Microeconomics, monopoly pricing, game theory
Section I: Monopoly pricing (50 points)
Milwaukee Utilities has a complete monopoly over the generation and transmission of energy. The following information on this company is given as follows:
Demand = 750 – 10Q
Average cost = 500 – 2Q
Where Q is measured in megawatts and prices and costs are measured in dollars.
a.) Does this firm’s production process satisfy the condition for a natural monopoly? When explaining your answer assume two hypothetical smaller firms q1 and q2 generate 5 and 10 megawatts of energy, respectively. (Hint, Milwaukee Utilities is a monopolist so it generates the sum of the energy generated by the two smaller firms. Hence, the smaller firms’ output is a subset of Milwaukee Utilities’ output.) (Hint, the term’production process’ used in question Ia, is interpreted as ‘cost characteristics’, i.e, do the cost characteristics satisfy the condition for a natural monopoly)
b.) How much energy would be sold and at what price if the monopolist sets price as a profit maximizing monopolist? Note: The marginal cost curve is twice as steep as the average cost curve.
c.) What is the firm’s profits at the monopoly price determined in part b?
d.) Now, suppose the monopolist adopts a two-part tariff pricing scheme for its customers such that the access fee is equal to the profit-maximizing marginal cost and the user fee is the difference between the profit maximizing monopoly price and marginal cost. Please calculate the user and access fees based on this information.
e.) Now suppose the monopolist practices 3rd degree price discrimination and charges the profit-maximizing price to the high reservation price customers and charges a 10 percent discount on the monopoly price to low reservation price customers. Note, low reservation price customers are those who would never pay the monopoly price. What is the price charged to the low reservation price customers? What is the profit generated by charging these prices? Are the profits greater than the profits in part ‘c’? Please explain.
f.) Now suppose the state public utility commission requires this monopolist to charge the competitive price, how much energy would be sold and at what price? What are the monopolist’s profits?
g.) Based on the profits obtained when forcing this monopolist to charge a competitive price, the regulator now requires this monopoly to set price equal to average cost (this is called second-best pricing). What is the monopolist’s profits when charging second-best prices?
Please show all work to receive full credit.
Section II: Game theoretic approach toward analyzing output behavior of rivals (50 points)
Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:
C(qx) = C(qy) =25qi (firm X and Y’s total cost curves), where i=x or y
MC(qy) =MC(qy) = 25 (firm X and Y’s marginal cost curves)
P=50-Q, (market demand), where Q = qx + qy .
C(q) and have the same cost structure: marginal cost and average cost both=25
a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.
b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.
c.) What four possible output combinations are available in this game?
d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.
e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.
f.) Does either firm have a dominant strategy? If so, what is it?
g.) Is there a Nash equilibrium for this game? If so, what is it?
h.) Is the outcome of this game a prisoner’s dilemma? Please Explain?
Please show all work to receive full credit.
Section I: Monopoly pricing (50 points)
Milwaukee Utilities has a complete monopoly over the generation and transmission of energy. The following information on this company is given as follows:
Demand = 750 – 10Q
Average cost = 500 – 2Q
Where Q is measured in megawatts and prices and costs are measured in dollars.
a.) Does this firm’s production process satisfy the condition for a natural monopoly? When explaining your answer assume two hypothetical smaller firms q1 and q2 generate 5 and 10 megawatts of energy, respectively. (Hint, Milwaukee Utilities is a monopolist so it generates the sum of the energy generated by the two smaller firms. Hence, the smaller firms’ output is a subset of Milwaukee Utilities’ output.) (Hint, the term’production process’ used in question Ia, is interpreted as ‘cost characteristics’, i.e, do the cost characteristics satisfy the condition for a natural monopoly)
b.) How much energy would be sold and at what price if the monopolist sets price as a profit maximizing monopolist? Note: The marginal cost curve is twice as steep as the average cost curve.
c.) What is the firm’s profits at the monopoly price determined in part b?
d.) Now, suppose the monopolist adopts a two-part tariff pricing scheme for its customers such that the access fee is equal to the profit-maximizing marginal cost and the user fee is the difference between the profit maximizing monopoly price and marginal cost. Please calculate the user and access fees based on this information.
e.) Now suppose the monopolist practices 3rd degree price discrimination and charges the profit-maximizing price to the high reservation price customers and charges a 10 percent discount on the monopoly price to low reservation price customers. Note, low reservation price customers are those who would never pay the monopoly price. What is the price charged to the low reservation price customers? What is the profit generated by charging these prices? Are the profits greater than the profits in part ‘c’? Please explain.
f.) Now suppose the state public utility commission requires this monopolist to charge the competitive price, how much energy would be sold and at what price? What are the monopolist’s profits?
g.) Based on the profits obtained when forcing this monopolist to charge a competitive price, the regulator now requires this monopoly to set price equal to average cost (this is called second-best pricing). What is the monopolist’s profits when charging second-best prices?
Please show all work to receive full credit.
Section II: Game theoretic approach toward analyzing output behavior of rivals (50 points)
Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:
C(qx) = C(qy) =25qi (firm X and Y’s total cost curves), where i=x or y
MC(qy) =MC(qy) = 25 (firm X and Y’s marginal cost curves)
P=50-Q, (market demand), where Q = qx + qy .
C(q) and have the same cost structure: marginal cost and average cost both=25
a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.
b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.
c.) What four possible output combinations are available in this game?
d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.
e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.
f.) Does either firm have a dominant strategy? If so, what is it?
g.) Is there a Nash equilibrium for this game? If so, what is it?
h.) Is the outcome of this game a prisoner’s dilemma? Please Explain?
Please show all work to receive full credit.
Lecture notes 9
MONOPOLIES
This set of lecture notes examines price and output determination in industries dominated by a monopoly. Even though true monopolies are rare, due in part to increased international competition, and due to cost saving technology that allows for greater entry, exploring this topic is still useful for predicting behavior of firms that meet many of the conditions of a monopoly. Indeed, major divisions of the U.S. Department of Justice and the Federal Trade Commission consider possible monopoly pricing and output behavior when determining whether to approve the prospective mergers.
A. REASONS A MONOPOLY MAY EXIST
Monopolistic market structures can arise for several reasons, which are listed below.
1.) Government sanctioned monopoly: In the past the U.S. government awarded market franchises to firms typically for products that were essential to business operations, such as transportation and utilities. The argument for these awards was also supported by the notion that a single provider of these services was more efficient than several firms providing the same service. For example it is quite inefficient to have two railroad carriers using parallel track to service the same routes.
2.) Firms that own patent: AT&T’s patent on vital telephone equipment led to its market dominance by the beginning of the 20th century.
3.) One firm controls the supply of resources: Prior to World War II ALCOA controlled the supply of Bauxite. This attributed to its monopoly position in the Aluminum industry.
4.) Natural Monopoly: Some products are produced at a lower cost by one company rather than by a combination of several firms. The condition for this type of cost outcome is termed subadditivity. Subadditivity simply requires that the cost of a single firm producing an output is less than the cost of multiple firms producing the same quantity. This is depicted by the following equation:
C(Q) < C(q1)+ C(q2) + ... C(qn ) and Q = q1 + q2 + ...qn
Where the left hand side of this equation is the cost of a single firm producing at output Q and the right hand side of the equation is the sum of the cost of several firms producing at this same output level. This is graphically depicted by Figure 9.A. To guarantee that the condition for subadditivity is met a total cost curve that increases at a decreasing rate is used. This graph suggests that the sum of the separate outputs q1 and q2 give total the total cost of C(q1) + C(q2) which is above the total cost C(q1 + q2) that is associated with the single producer of this product.
C
Figure 9.A
C(q1) + C(q2)
C(q1+q2)
C(q)
C(q2)
C(q1)
q
1 q2 q1 + q2=Q
Note that from previous lectures, a total cost curve that increases at an increasing rate has a corresponding decreasing average cost curve. Thus, it would seem that firms facing declining average cost should satisfy the requirements for subadditivity. Indeed, the following proof supports this notion.
Decreasing average cost is depicted as follows:
(1) C(qi)/qi > C(Q)/Q; where 0 (2) multiplying equation (1) by qi gives C(qi) > (C(Q)/Q) qi (3) summing over ‘I’ gives iC(qi) > (C(Q)/Q) iqi (4) Since iqi = Q then equation (2) can be rewritten as iC(qi) > C(Q), which is the condition for subadditivity. Recognizing that decreasing average cost satisfies the condition for a natural monopoly, we will use a downward sloping average cost curve when graphically examining the pricing behavior of a monopolist.
B. CONDITIONS FOR MONOPOLY STRUCTURE
Before analyzing price determination for a monopolistic market structure it is important to recognize the market conditions that are associated with such an industry structure. 1.) One seller: The industry is dominated by a single firm. For example, Intel in the microchip processing industry. 2.) The firm is a price setter: This suggests that the firm is able to deviate from setting price at the market equilibrium. 3.) High barriers to entry and exit: This suggests that potential entrants face substantial start-up cost. For example, I would be fairly difficult to acquire all the capital needed to compete with the regional Bell operating companies. Barriers to exit suggest that the incumbent monopoly incurs substantial sunk cost. For example Ameritech would find it fairly difficult to recoup all of its capital investment if it attempts to exit the communications industry. 4.) Few close substitutes: This suggests a relatively elastic demand curve. 5.) The market demand is the firm’s demand curve: This suggests a downward sloping demand curve with a corresponding marginal revenue curve that has twice the slope as the demand curve (This was proven in earlier lecture notes.)
C. LONG-RUN EQUILIBRIUM PRICE AND OUTPUT
Using the profit maximizing condition of marginal cost equaling marginal revenue allows for examining price and output determination in a monopolistic market. Assuming that the monopolist is a natural monopoly gives a downward sloping average cost curve with a marginal cost curve that always lies beneath it. The graphical representation of the monopolist is depicted when superimposing the monopoly demand and marginal revenue curve with these cost curves. Figure 9.B presents just such a graph. Figure 9.B $ Pm Z ACm V AC MC MR Demand qm q The profit maximizing output level is represented by qm and occurs where MC=MR. The corresponding price is taken from the demand curve and has the value of Pm for this graph. The corresponding unit cost at the monopoly output level is taken from the average cost, and is represented by the value ACm. The difference between the monopoly price and unit cost summed for each unit output up to the monopoly output level gives the monopoly profit. This is depicted by the rectangle Pm,Z,V,ACm. Note that unlike the situation with competitive markets the absence of potential competitors suggests that this is the long-run equilibrium because the monopolist does not face any profit erosion from the entry of such rivals.
D. COMPARISON OF MONOPOLY PRICING AND COMPETITIVE PRICING
Monopoly pricing has important implication for consumer welfare. Indeed, setting high prices may suggest a loss of total surplus. The monopoly price is compared to the competitive equilibrium to examine this possibility. Using the condition for competitive price requires setting price equal to the firms demand curve (MC=P). The equilibrium price and quantity from this pricing behavior is represented by Pc and Qc, respectively on Figure 9.C. The monopoly prices and quantity are respectively, Pm and Qm. This suggests that monopoly pricing is associated with such a firm selling fewer products than the competitive equilibrium dictates and at higher prices. Furthermore the total surplus loss is represented by the shaded area V. In sum, monopoly pricing does not promote an efficient market for consumers. It should be noted however, that forcing the natural monopolist to satisfy the competitive pricing condition leads to the firm facing negative profits because marginal cost is always less than average cost for a natural monopoly. Hence, setting price equal to marginal cost results in a price that is less than average costs. This suggest that any pricing regulation of such a firm should consider incorporating the constraint that sets a firm’s price equal to average cost. Figure 9.C $ Pm V AC Pc MC MR Demand qm qc q
E. PRICE DISCRIMINATION
Rather than engage in monopoly pricing such a firm may choose to generate greater profits by practicing price discrimination. This pricing behavior is defined as charging different consumers different prices for the same commodity without cost justification. The classic example of this is Standard Oil’s pricing its product at below competitive prices in regions where rivals existed during the turn of the century. A graphical depiction of price discrimination is shown in Figure 9.D. This graph presents the demand curves for two consumer groups (D1 and D2) along with the corresponding marginal revenues (MR1 and MR2). Since only one firm supplies this product there is only one marginal cost curve, which is depicted by MC. To determine the price for each consumer group the monopolist initially determines the profit maximizing output level by setting the joint marginal revenue curve equal to marginal cost. The joint marginal revenue curve is the horizontal sum of the two groups marginal revenue curves. The marginal cost corresponding to the profit maximizing output level is depicted by MCm. This is the marginal cost faced by the price discriminating monopolist when selling the profit maximizing amount of goods. Thus far, then, the procedure for setting discriminatory prices does not differ from setting the standard monopoly price. However, at this juncture, instead of setting price off of the joint demand curve, (Remember the monopoly demand curve is the horizontal sum of consumers’ demand curves), prices are determined by separately equating the profit maximizing level of marginal cost with each consumer group’s marginal revenue curve. On Figure 9.D this gives the respective price and output levels of P1 and Q1 for consumer group one, and P2 and Q2 for consumer group two. The outcome from such pricing suggest that all else equal (for the same output level) a price discriminating monopolist will set a higher price for consumers who face a less elastic demand curve. This makes perfect sense, because this consumer group is less sensitive to price changes. For example restaurants typically charge lower prices to senior citizens for the same product served to other consumers primarily because seniors are thought to be highly price sensitive given that they receive a fixed income. Mathematical support of this notion is provided by the following: Since price discrimination occurs when MR1=MCm=MR2 and as proved earlier the value of marginal revenue is as follows MRk=Pk(1-(1/| k|)), where k indexes consumer groups and represents the own price demand elasticity, then the following holds: P1(1-(1/|1|)) = P2(1-(1/|2|)) or P1/P2= (1-(1/|2|))/(1-(1/|1|)) This equation suggests that the price ratio is less than one if the demand elasticity for consumer group 1 is less than that of consumer group two. In other words P1 is less than P2 if the demand curve for consumer group two is more elastic than that for consumer group one. The type of price discrimination that we have just examined is termed 3rd degree price discrimination because prices are only set for two consumer groups. A second category of price discrimination is depicted if prices were set for some number of consumer groups greater than two but not such that each consumer faced a different price. This example is presented in Figure 9.E. Note that the monopolist is able to further increase producer surplus at the expense of consumers. Indeed the remaining consumer surplus depicted in Figure 9.E is the sum of the triangles A, B and C. A practical example of second degree price discrimination is the setting of different utility prices throughout the day. Figure 9.D $ P2 MC P1 MCm D1 D2 D1 + D2 MR1 MR2 MR1+ MR2 q Figure 9.E $ A P2 MC B P1 Pe C Demand q2 q1 qe q Lastly, another category of price discrimination is first degree price discrimination. This type of discrimination occurs when a seller charges each consumer their reservation price. Hence, the seller receives all of the producer surplus. This is depicted by Figure 9.F. A practical example of this is the approach used to sell autos or appliances, in which sales people allow for haggling over prices. It should be noted, however, that engaging in this practice generates extra cost for the firm since products that are not sold using such methods do not require the employment of large sales forces. Figure 9.F $ Additional MC Producer Surplus Pe Demand qe q
Section I: Monopoly pricing (50 points) Milwaukee Utilities has a complete monopoly over the generation and transmission of energy. The following information on this company is given as follows:
Demand = 500 – 6Q
Average cost = 250 – Q Where Q is measured in megawatts and prices and costs are measured in dollars.
How much energy would be sold and at what price if
a.) The firm sets price as a profit maximizing monopolist? Note: The marginal cost curve is twice as steep as the average cost curve.
b.) What is the firm’s profits at the monopoly price determined in part a?
c.) Now, suppose the firm adopts a two-part tariff pricing scheme for its customers such that the access fee is equal to the profit-maximizing marginal cost and the user fee is the difference between the profit maximizing monopoly price and marginal cost. Please calculate the user and access fees based on this information.
d.) Now suppose the firm practices 3rd degree price discrimination and charges the profit-maximizing price to the high reservation price customers and charges a 10 percent discount on the monopoly price to low reservation price customers. Note, low reservation price customers are those who would never pay the monopoly price. What is the price charged to the low reservation price customers? What is the profit generated by charging these profits? Are the profits greater than the profits in part ‘b’? Please explain.
e.) Now suppose the state public utility commission requires this firm to charge the competitive price, how much energy would be sold and at what price? What is the firm’s profits?
f.) Based on the profits obtained when forcing this monopoly to charge a competitive price, the regulator now requires this monopoly to set price equal to average cost (this is called second-best pricing). What is the firm’s profits when charging second-best prices?
Please show all work to receive full credit.
Section II: Game theoretic approach toward analyzing output behavior of rivals (50 points) Firms X and Y are duopolists facing the same two strategy choices. They can either tacitly collude or they can compete in a Cournot fashion. The market demand for their product, as well as their respective cost curves are as follows:
C(qx) = C(qy) =50qi (firm X and Y’s total cost curves), where i=x or y
MC(qy) =MC(qy) = 50 (firm X and Y’s marginal cost curves)
P=500-5Q, (market demand), where Q = qx + qy .
C(q) and have the same cost structure: marginal cost and average cost both=50
a.) Calculate the respective output levels of each firm if they collude to set monopoly prices.
b.) Calculate the respective output levels of each firm if they adhere to the Cournot model.
c.) What four possible output combinations are available in this game?
d.) Derive the for possible profit outcomes for each firm that arise from producing the four possible output combinations available in this game.
e.) Use these profit outcomes to construct a 2×2 normal representative matrix for this game.
f.) Does either firm have a dominant strategy? If so, what is it?
g.) Is there a Nash equilibrium for this game? If so, what is it?
h.) Is the outcome of this game a prisoner’s dilemma? Please Explain? Please show all work to receive full credit.
Section I: Monopoly pricing Milwaukee Utilities has a complete monopoly over the generation and transmission of energy. The following information on this company is given as follows:
Approach used to answer succeeding questions: Graph that depicts monopoly and 3rd degree price discrimination and the competitive price set by the regulator for this example: $
PH =PM
PL AC
MC
PC MR D
QM Q* QC Q
Since, Average revenue (Demand) = 500 -6Q
And Average cost = 250 – Q
Then
Marginal revenue = 500 -12Q
Marginal cost = 250 -2Q So for monopoly pricing (MR=MC) 500-12Q=250-2Q 500-6Q=250-2Q
250=20Q 250=4Q
QM =25 QC =62.5 So, for the low reservation price customer
PL = 350- (.10×350)=315 g.) the firm sets price as a monopoly?
Ans. So for monopoly pricing (MR=MC)
500-12Q=250-2Q
QM =25
P=500-6Q, so for the monopoly output level P=500-(6×25) =$350= PM h.) What is the firm’s profits at the monopoly price determine in part a?
Π= (P×Q) – TC; note TC=AC×Q
= $3125.
i.) Now, suppose the firm adopts a two-part tariff pricing scheme for its customers such that the access fee is equal to the profit-maximizing marginal cost and the user fee is the difference between the profit maximizing monopoly price and marginal cost. Please calculate the user and access fees based on this information.
Ans. User fee=350-200 = 150
Access fee =250-(2(25) =200
j.) Now suppose the firm practices 3rd degree price discrimination and charges the profit-maximizing price to the high reservation price customers and charges a 10 percent discount on the monopoly price to low reservation price customers. Note, low reservation price customers are those who would never pay the monopoly price. What is the price charged to the low reservation price customers? What is the profit generated by charging these profits? Are the profits greater than the profits in part ‘b’? Please explain.
Answer: The monopoly price is the price charged to the high reservation price consumers so PH = 350. The price charged to the low reservation price consumers is 10% less that the monopoly price so PL = 315. Remember the monopoly output is 25=QH and the number of customers at the low discount rate is 5.8333=QL. Hence, the firm’s profit when engaging in the described 3rd degree price discrimination is 3125+413.192=3538.192. The firm generates higher profits compared to single monopoly pricing because it obtains an additional amount of profit equaling 413.192 due to charging the lower price to low reservation price consumers.
k.) Now suppose the state public utility commission requires this firm to charge the competitive price, how much energy would be sold and at what price? What is the firm’s profits?
Answer:
(P=MC)
500-6Q=250-2Q
QC =62.5
Π =(125×62.5) – (187.5×62.5) = -3906.25
Note that the firm experiences a loss because its average cost decreases as output increases, hence marginal cost is always less than average cost for a given output level. l.) Based on the profits obtained when forcing this monopoly to charge a competitive price, the regulator now requires this monopoly to set price equal to average cost (this is called second-best pricing). What is the firm’s profits when charging second-best prices?
Answer:
(P=AC)
500-6Q = 250-Q. Thus, Q=50 and P=200 and π=0
Section III: Game theoretic approach toward analyzing output behavior of rivals—25 points
i.) If the two firms collude and play as monopoly, they will produce the same quantity and set the same price.
Ans. Here’s the approach that uses calculus:
P=500-5Q
Where 1/2Q= qx =qy
Total revenue is
TR=P×Q = (500-5Q)Q =-5Q2 + 500Q
The profit maximizing condition for monopoly is MRMC
-10Q +500 = 50
So, Q=45/10
Thus the respective output of each firm is 22.5 if they collude and set monopoly prices.
Here’s the approach that does not use calculus:
P=500-5Q
Since the MR curve is twice as steep as the demand curve MR=500-10Q
Setting MR=MC give the following: 500-10Q= 50, hence Q=45
Thus, the respective output of each firm is 22.5 if they collude and set monopoly prices. j.) Ans. Here’s the approach that uses calculus
In the Cournot model, each firm chooses price and output to maximize its own profit.
For firm X;
(1)
FOC:
(2)
For firm Y, it will produce
(3)
Solve (2) and (3) simultaneously,
qx = qx =30 (4)
Here’s the approach the doesn’t use calculus
P= 500 – 5qx -5qy
Since the slope of the MR curve is twice as steep as the slope of the demand curve
MR1 =500 – 10qx -5qy
Setting MR1 =MC gives 500 – 10qx -5qy = 50
Thus, 450-5qy= 10qx So the reaction function for firm X is qx= 45-(1/2)qy
The same approach gives qy= 45-(1/2)qx for firm Y.
Solving simultaneously gives
Thus, qx and qy equal 30 if they adhere to the Cournot model
Here are the answers for the rest of this question.
c.) qx =22.5 and qy=30
qx =30 and qy=22.5
qx =30 and qy=30
d.) The potential profit levels for Firm X are as follows: (x=5062.5 if both firms collude (x=4500 if both firms adhere to the Cournot model (x=4668.75 if Firm X produces at the collusion output level and Firm Y produces at the Cournot output level (x=6225 if Firm Y produces at the collusion output level and Firm X produces at the Cournot output level The potential profit levels for Firm Y are as follows: (y=5062.5 if both firms collude (y=4500 if both firms adhere to the Cournot model (y=4668.25 if Firm Y produces at the collusion output level and Firm X produces at the Cournot output level (y=6225 if Firm X produces at the collusion output level and Firm Y produces at the Cournot output level
e.) Firm X’s strategy
Collude Cournot qx =22.5 qx = 30
(y (y Collude qy = 22.5
Firm Y’s
Strategy Cournot qy= 30
f.) Yes. Cournot for both firms.
g.) Yes. Cournot for both firms.
h.) Yes, since collusion would maximize both firms’ pay-off.
Section III: Game theoretic approach toward analyzing output behavior of rivals in a repeated game—25 points
Here are the answers
a.) Yes. Both firms compete.
b.) Yes. Both firms compete.
c.) (2=20. Yes, because 20>5.
d.) (2=65
e.) (2=100
f.) No. 65<100.
g.) The payoff is 110 for firm-2.
h.)
Firm-1 Collude entire 10 periods (2 (2 Collude 100 90 entire 10 periods
Firm-2 Collude 1st nine 95 periods and cheat in 10th period
i.) Yes. Both firms cooperate and collude for the first 9 periods then compete (cheat) the last period.
j.) Yes, since both firms would be better off colluding throughout the 10 period game.
k.) No. Firm 2’s profit falls by five for each period. (i.e. (2=100 if it cheats in period 10 and(2=95 if it cheats in period 9…and last, (2=65 if it cheats in period 1.)
_1321721635.unknown
Demand = 500 – 6Q
Average cost = 250 – Q
Where Q is measured in megawatts and prices and costs are measured in dollars.
How much energy would be sold and at what price if
So for Competitive Pricing (P=MC)
=
, which is
qx =22.5 and qy=22.5
(x
(x
$5062.5
$5062.5
$4668.75
$6225
$6225
$4668.75
$4500
$4500
Collude 1st nine periods and
cheat in 10th period
(1
(1
100
110
110
90
95