity Commodities Elasticity Electricity (in home) 0.15 0.25 Natural Gas 0.35 Restaurant Meals 1.9 2.5 --- --- Coffee 0.25 --- Milk -0.15 Bread 0.20 -0.10 --- --- a) Which commodities are normal and which are inferior? b) Which commodities are complements and which are substitutes? c) Which commodities have elastic and which have inelastic demand? d) What will happen to the total revenue of bread if its price increases? e) What will happen to the quantity demanded of coffee if the price of natural gas increases by 1%? f) What will happen to the quantity demanded of coffee if the price of milk increases by 1%? Multiple Choice Questions 1) Which of the following statements concerning the value of demand elasticity is/are true? a) Demand elasticity is either greater than one, equal to one, or less than one. b) The value of demand elasticity is always negative. c) Elasticity of demand is always stated in absolute value. d) A relatively flat demand curve is a relatively elastic demand curve. e) All of the above. 2) Refer to the graph below. Only one of the statements below is entirely correct. Which one? a) This demand curve is relatively elastic because the price increase is greater than the quantity decrease. b) This demand curve is relatively inelastic because the increase in price is proportionally larger than the decrease in quantity demanded. c) This demand curve is unitary elastic because the 20% increase in price leads to a 10% decrease in quantity demanded. 3 d) This demand curve is perfectly elastic because a change in price prompts a change in quantity demanded. 3) Refer to the graph below. Between the two points indicated on this demand curve, a) Changes in price and quantity are identical. b) the value of elasticity equals one. c) the elasticity value is the same as the value of the slope of the line. d) All of the above. 4) Refer to the graph below. Using the midpoint elasticity formula, the value of price elasticity of demand equals: a) 6.0 b) 2.5 c) 0.27 d) 3.7 e) None of the above. 5) Which of the following points along this demand curve are inelastic? 4 a) The entire range from B to C. b) The range from A to C. c) Point A only. d) The range from B to A. 6) Which of the statements below is/are correct? a) When demand is elastic, a reduction in price leads to a decrease in total revenue. b) When demand is elastic, a reduction in price leads to an increase in total revenue. c) When demand is inelastic, a reduction in price leads to an increase in total revenue. d) Both a and c. e) Both b and c. 7) Refer to the graph below. Which move leads to a decrease in revenue? a) The move from A to B. b) The move from C to D. c) Both the move from A to B and the move from C to D result in lower revenue because price is lower in both cases. d) Neither the move from A to B nor the move from C to D decreases revenue because the quantity sold is increasing in both cases. 8) Refer to the formula below. This is the formula for: a) Price elasticity of demand. b) Cross-price elasticity c) Income elasticity. d) Price elasticity of supply 9) Along any straight-line demand curve, a) The price elasticity varies, but the slope remains the same b) The slope varies, but the price elasticity remains the same c) The price elasticity and the slope remains the same d) The price elasticity and slope vary 5 10) The demand for the good is ___. So, when the price of a good falls, revenues of producers decrease. a) relatively elastic b) relatively inelastic c) perfectly elastic d) none of the above 11) A perfectly horizontal demand curve has a price elasticity of a) one b) zero c) less than one d) infinity 12) If the units in which the quantity demanded is measured are changed (from kg to gr), then the price elasticity of demand will a) increase by a factor of 100 b) decrease by a factor of 100 c) be unaffected d) be unpredictable 13) Income elasticity of demand measures the extent to which a) the product's price will change when there is a change in income. b) revenue will change when there is a change in income. c) the quantity demanded of a product will change when income changes. d) income will change when the product's price increases or decreases. 6