Reference no: EM131019240
Homework 5-
Monopoly:
1. Suppose there is an industry that is served by a single firm: this is a monopoly. Furthermore, suppose that this firm's total cost is given by the equation TC = 100 + Q2 + Q where Q is the quantity of output produced by the firm. The firm's MC equation based upon its TC equation is MC = 2Q + 1. You also know that the market demand for this product is given by the equation P = 1000 - 2Q where Q is the market quantity.
a. This monopolist is a single price monopolist. What is the monopolist's profit maximizing quantity and price in this market given this information? In your answer make sure you identify what the firm's marginal revenue (MR) curve is.
b. Given your answer in part (a) calculate the firm's total revenue, total cost and profit at this profit maximizing price and quantity. Is this a short-run or long-run equilibrium? Explain your answer.
c. Given your answer in part (b), what do you anticipate will happen in this market in the long-run?
Strategic interactions of Duopolists:
2. Ford and Lexus are competing in the market for SUV's. For simplicity assume that there are no other rivals in the SUV market. The companies are planning to introduce a new model in this fall. They need to decide whether to invest lots of money in advertisements or not. The profits of the two firms are interdependent. The following table describes the situation. Each row represents an action taken by Ford, and each column an action taken by Lexus. The first (second) number in parenthesis means profits for Ford (profits for Lexus respectively).
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Lexus
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Aggressive Advertisement
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Normal Advertisement
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Ford
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Aggressive Advertisement
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(7, 7)
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(12,5)
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Normal Advertisement
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(5,12)
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(10,10)
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a. Find the dominant strategy of each firm if the two firms do not cooperate with one another.
b. Does this dominant strategy represent a Prisoner's Dilemma? Will the firms be able to achieve the outcome (10, 10)? Explain your answer.
c. Suppose that both firms make an agreement in advance to use normal advertisement so that both firms get 10 in profits. Why might the agreement not work?
Oligopoly:
3. There are only two companies producing baseball caps in Milwaukee, Mycap and Yourcap. The demand function for baseball caps in this market is P=10-Q. The marginal cost is constant and can be expressed as MC(=ATC) is 2.
a. The companies try to coordinate their actions and set quantity and price like a single monopolist. Once they set this profit maximizing price and quantity, the plan is to split the resulting profit equally. What is the profit of each company if they both adhere to the plan?
b. One of the companies, Yourcap, deviates from the plan, and sets its price equal to $4. What is the profit of Yourcap? What is the profit of Mycap? (Hint: No one wants to buy overpriced goods!)
c. Both companies set price equal to $4, and then split profit equally. What is each company's profit?
d. Now the firms have two options: to charge the joint monopoly price as found in part (a), or to set their price equal to $4. Fill in a payoff matrix that represents these choices (use the template provided below).
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Mycap
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Yourcap
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Monopoly
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P= $4
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Monopoly
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P= $4
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e. What is the dominant strategy for Mycap?
f. What is the dominant strategy for Yourcap?
g. What is the outcome of this game?
h. Explain the intuition for your answer in part (g).
Monopolistic competition:
4. Janet lives in Aberdeen and produces EcoIce, a brand of premium low-fat ice cream. The ice cream industry in Aberdeen is monopolistically competitive. In order to retain her market position and differentiate EcoIce from other products, Janet keeps introducing two new natural flavors on the second Friday of each month and offering innovative packaging. The chart below describes the demand for EcoIce at various prices. The marginal cost of producing one scoop of ice cream is $0.40, and there are no fixed costs.
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Price
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Quantity demanded
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| $2.00 |
0
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$1.60
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2
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$1.20
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4
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$0.80
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6
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$0.40
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8
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$0.00
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10
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a) How many scoops of ice cream should Janet produce in the short run to maximize profits? What price should she charge? (Hint, this problem will be easiest if you calculate an algebraic expression for demand, given the information in the table).
b) Calculate her economic profits in the short run.
c) What would be the long run price and quantity if instead this were a perfectly competitive market?
Since economic profits are positive, new firms are attracted to the industry. In particular, a new firm that makes ice cream from the Colorado Rocky Mountains' water, ColorIce, enters the industry and the demand for Janet's ice cream decreases by 2 units at each price.
d) Derive a new demand equation for EcoIce.
e) According to the economic theory, what should happen to the price of EcoIce after ColorIce entered the market?
f) Find Janet's new profit maximizing quantity, price, and profits.
g) Illustrate your solution to parts (a) and (f) with a graph.
Examples of Externalities:
5. For each of the following examples, state whether there are externalities (positive, negative, or none), and then explain your answer.
a. Listening to a football game with a low quality earphone (not soundproof and quite noisy) at the same time that you are attending a class lecture.
b. Asking good questions in class.
c. Smoking in your own bedroom (suppose there is no smoke sensor in your room).
d. The laboratory dumps toxic chemicals from its research project into Lake Mendota.
e. The fraternity next to your dorm plays loud music, keeping you from studying.
An Externality Problem:
6. Watertown is a small town surrounded by many small lakes. Winters in Watertown are very cold but (for some unknown reason) people love to ice-fish on the lakes around Watertown. People travel from nearby cities to ice-fish in the winter. As a result of this influx of people too many fish are caught in the Watertown lakes. Fishing experts estimate that the external costs of this over fishing is equal to $10 per fish caught. Suppose that the marginal private benefit (MPB) of fishing is given by the demand curve P = 250 - Q and that the marginal private cost (MPC) of the fishing is given by the curve MPC = Q.
a. Assume that the optimal output is produced at where P=MPC. Find the market equilibrium price and quantity for ice-fishing.
b. Given your answer in part (a), what is the numerical value for the external cost from fishing?
c. Given your answer in part (a), and the fact that there is an external cost that the market is not internalizing, are too many or too few fish being caught in Watertown?
d. Now, suppose that there is a movement to consider the external costs of this fishing. Provide an equation that expresses the marginal social cost of fishing: this equation would be equal to the horizontal summation of the marginal private cost curve and the external cost of fishing.
e. What would the socially optimal amount of fishing be in Watertown if the external costs associated with this fishing were taken into account? To find the socially optimal amount of fishing in Watertown you will want to equate the Marginal Social Benefit to the Marginal Social Cost. In this example, the Marginal Social Benefit is equal to the Marginal Private Benefit and you have found the MSC in step (b) of this problem.
f. Given your answers in parts (a) through (e), what is the deadweight loss in the market for fishing in Watertown when the externality is not accounted for in the market?
g. What size excise tax would Watertown need to impose on the fishing market in order for the socially optimal amount of fish to be caught?
Basic Monopoly, First & Second Degree Price Discrimination:
7. Suppose you know the following about an industry that is a monopoly.
Market Demand: P = 200 - .5Q
Marginal Cost = 40
There are no fixed costs
a) What is the marginal revenue curve for this monopoly?
b) Find the profit maximizing quantity for this monopolist if it charges a single price for the good.
c) Find the profit maximizing price for this monopolist if it charges a single price for the good.
d) What do profits equal for this single price monopolist?
e) What is the value of consumer surplus for this single price monopolist?
f) What is the value of deadweight loss for this single price monopolist? (Hint: you will want to determine the efficient quantity that should have been produced by equating marginal cost to demand first).
Suppose now that this monopoly can perfectly price discriminate (1st degree price discrimination).
g) What is the profit maximizing level of output for this monopolist if they practice first degree price discrimination?
h) When this firm practices first degree price discrimination, what is the value of its profits?
i) What is the value of consumer surplus in this market when the firm practices first degree price discrimination?
j) What is the value of deadweight loss generated in this market when the firm practices first degree price discrimination?
Suppose now that the monopolist cannot perfectly price discriminate, and instead decides to be a 2nd degree price discriminator.
The monopolist decides to sell some units of the good at $120, and other units of the good at $80.
k) How many units will the monopolist sell at $120?
l) How many additional units does the monopolist sell at $80?
m) Calculate profits for this monopolist.
n) Calculate consumer surplus in this industry.
o) Calculate deadweight loss in this industry when this firm practices second degree price discrimination as described in this problem.
Suppose now that the monopolist decides to sell additional units at $40.
p) How many additional units does the monopolist sell at $40?
q) Calculate consumer surplus in this industry now that the monopolist is selling the good at these three different prices.
r) Calculate deadweight loss in this industry now that the monopolist is selling the good at these three different prices.
Public Goods:
8. Suppose that there are two people, Joe and Mary, who live in a town located on a rocky seashore. Both of the individuals who live in this town are commercial fishermen and they have both run aground on dark and stormy nights. They realize that their community would benefit greatly if there was a lighthouse in their town. Joe's demand for lighthouses is given by the equation P = 10 - L where P is the price of a lighthouse and L is the quantity of lighthouses. Mary's demand for lighthouses is given by the equation P = 5 - .5L. The marginal cost of providing a lighthouse is equal to $3.
a. Are lighthouses in this community nonrival? Nonrival means that more than one person can enjoy the consumption benefits of a good without diminishing the consumption benefits that are available to other people. Is this true for lighthouses? Explain your answer.
b. Are lighthouses in this community non-exclusive? Nonexclusive means that once the good is provided, it is possible for people to enjoy and consume the good even if they did not pay for it. Is this true for lighthouses? Explain your answer.
c. Are lighthouses a public good? A public good is both nonrival and nonexcludable. Does a lighthouse meet both of these criteria? Explain your answer.
d. What is the equation(s) for the market demand for lighthouses? To find the market demand for lighthouses you need to vertically sum the individual demand curves. We vertically sum the demand curves because the good is nonrival: my consumption of the good does not diminish your ability to consume the good. So, the question becomes one of asking how much each of us is willing to contribute towards providing the public good. To vertically sum the demand curves, hold quantity constant and ask how much each individual will pay for that amount of the good. So, for example when Q = 1, Joe is willing to pay $9 while Mary is willing to pay $4.50. Together they are willing to pay $13.50 for 1 lighthouse. To find another point of this market demand for lighthouses consider a different quantity of the good. [Careful here: it is possible that you could get a kink in the demand curve, although in this example we have constructed an easy situation with no kink!]
e. What is the socially optimal number of lighthouses? The socially optimal number of lighthouses will occur where the market demand curve (found by vertically summing the individual demand curves since the good is nonrival) is equal to the MC curve.
f. If the socially optimal number of lighthouses is provided, how much will Joe pay per lighthouse and how much will Mary pay per lighthouse?