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					                                 Chapter 3: Markets and Equilibrium

A. Supply and Demand
        The demand curve represents the quantity of a good or service a consumer will choose to
purchase as a function of the price of that good or service. Under normal circumstances, the
quantity demanded will decline as the price of the good or service increases. Hence, the demand
curve is downward sloping. The supply curve represents the quantity of a good or service a firm
will choose to provide as a function of the price of that good or service. Under normal
circumstances, the quantity supplied will increase as the price of the good or service increases.
Hence, the supply curve is upward sloping. Figure 1 depicts normal supply and demand curves.
When the price of the good or service is at a level that the quantity demanded by consumers
equals the quantity supplied by firms, supply and demand curves will intersect and the market is
said to be in equilibrium. In Figure 1, the market is in equilibrium at price level P0, when
suppliers provide and consumers purchase quantity Q0. Market equilibrium at Q0 occurs when no
agent has an incentive to change his behavior; each is behaving optimally under his
circumstances.



                            P
                                                   D
                                                                             S


                            P0




                                                            Q0             Q
                             Figure 1: Supply, Demand and Equilibrium

Consumer and Producer Surplus
        Figure 2 depicts some of the benefits of competitive output and pricing. First, notice that
the market price is below much of the demand curve to the left and much above the supply curve
to the left. This means that the price and output levels combine to create surplus, which can be
thought of as benefits accruing to consumers and producers beyond the trade that takes place
between them. That is, the price P0 exceeds the producer reservation price for all but the final of
the Q0 units sold.1 Similarly, the price P0 is less than the consumer reservation price for all but
the final of the Q0 units purchased.
        In Figure 2, the total surplus is the area within the triangle with angles PD0, PS0 and E.
This triangle depicts the additional profit that producers realize when they sell all of their output
1
  A reservation price is simply the maximum price that a consumer would be willing to pay or the minimum price
that a producer would be willing to accept.


                                                        1
at price P0 when they would be willing to sell some of their output as low as price PS0. Similarly,
this triangle depicts the additional utility that consumers realize when they buy at price P0 when
they would be willing to buy some of their output at as high as price PD0. The area within the
triangle with angles PS0, P0 and E reflects producer surplus and the area within the triangle with
angles PD0, P0 and E reflects consumer surplus.

                         P
                        PD0       D
                                                                    S
                              Consumer
                              Surplus                 E
                         P0
                               Producer
                               Surplus

                        PS0



                                                     Q0           Q
                          Figure 2: Producer and Consumer Surplus

Comparative Statics: Shifting Demand and Supply Curves
         When a material factor other than the price of the commodity changes, there will be a
shift in the supply and/or demand curve. Figure 3 depicts an outward shift in the demand curve
from D0 to D1. This means that at every price level of the commodity, consumers will wish to
purchase more of the commodity. Many factors could lead to an outward shift in the demand
curve. Among these many factors might be favorable changes in consumers’ tastes, increases in
consumers’ income levels, increases in the prices of substitute or competitors’ products or
decreases in price levels of complementary goods. A per-unit government subsidy to consumers
can produce an outward shift in the demand curve. Note that this outward demand curve shift
leads to increases in equilibrium price and consumption levels for the commodity. Similarly,
Figure 4 depicts an inward shift in the demand curve from D0 to D1. This means that at every
price level of the commodity, consumers will wish to purchase less of the commodity. Many
factors could lead to an inward shift in the demand curve. Among these many factors might be
unfavorable changes in consumers’ tastes, decreases in consumers’ income levels, decreases in
the prices of substitute or competitors’ products or increases in price levels of complementary
goods. A sales tax imposed on consumers can produce an outward shift in the demand curve.




                                                 2
                          P
                                                       D1
                                              D0
                                                                   S
                         P1

                         P0




                                                                       Q
                                                       Q0   Q1
                              Figure 3: Outward Demand Curve Shift


                          P

                                              D0
                                                                   S
                                   D1
                         P0


                         P1



                                                                       Q
                                         Q1            Q0
                              Figure 4: Inward Demand Curve Shift

        Shifts in the supply curve also affect equilibrium consumption and price levels. Figure 5
depicts an inward shift in the supply curve from S0 to S1. This means that at every price level,
firms will be willing to sell less of the commodity. Many factors could lead to an inward shift in
the supply curve. Among these many factors might be increases in the price of raw materials or
other input costs. A value-added tax imposed on producers can produce an inward shift in the
supply curve. Note that this inward supply curve shift leads to an increase in the equilibrium
price level of the commodity while decreasing the quantity to be sold. Similarly, Figure 6 depicts
an outward shift in the supply curve from S0 to S1. This means that at every price level, firms
will be willing to sell more of the commodity. Many factors could lead to an outward shift in the
supply curve. Among these many factors might be technology improvements or decreases in the


                                                   3
price of raw materials or other input costs. A per-unit government subsidy to producers can
produce an outward shift in the supply curve. Note that this outward supply curve shift leads to a
decrease in the equilibrium price level of the commodity while increasing the quantity to be sold.


                          P                                S1
                                            D
                                                                   S0
                         P1

                         P0




                                                                      Q
                                             Q1       Q0
                              Figure 5: Inward Supply Curve Shift


                          P

                                            D
                                                                   S0


                         P0
                                                                 S1
                         P1



                                                                      Q
                                                      Q0    Q1
                              Figure 6: Outward Supply Curve Shift

Sales Taxes
       As we discussed earlier, governments can alter market prices and consumption levels
with taxes and subsidies. These reactions are reflected by shifting demand and supply curves as
in Figures 3 through 6. These policies can also produce shortages and surplus production, along
with dead weight losses. Dead weight losses are the losses associated with deviation from the
“best outcome.” Usually, dead weight losses are the result of market imperfections such as


                                                  4
government interference.
        Consider the impact of a sales tax on consumers, as depicted in Figure 7, where the per-
unit sales tax is represented by the difference P2 – P1. Sales tax revenues total (P2 – P1)(Q0 - Q1),
the area of the rectangle enclosed within these bounds. The sales tax reduces the quantity of the
commodity produced and consumed from Q0 to Q1 along with the price that producers receive
from P0 to P1. Additionally, the sales tax increases the price that consumers pay to P2.

                           P
                               Consumer
                               Surplus
                          P2
                                                                       S

                                                Dead
                          P0   Tax Revenue      weight
                                                loss
                               to Government

                          P1
                               Producer
                               Surplus                            D0
                                     Producer       D1
                                     Revenue
                                                                           Q
                                               Q1            Q0
                                 Figure 7: Sales Tax and Surplus

Price Ceilings and Floors
        Market equilibriums exist when market clearing prices exist for the commodity. When
the market clears, the commodity price has ensured that supply equals demand for the
commodity and there are no shortages or surpluses. However, consider the effect of a
government-imposed price ceiling, depicted in Figure 8. Here, suppose that the government has
imposed a price ceiling of PMAX < P0 on gasoline where P0 is the market clearing price for
gasoline. This binding ceiling induces a market shortage equal to Q0 = Q* because producers are
not willing supply as much as the market demands at this maximum price level. A price ceiling
set above the market clearing price would not be binding.




                                                         5
                        P
                                            D
                                                                  S


                        P0

                     PMAX



                                            Shortage
                                          Q*        Q0             Q
                                    Figure 8: Price Ceiling

Similarly, we see in Figure 9 that a binding price floor imposed at PMIN would produce a
shortage equal to Q0 = Q* in the market.



                        P

                     PMIN                                         S


                        P0


                                                              D


                                            Shortage
                                          Q*        Q0             Q
                                     Figure 9: Price Floor

B. Perfect Competition
        Perfect or pure competition exists where no single participant in the market can have an
influence in the price of a homogeneous commodity because of the competition exerted by other
market participants. Perfect competition is normally characterized by a sufficiently large number
of prospective buyers and a sufficiently large number of prospective sellers such that none can
possess any market power. All producers are said to be price takers. The industry will be
characterized by free entry and free exit. The supply curve for an industry composed of those of
an infinite (or sufficiently large) number of identical producers will simply be the horizontal


                                                6
summation of all of the individual firm supply curves. This market supply curve will appear to
be quite similar to the supply curve of any individual producer in that it will be downward
sloping and shaped like any of the individual identical producer supply curves. However, the
demand curve faced by an individual producer will appear quite different from that of the
industry demand curve. Figure 10 depicts a market demand curve for the industry. This curve, in
Figure 10, is represented by the downward sloping line. The demand curve for a single firm’s
production in this perfectly competitive market will lie on the vertical axis at a price level
exceeding P0, will be horizontal between Q = 0 and the market demand curve and will be the
market demand curve at price levels below P0. This means that the firm in the perfectly
competitive market will not be able to sell any of its output at a price above P0 because of the
intense competition in its industry. If the firm sets its price higher than the competitive price, its
sales will be zero. At a price level equal to P0, the firm can sell as many units of its production as
it wishes, subject to not exceeding the market demand for the product. The firm’s supply curve
will normally limit its output at a Q level beneath the market demand level. At a sufficiently high
production level, where the firm undercuts the market price, the firm’s demand curve will be the
market demand curve.
         Figures 10 and 11 depict the demand curve faced by the individual firm. Figure 11
ignores that part of the demand curve that substantially exceeds (lies sufficiently far to the right
of) the firm’s supply curve. The demand curve is said to be perfectly elastic in this range. Recall
that marginal revenue equals the additional money received from the producer from an additional
sale of its product. Average revenue is simply the total revenue divided by total output in units.
Note in Figure 11 that for the perfectly competitive firm, the demand curve is identical to the
marginal revenue and average revenue curves when the firm’s output is less than that of the
market as a whole. Output for the perfectly competitive firm will be at production level Q0.
         Pure competition has the desirable characteristic of allocative efficiency. Allocative
efficiency is the property where limited resources in an economy are allocated to ensure an
optimal mix of commodities to consumers. Allocative efficiency occurs when prices of
commodities equal their marginal production costs (that is, P = MC). In pure competition, the
price of a commodity equals its marginal cost. Furthermore, the pure competition price of a
commodity will equal its average cost, enabling the firm to fully recover its costs, providing it a
fair return. Of course, it is important to note that both of these qualities require that the firm’s
demand function be horizontal, which is the case under the scenario of pure competition. But is
this scenario possible in reality?




                                                  7
                        P

                                          Market Demand


                        P0
                             D = MR = AR                    D = AR




                                                                 Q
               Figure 10: Pure Competition: Individual Firm Demand Curve



                        P
                                                                  S

                              D = MR = AR
                        P0




                                                    Q0               Q
        Figure 11: Pure Competition: Individual Firm Supply and Demand Curves

Example
        In this example, we will compute equilibrium output and price levels for an industry.
Suppose that the aggregate revenue function for a given industry is given by TR = 1000Q -
.01Q2. The total cost function for industry production is given by TC = Q + .005Q2. We obtain
the industry demand function on Figure 12 by dividing the total revenue function by Q: D = AR
= TR/Q = 1000 - .01Q. The industry marginal revenue function is obtained by finding the
derivative of the total revenue function with respect to Q: MR = dTR/dQ = 1000 - .02Q.
Similarly, we obtain the following average cost and marginal cost (supply) functions for the
industry: AC = TC/Q = 1 + .005Q and S = MC = dTC/dQ = 1 + .01Q. The marginal cost
(supply) function is also depicted in Figure 12.
        Now, we will determine equilibrium output and price levels for this competitive industry.
Output is obtained such that MC = AR. MC = AR when: 1 + .01Q = 1000 - .01Q, that is, when


                                                8
999 = .02Q or when Q = 49,950. Each firm’s output will be 49,950/J where J is the number of
firms in the industry. When industry output is 49,950, the output price level will be P = AR =
MC = 500.5.
                        P
                      1000

                                           Industry Demand: P = 1000 - .01Q

                   P0=500.5
                               D = MR = AR                   D = AR




                                              Q0 =49,550/J        Q
               Figure 11: Pure Competition: Individual Firm Demand Curve



                         P
                                                                   S =1+.01Q

                               D = MR = AR = 500.5
                    P0=500.5




                         1

                                             Q0 = 49,550/J            Q
        Figure 12: Pure Competition: Individual Firm Supply and Demand Curves

Pareto Efficiency
       Interpersonal utility comparisons are normally practically meaningless. Nevertheless, it
does make sense to set some sort of objective for allocation and welfare. Pareto efficiency exists
when there is no allocation, redistribution or exchange that will make any agent better off
without worsening another’s position. Similarly, a Pareto efficient exchange makes one or more
agents better off without worsening another agent’s position. Appendix 3.A uses Edgeworth
boxes to analyze Pareto efficient exchanges.

C. Monopoly


                                                 9
        Monopoly in an industry exists when there is only one producer of a commodity with no
close substitutes. This single producer can function as a price maker or price seeker that is, the
monopoly has market power in setting the price of its output. It will set the price of its output so
as to maximize its profits. As we will demonstrate shortly, profits are maximized at an output
level where marginal revenue equals marginal costs. The demand curve for the industry is the
demand curve for the single monopoly firm. Monopoly and market power are the result of
barriers to entry, which can include product differentiation, unique resources, intellectual
property such as patents and copyrights, scale and scope economies and regulation. If monopoly
profits exist in an industry, other firms will have an incentive to enter this industry, securing their
own profits by undercutting the monopoly price. If other firms are unable to enter the industry,
the monopoly is able to retain its market power and monopoly prices.
        Before we consider issues related to monopoly output and profits, we will examine
Figure 13. The bottom diagram maps total revenue (TR) as a function of output. Notice that the
firm experiences diminishing marginal revenue as output increases. This is reflected in the upper
diagram with the marginal revenue curve.



                          P


                                             D = AR




                                        MR


                                                                    Q




                                                  10
                       TR




                                TR




                                                                 Q
            Figure 13: Marginal Revenue, Average Revenue and Total Revenue

        The demand, marginal revenue and average revenue curves in Figure 13 are also depicted
in Figure 14. Per unit profit is simply the difference between average revenue (P = AR) and
average costs (AC). The firm will select the production level that maximizes total profits. Q0 in
Figure 14 is the profit-maximizing or optimal production level for the firm. At this production
level, profits are maximized because marginal costs equal marginal profits. Any production level
beyond this point will increase costs more than profits. Any smaller production level will leave
some profitable production unexploited. Total economic profit at this optimal production level
equals the product of the difference between average revenue (AR = P0) and average costs (AC0)
multiplied by output Q0, consistent with the area (product of dimensions) of the box in Figure 14.

                   Price
                   Cost
                   Revenue
                                                       MC=S
                                                                   AC
                        P0
                              Economic
                              Profit
                      AC0                                        D = AR

                                     MC
                                                      MR
                                            Q0                   Q
                             Figure 14: Monopoly Price and Output




                                                 11
        While the production level Q0 is consistent with monopoly profit maximization, it does
not achieve optimal allocative efficiency for the economy. First, notice that supply does not
equal demand at the profit-maximizing output level Q0. The level Q0 reflects a shortage, where
monopoly output is less than competitive output. In addition, the monopoly product price will
exceed the competitive product price. In the example illustrated in Figure 14, consumers pay the
price level P0, significantly higher than marginal costs at this production level.
        Costs of allocative inefficiency are depicted in Figure 15, within the area bordered by the
dashed line intercepting at Q0, the demand curve D and the supply curve MC=S. This area is the
deadweight loss of the monopoly, reflecting loss of consumer and producer surplus illustrated in
Figure 2 less the producer economic profit illustrated in Figure 14.



                      Price
                      Cost
                      Revenue
                                 Consumer                           MC=S
                                             Surplus
                           P0
                                  Producer
                                  Surplus
                                               Producer
                                                           Dead
                   Competitive
                   Price          Producer       Surplus   weight
                                  Surplus                  loss
                                                                           D = AR

                                             MC
                                                               MR
                                                       Q0                  Q
                            Figure 15: Monopoly Dead Weight Loss

Example
         We will continue our prior example where the industry demand function is D = AR =
TR/Q = 1000 - .01Q. The marginal revenue function for this industry is MR = dTR/dQ = 1000 -
.02Q. The marginal cost (supply) function for the industry is S = MC = dTC/dQ = 1 + .01Q. If
this is a single firm, monopoly industry, what will be its output and price levels?
         Output for this monopoly is obtained such that MC = MR. MC = MR when: 1 + .01Q =
1000 - .02Q, that is, when 999 = .03Q or when Q = 33,300. When output is 33,300, the price
level will be P = MR = MC = 334. These levels are represented in Figure 16.
         Producer surplus is calculated as the area of the rectangle with the height (667 – 334) and
the width (33,300 – 0): 333 * 33,300 = 11,088,900 plus the area of the triangle with width 33,333
and height (334-1) = .5*33,333*333 = 5,544,450. Thus, total producer surplus equals 11,088,900
+ 5,544,450 = 16,633,350. Notice this rectangle and triangle on Figure 16. Consumer surplus is
calculated as the area of the triangle with height (1000 – 667) and the width (33,300 – 0). The
height of the triangle on Figure 16 is due to the vertical intercept (1000) of the demand function.
Since the area of a triangle equals the product of half its height and width, consumer surplus
equals ½ * 333 * 33,300 = 5,544,450. Thus, total surplus in this monopolistic market is
16,633,350.



                                                       12
        Dead weight loss is the loss of consumer surplus associated with a market inefficiency or
imperfection. In this case, the imperfection results from monopoly power. In the competitive
market, consumer surplus would be ½ * (1000 – 500.5) * 49,550 = 12,385,022.5. Producer
surplus in this competitive market would be ½ * 49,550 * (500.5 – 1) = 12,385,022.5. Thus total
competitive surplus is 24,770,045. Thus total competitive surplus is 24,770,045. This implies
that the monopoly dead weight loss is 24,770,045 – 22,177,800 = 2,592,245.



                      Price
                      Cost
                      Revenue
                                  Consumer
                  Monopoly                    Surplus
                  Price = 667                  Producer
                                  Producer       Surplus
                                  Surplus                  Dead                 S = MC
                  Competitive                              weight
                  Price = 500.5    Producer                loss
                                   Surplus
                  Monopoly
                  marginal                                                      D = AR
                  cost = 334
                                                                    MR
                                                Monopoly             Competitive
                                                Output=33,300        Output=49,550 Q
                     Figure 16: Monopoly Surplus and Dead Weight Loss

Forms of Monopoly and Price Discrimination
        Monopoly or market power can exist in a number of scenarios. First, natural monopoly
may exist where fixed costs or costs of entry are sufficiently high to discourage or prevent
competing firms from entering the market. In many instances, governments have recognized that
natural monopolies exist and have regulated them with respect to their price and output levels.
Such monopolies are called regulated monopolies. Examples of such so-called natural
monopolies have included local electricity producers, local water companies and providers of
telephone and cable television services.
        Producers that are able to coordinate their activities may be able to conspire to fix prices
and/or output. An organization of producers that fix prices or output is called a cartel.
Essentially, a cartel results from an agreement to restrain competition so as to maximize
monopoly profits. OPEC, the Organization of Petroleum Exporting Countries was formed for the
purpose of enabling oil producing exporters to coordinate their price and output setting activities.
        Monopolistic competition and oligopoly are two additional important types of limited
competition. Monopolistic competition is characterized by multiple firms attempting to gain
market power by distinguishing their output from the output of their competitors. Oligopoly
exists where a small number of firms producing a homogeneous product seek strategies and
reactions to competitor strategies in the price and output setting processes.
        Whereas monopolies refer to single producer industries, monopsony power may be held
by single buyers. For example, a single large food producer might be able to maintain
monopsony power as the single buyer for agricultural produce such as wheat.


                                                           13
        Price discrimination refers to the practice of selling different units of the same
commodity at different prices. First-degree price discrimination is the sale of identical
commodities at different prices to each individual consumer. In the extreme case, each consumer
pays for each unit of the commodity the maximum that he would be willing to pay. This scenario
is known as perfect price discrimination. Second-degree price discrimination occurs when
producers charge lower prices for higher quantities. This is also referred to as non-linear pricing.
Third degree price discrimination occurs when a given customer pays the same price for each
unit purchased, but different customers pay different amounts. Third degree price discrimination
is based on segmenting the market to distinguish groups that will pay more for the commodity.
Third degree price discrimination seeks to derive the most sales from each segmented “group” of
consumers. Special pricing for senior citizens, children, students and regional pricing are forms
of third degree discrimination. In another example, airlines might be able to price discriminate
against business travelers by charging more for tickets that don’t require Saturday night
stayovers.




                                                 14
                                             Exercises

1. If the demand function for an industry is D = 500 - .01Q and its supply function is 5 + .04Q,
what will be its competitive equilibrium output and price levels?

2. What would be the monopoly output and price levels for Question 1 above?

3. How would your answer to Question 1 change if the government were to charge consumers a
sales tax equal to 50 per unit sold? Ignore Question 2.

4. Suppose that the aggregate total revenue function for a given industry is given by TR = 1000Q
- .01Q2. The aggregate total cost function for industry production is given by TC = Q + .005Q2.
  a.   What are the industry aggregate demand and marginal revenue functions?
  b.   What are the industry aggregate average cost and supply functions?
  c.   What are equilibrium output and price levels for this industry, assuming that it is
competitive?
  d.   If this industry were a single-firm monopoly, what would be its output and price levels?
  e.   What are producer and consumer surplus levels in the monopolistic market in part d?
  f.   Draw an appropriate diagram to depict the consumer and producer surplus along with the
monopoly dead weight loss in parts d and e.
  g.   Calculate the dead weight loss associated with monopoly output in this example.

5. The total revenue function for an industry is given by TR = 20Q - .001Q2. Thus, the total
revenue function for any of the J identical firms in this industry is given by TR = (1/J) * (20Q -
.001Q2) where Q is aggregate output in the industry. The total cost function for a given firm in
the industry is given by TC = 2Q + .001Q2.
  a.    What are the market (aggregate) demand and marginal revenue functions faced by this
industry?
  b.    What are the average total cost and marginal cost functions for each firm in this industry?
  c.    If only a single firm functions in this economy such that it is a monopoly, what would be
its output and price levels?
  d.    What would be the monopoly profit in this industry?
  e.    At what production level are average costs minimized for a single firm in this industry?
  f.    What is the minimal average cost level assuming a single firm operates in this industry?
  g.    What is the long-term pure competition price in this industry?
  h.    What is the level of consumer surplus for the pure competition scenario in part g?
  i.    What is the level of producer surplus for the pure competition scenario in part g?
  j.    Relative to the pure competition surplus, what is the deadweight loss associated with the
monopoly output level in part c?


6. The total revenue function for an industry is given by TR = 20Q - .001Q2. Thus, the total
revenue function for any of the J identical firms in this industry is given by TR = (1/J) * (20Q -
.001Q2). The total cost function for a given firm in the industry is given by TC = 1000 + 2Q +
.001Q2, where 1000 is the fixed cost incurred by each firm in the industry.


                                                 15
  a.    What are the market demand and marginal revenue functions faced by this industry?
  b.    What are the average total cost and marginal cost functions for each firm in this industry?
  c.    If only a single firm functions in this economy such that it is a monopoly, what would be
its output and price levels?
  d.    What would be the monopoly profit in this industry?
  e.    At what production level are average costs minimized for a single firm in this industry?
  f.    What is the minimal average cost level assuming a single firm operates in this industry?

7. Which results in greater producer profits: Perfect price discrimination or pure monopoly
output?




                                                16
                                           Solutions

1. Equilibrium occurs when supply equals demand. Set D = 500 - .01Q = S = 5 + .04Q. Q* =
495/.05 = 9900. Substitute 9900 for Q in either the supply or demand functions to obtain P* =
401.

2. If D = 500 - .01Q, then MR = 500 - .02Q. This is because D = AR. TR = AR * Q. Thus, MY
= dTR/dQ = 500 - .02Q. Monopoly output occurs when supply equals marginal revenue. Set MR
= 500 - .02Q = S = 5 + .04Q. Q* = 495/.06 = 8250. Substitute 8250 for Q in the demand function
D to obtain P* = 417.5.

3. Equilibrium still occurs when supply equals demand. Set D = 450 - .01Q = S = 5 + .04Q. Q*
= 445/.05 = 8900. Substitute 8900 for Q in either the demand function to obtain P* = 361. The
producer receives 361 - 50 = 311. This value can also be obtained by substituting Q* = 8900 into
the supply function.

4.a. We obtain the industry demand function by dividing the total revenue function by Q: D =
AR = TR/Q = 1000 - .01Q. The marginal revenue function is obtained by finding the derivative
of the total revenue function with respect to Q: MR = dTR/dQ = 1000 - .02Q.
  b. We obtain the following average cost and marginal cost (supply) functions: AC = TC/Q = 1
+ .005Q and S = MC = dTC/dQ = 1 + .01Q.
  c. Competitive output is obtained such that MC = AR. MC = AR when: 1 + .01Q = 1000 -
.01Q, that is, when 999 = .02Q or when Q = 49,950. When output is 49,950, the output price
level will be P = AR = MC = 500.5.
  d. Output for this monopoly is obtained such that MC = MR. MC = MR when: 1 + .01Q =
1000 - .02Q, that is, when 999 = .03Q or when Q = 33,300. When output is 33,300, the price
level will be P = 1000 - .01*33,300 = 667. Separately, MR = MC = 334.
  e. Producer surplus is calculated as sum of the following areas:
        the rectangle with height (667 – 334) and width (33,300 – 0): 333 * 33,300 = 11,088,900
        the triangle with width 33,333 and height (334-1) = .5*33,333*333 = 5,544,450
Thus, total producer surplus equals 16,633,350. Consumer surplus is calculated as the area of the
triangle with height (1000 – 667) and the width (33,300 – 0). Since the area of a triangle equals
the product of its height and width, consumer surplus equals ½ * 333 * 33,300 = 5,544,450.
  f. The diagram is drawn as follows:




                                               17
                     Price
                     Cost
                     Revenue
                                 Consumer
                 Monopoly                    Surplus
                 Price = 667                  Producer
                                 Producer       Surplus
                                 Surplus                  Dead                     S = MC
                 Competitive                              weight
                 Price = 500.5    Producer                loss
                                  Surplus
                 Monopoly
                 marginal        Producer                                          D = AR
                 cost = 334      Surplus

                                                                   MR
                                               Monopoly            Competitive
                                               Output=33,300       Output=49,550   Q
                            Monopoly Surplus and Dead Weight Loss
 g. In the competitive market, consumer surplus would be ½ * (1000 – 500.5) * 49,550 =
12,385,022.5. Producer surplus in this competitive market would be ½ * 49,550 * (500.5 – 1) =
12,385,022.5. Thus total competitive surplus is 24,770,045. Total monopoly surplus can be
calculated in part e to be 16,633,350. This implies that the monopoly dead weight loss is
24,770,045 – 16,633,350 = 8,136,695.

5.a. D = AR = TR/Q = 20 - .001Q
     MR = dTR/dQ = 20 - .002Q
  b. AC = TC/Q = 2 + .001Q
     MC = dTC/dQ = 2 + .002Q
  c. The monopoly will set price and output levels such that MR = MC. Thus, the output level
will solve the following: 20 - .002Q = 2 + .002Q. Thus, Q = 4500, the monopoly output. This
means that the output price for the monopoly will be D = 20 - .001Q = 20 – 4.5 = 15.5.
 d. Monopoly average costs would be AC = 2 + 4.5 = 6.5. Thus, the monopoly profit will be (P
– AC) * Q = (15.5 – 6.5) * 4500 = 40,500.
 e. Average production costs for a firm are minimized when MC = AC. The production level
consistent with minimal average costs is obtained by solving 2 + .002Q = 2 + .001Q for Q. Thus,
the minimal average cost production level is Q = 0. This would imply that the minimum cost
number of firms in the industry would be infinite.
 f. If Q = 0, AC = 2 (mathematically).
 g. Select Q such that for the industry, MC = AR. In the long run, with perfect competition, the
marginal cost for the industry with an infinite number of firms equals 2 since per-firm production
will approach 0. Thus, MC = AR when: 2 = 20 - .001Q and Q = 18,000; AR = MC = 2.
 h. Q* = 18,000; P* = 2; D0 = 20; PD = 20 - .001Q
If you are unfamiliar or rusty with calculus, ignore the integrals in this and in other problems.
You can easily work with the triangles and rectangles that follow to calculate surplus values.




                                                          18
We can also obtain this result by noting that the area of the triangle representing consumer
surplus is .5 multiplied by the product of the base and height: .5 * 18,000 * 18 = 162,000.
 i. Industry output is 18,000; Since there are an infinite number of producers, per firm
production = Q* = 0. P* = 2; S0 = 2; PS = 2 + .002Q




We can also obtain this result by noting that the area of the triangle representing producer surplus
is .5 multiplied by the product of the base and height: .5 * 0 * 2 = 0.
  j. First, the total surplus under pure competition is 162,000. The consumer surplus under
monopoly is computed as follows:




If you are unfamiliar or rusty with calculus, ignore the integrals in this and in other problems.
You can easily work with the triangles and rectangles that follow to calculate surplus values. We
can also obtain this result by noting that the area of the triangle representing consumer surplus is
.5 multiplied by the product of the base and height: .5 * 4,500 * (20-15.5) = 10,125. The
monopoly marginal cost at an output of 4,500 equals 2 + .002*4500 = 11. Under monopoly,
producer surplus is determined:




We can also obtain this result by noting that the area of the triangle representing producer surplus
is .5 multiplied by the product of the base and height plus the area of the rectangle representing
additional producer surplus from the higher price: (.5 * 4,500 * (11 – 2)) + 4,500 * (15.5 – 11) =
20,250 + 20,250 = 40,500. Thus, total deadweight monopoly loss equals 162,000 – 10,125 –
40,500 = 111,375.

6.a. D = AR = TR/Q = 20 - .001Q
     MR = dTR/dQ = 20 - .002Q
  b. AC = TC/Q = 1000/Q + 2 + .001Q
     MC = dTC/dQ = 2 + .002Q
  c. The monopoly will set price and output levels such that MR = MC. Thus, the output level
will solve the following: 20 - .002Q = 2 + .002Q. Thus, Q = 4500, the monopoly output. This
means that the output price for the monopoly will be D = 20 - .001Q = 20 – 4.5 = 15.5.
 d. Monopoly average costs would be AC = 1000/4500 + 2 + 4.5 = 6.722. Thus, the monopoly
profit will be (P – AC) * Q = (15.5 – 6.722) * 4500 = 39,500.
 e. Average production costs for a firm are minimized when MC = AC. The production level
consistent with minimal average costs is obtained by solving 2 + .002Q = 1000/Q + 2 + .001Q
for Q. Thus, the minimal average cost production level is Q = 1000.
 f. If Q = 1000, AC = 1000/Q + 2 + .001Q = 4.




                                                 19
7. Perfect price discrimination leads to greater profits. First, perfect price discrimination
produces the highest price for the producer that customers are willing to pay for each unit sold.
Second, it leads to higher output, to the perfect competition level, producing positive profits on
each unit of this additional output.




                                                 20
                  Appendix 3.A: Pareto Efficiency and 2-Person Exchange

        Interpersonal utility comparisons are normally practically meaningless. Nevertheless, it
does make sense to set some sort of objective for allocation and welfare. Pareto efficiency exists
when there is no allocation, redistribution or exchange that will make any agent better off
without worsening another’s position. Similarly, a Pareto efficient exchange makes one or more
agents better off without worsening another agent’s position.
        Consider, for example, the allocations and indifference maps for Agents A and B
depicted in Figure A.1. These two agents could both benefit from a Pareto efficient exchange, as
depicted in Figure A.2. The two indifference curves are combined into an Edgeworth Box in
Figure A.2. A Pareto efficient exchange would occur if Agent A were to give up some
commodity 2 in exchange for some commodity 1 from Agent B such that both revised
allocations fell within the Region for Pareto Efficient Exchange.
                             x2

                                          A




                                                                      x1


                             x2




                                                     B



                                                                      x1

                      Figure A.1: Indifference Maps for Agents A and B




                                                21
                                                       Agent B’s
                                  x1                   Indifference Map
                             x2 Initial
                                Endowments


                                                       Region for Pareto
                                                       Efficient Exchange




                                 Contract                                   x2
                                 Curve
                       Agent A’s
                                                                      x1
                       Indifference Map
                                   Figure A.2: Edgeworth Box

        Figure A.2 depicts the region of Pareto efficient exchange, lying between the two
indifference curves on which Allocations A and B lie. Any exchange that places both Agents A
and B’s allocations within this region is Pareto efficient. In addition, Figure A.2 depicts a
contract curve, which represents the set of Pareto efficient allocations. Any allocation on the
contract curve is Pareto efficient or Pareto optimal, meaning that no Pareto efficient transaction
can occur between the two agents. This means that under the current endowments, no agent can
be made better off without hurting the other agent. Notice that the contract curve lies within the
region for Pareto Efficient Exchange, though no deviation from this curve would be Pareto
efficient. Also note that the contract curve is comprised of the points of tangency between the
two agents’ indifference curves.




                                                22
                              Appendix 3B: Antitrust Regulation

U.S. Antitrust Laws
        Free market economies serve markets more effectively when healthy competition forces
business to provide better goods and services at lower prices. To preserve or create more healthy
competition, the U.S. government has enacted a series of antitrust laws designed to keep
companies from engaging in activities that would diminish competition. First among these is the
Sherman Antitrust Act of 1890, applicable to interstate and foreign trade, which prohibits
conspiracies, contracts and business combinations in restraint of trade or to monopolize an
industry. Because courts faced difficulties interpreting the act, its initial enforcement was
minimal. Two exceptions were the 1911 government victories against Standard Oil and
American Tobacco. Both companies were broken up.
        The Clayton Act 1914 was intended to clarify and extend the Sherman Act, allowing for
enhanced enforcement and making it easier to cease monopoly activity at an earlier stage in its
process. The Clayton Act prohibited price discrimination and tying contracts, overlapping
directorships among competing companies and acquiring stock of other firms if such acquisitions
were to reduce competition. Whereas the Sherman Act forbade takeovers and other anti-trust
activities that restrained trade, the Clayton Act went further, forbidding takeovers and activities
that may lead to a restraint of trade. Nonetheless, enforcement remained difficult. For example,
the government lost one of its first major post-Clayton cases against U.S. Steel shortly after
World War I. During the late 1930's and 1940's, the government unsuccessfully pursued Alcoa,
the only major producer of primary aluminum. The government did prevail over the motion-
picture industry, forcing the major producers to divest themselves of movie theaters.
        The Federal Trade Commission Act of 1914 provided for the regulatory body to enforce
antitrust legislation and prohibited unfair methods of competition. The Robinson-Patman Act of
1936, an amendment to the Clayton Act, limits sales that discriminate in price to equally-situated
customers (distributors) when the effect of such sales is to reduce competition. The Celler-
Kefauver Amendment of 1950 extended the Clayton Act to cover firms purchasing assets from
other firms and acquirers significantly reducing competition or significantly increasing market
shares even within states. This act also gave the government power to prohibit mergers that
increased market concentration. The Hart-Scott-Rodino Antitrust Improvements Act of 1976
required that prospective acquiring firms file takeover proposals with the FTC and the
Department of Justice so that these agencies have the opportunity to review and pass judgment
on all proposed takeover transactions. A number of exemptions were to apply, including
transactions for less than $15 million.
        As discussed earlier, in 1968, the Justice Department issued guidelines based on
concentration ratios concerning levels of industry concentration. In 1982 and 1984, the revised
guidelines were based on the Herfindahl-Hirschman Index. Guidelines issued in 1984 attempted
to incorporate the use of product price elasticities in determining takeover and firm market power
effects. More recent Justice Department Guidelines issued in 1997 are intended to clarify
standards used by the Department to challenge corporate acquisitions under the Clayton Act.
        One of the major problems with using the Herfindahl-Hirschman Index is to determine
exactly what constitutes an industry. While the SIC and NAIC systems provide for numerical
indexing procedures for categorizing industries, it is not clear exactly how the distinction
between industries should be drawn for antitrust purposes. In addition, it is not clear how
international competition or local and regional markets distinctions should affect computation of



                                                23
the indices. In any case, current guidelines focus on the smallest group of products or geographic
region that would be impacted by the proposed takeover.
        Antitrust efforts by the U.S. government have met with mixed results. For example, in
1968, the U.S. Department of Justice began a protracted though unsuccessful effort to
decompose IBM into competing companies. At the time, IBM enjoyed a 70% market share in the
computer industry. However, many observers believe that technological advancements and the
personal computer market would have rendered this action unnecessary. After huge expenditures
on both sides (at one point during the process, IBM had retained 200 attorneys), the Justice
Department action was dismissed without merit in 1982.
        In 1974, the Department of Justice launched what may have been its most significant
antitrust action, forcing AT&T to settle in 1982 to a major divestiture (breakup) of local
telephone companies. Local service providers (“Baby Bells”) were spun off by AT&T in 1984,
with AT&T shareholders receiving shares in each of seven spin-offs. Prior to this litigation,
AT&T had operated as a legally sanctioned monopoly. Sprint and MCI were then able to
compete effectively in long-distance markets. While AT&T’s long distance share fell from over
90% from 1984 to less than 50% in 1996, its volume of calls more than tripled.
        In 1997, the Justice Department initiated action against Microsoft charging it with
violating a 1994 consent decree by bundling its Internet Explorer browser with its Windows
operating system. While the Clinton administration had argued that the company maintained a
monopoly in operating systems and sought to break it up, the Bush administration dropped the
break-up efforts by September 2001.
        The U.S. Department has blocked numerous mergers during the late 1990s on the
grounds of anti-trust concerns. Among these proposed deals have been WorldCom and Sprint,
Office Depot and Staples and Reynolds and Alcoa. In addition, European anti-trust regulators are
scrutinizing more mergers between U.S. firms doing business in Europe.

European Anti-Trust Law
        While the Sherman Act and subsequent legislation has had a tremendous impact on
competition in the U.S., E.U anti-trust regulations have affected both European and U.S.
combinations. Articles 81 and 82 of the European Community Treaty prohibiting cartels and
other “concerted practices” distorting competition along with prohibiting the willful acquisition
or maintenance of monopoly power are similar to Sections 1 and 2 of the Sherman Act outlawing
concerted action to restrain trade. Consider, for example, the proposed merger of General
Electric and Honeywell International Inc., two U.S.-based corporations, which was blocked by
the European Union in 2001 even though U.S. antitrust regulators had already approved the deal.
Jack Welch, then CEO of General Electric, complained, “European regulators’ demands
exceeded anything I or our European advisers imagined and differed sharply from antitrust
counterparts in the U.S. and Canada.”
        The U.S. software and operating systems producer, Microsoft, has been in nearly
continuous conflict with EU anti-trust regulators over its dominance in EU markets. This conflict
has been, in part, fueled by The European Committee for Interoperable Systems, which includes
International Business Machines Corp., Oracle Corp., RealNetworks Inc., Nokia Corp. and Sun
Microsystems Inc. This committee has filed complaints asking EU regulators to end Microsoft
practices that strengthened its existing monopolies and extended its market dominance into
current and future product markets. In 2004, EU regulators imposed nearly ∈500 in anti-trust
related fines.



                                                24
                                Appendix 3.C: Price Discrimination

Price Discrimination and First Degree Price Discrimination
        Price discrimination refers to the practice of selling different units of the same
commodity at different prices. First-degree price discrimination is the sale of identical
commodities at different prices to each individual consumer.2 Each consumer pays for each unit
of the commodity the maximum that he would be willing to pay. This scenario is known as
perfect price discrimination. Under first degree price discrimination, output is the same as in
competitive equilibrium, therefore, it is Pareto optimal. Customer surplus is zero and producer
surplus is maximized.

                           P
                          PD0     D = Market Demand
                                                                    S

                                Producer
                           P0
                                Surplus


                          PS0             Producer

                                          Costs

                                                      Q0           Q
                   Figure 1: Producer Surplus: First-Degree Price Discrimination

Second Degree Price Discrimination
        Second-degree price discrimination occurs when producers charge different prices for
different quantities. Prices vary from customer to customer, but a given customer pays the same
price for each unit. This is also referred to as non-linear pricing. Frequently, this takes the form
of quantity discounting or quality differences (e.g., first class and coach class airline service).
        For our example, we will assume that a producer knows that there are two types of
consumers for their commodities, cannot distinguish “high demand” or type 2 who are willing to
pay more and “low demand” or type 1 who are not. Producers cannot distinguish these two types
of customers from one another, except through the quantities of their purchasers. High-demand
customers have an obvious incentive to disguise themselves as low demand customers.
Producers discourage this by offering pricing discounts to high-demand customers who commit
to purchasing quantities that exceed levels that low demand would not accept. Thus, through
their quantity purchases reacting to producer strategies, customers self-select their pricing group
so as to maximize their own surplus. This is represented in Figure 2, which depicts demand
curves for both Customer type 1 and customer type 2. For sake of simplicity, we assume zero
marginal costs.

2
    Pigou [1920]


                                                     25
                                  Producer Surplus
                        P         from Type 1
                                  Customer; Surplus
                                  from Type 2
                      PD02     D2 Customer

                      PD01                       Type 2 Customer
                                                 Surplus


                              D1                            Additional
                                                            Producer Surplus
                                                            from Type 2
                                                            Customer



                        0
                                               Q10                 Q20   Q

                Figure 2: Second Degree Price Discrimination: Self Selection

        First, the producer would like to charge both type 1 and type 2 customers prices
consistent with perfect price discrimination. If successful, this strategy would lead to total
producer revenues (profits and surplus, since marginal costs are assumed to be zero) equal to the
sum of the area under D1 and the area under D2. However, customers of type 2 would retain more
surplus if they disguised themselves as type 1 customers, accepting smaller quantities at smaller
prices. Realizing this, the discriminating producer will react by offering the type 2 high demand
customer an additional quantity of the commodity, increasing sales to the type 2 customer to .
This will produce revenues represented by the area under D1 for the first       units along with
revenues represented by the area under D2 for the next       -     units from type 2 customers. In
addition, this strategy will produce revenues represented by the area under D1 from type 1
customers for their purchase of      units.
        However, this strategy still does not maximize the price discriminator’s profits. The
producer will seek to reduce its sale of units to type 1 customers at lower prices in order to
encourage type 2 customers to purchase additional units at higher prices. This strategy is
reflected in Figure 3. Here, the producer loses revenue from the type 1 customer, but increases
revenues from type 2 customers. The producer will continue to increase type 1 customer prices
and seek higher prices from type 2 customers until the marginal producer surplus losses from
type 1 customers exactly offset marginal producer surplus gains from type 2 customers. This
final pricing scenario is depicted in Figure 4.




                                                26
                        P
                                     Type 2 Customer
                      PD02      D2   Surplus
                                                 Gained Surplus
                                                 from Type 2
                      PD01                       Customers



                              D1                                  Lost Surplus
                                                                  from Type 1
                                                                  Customers




                        0
                                          Q’     Q10                   Q20       Q

            Figure 3: Second Degree Price Discrimination: Quantity Adjustment


                        P
                                     Type 2 Customer
                      PD02 D2        Surplus
                                                 Gained Surplus
                                                 from Type 2
                      PD01                       Customers



                             D1                                   Lost Surplus
                                                                  from Type 1
                                                                  Customers




                        0
                                     Q’        Q10                     Q20       Q

                        Figure 4: Second Degree Price Discrimination


Third Degree Price Discrimination
       Third degree price discrimination occurs when a given customer pays the same price for
each unit purchased, but different customers pay different amounts. Third degree price
discrimination is based on segmenting the market to distinguish groups that will pay more for the
commodity. Third degree price discrimination seeks to derive the most surplus from each
segmented “group” of consumers. Special pricing for senior citizens, children, students and
regional pricing are forms of third degree discrimination. These groups may have been identified
as “low demand” or low price elasticity customers. Third degree price discrimination may lead to
indeterminate production outputs because of kinked marginal revenue curves and potential


                                                   27
multiple intersections with marginal cost functions. Conditions needed for successful price
discrimination include the ability to distinguish and segment customers who differ in their
willingness to pay and the lack of customer ability to arbitrage.




                                               28

				
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