Homework 5-

1. Perfect competition:

A local microbrewery has total costs of production given by the equation TC=500+10q+5q2. This implies that the firm's marginal cost is given by the equation MC=10+10q (you do not need to be able to show this). The market demand for beer is given by the equation QD=105 - (1/2)*P.

a) Write the equations showing the brewery's average total cost and average variable cost and average fixed cost, each as a function of q. Show the firm's MC, ATC and AVC on one graph.

b) What is the breakeven price and breakeven quantity for this firm in the short run?

c) What is the shutdown price and shutdown quantity for this firm in the short run?

Short-run Equilibrium

d) If the market price of the output is $50, how many units will this firm produce?

e) Given a market price of $50, how many firms are in this market?

Long-run Equilibrium

f) Assuming the beer industry is perfectly competitive, what output would be produced by the firm in long-run equilibrium? What would be the long-run equilibrium price?

g) How many firms will be in the industry in long-run equilibrium?

2. Monopoly:

Suppose Charter Communications is a monopolist in providing cable television services to local consumers in Madison. The market demand curve faced by Charter Communications is P = -Q + 30, and Charter's cost is given by TC=Q²/2 + 20, and Charter Communication's marginal cost is given by MC=Q.

a) What is the equation for Marginal Revenue for this monopolist?

b) Draw the Demand curve, Marginal Revenue curve, and Marginal Cost curve for this monopolist in a graph.

c) What is the monopolist's profit-maximizing production quantity, QM? What price, PM , will the monopolist charge?

d) Compute the Consumer surplus, producer surplus and profits for the monopolist

Now, suppose there is a technological change for the monopolist and the result of this technological change is that the firm's cost curves change. Charter Communications total cost is now given by TC = 10Q, and its marginal cost is given by MC = 10.

e) What is the monopolist's profit-maximizing production quantity Q_M? What price, P_M, will the monopolist charge?

f) Suppose this market was a perfectly competitive market (i.e., the monopolist's demand curve is still the market demand curve, but now there are many firms providing cable television services for the market). Given the market is perfectly competitive, what would be the equilibrium price (P_pc) and quantity (Q_pc) in this competitive market? Assume that each firm's MC curve is given by MC = 10 for this question.

Now, let us compare the monopoly and perfect competition outcomes. Consider the last technology where the firm faces TC = 10Q and MC=10.

g) What is the difference between the consumer surplus in the monopoly case and the consumer surplus in the perfect competition case?

h) What is the difference between the producer surplus in the monopoly case and the producer surplus in the perfect competition case?

i) What is the dead weight loss caused by the monopolist?

3. Natural monopoly:

a) Suppose Madison Gas and Electric (MGE) is a natural monopoly in Madison for electricity. This firm faces a demand function P =20 -2Q and has a total cost function TC = 12+8Q. We can find this firm's marginal cost function by taking the first derivative of the total cost function with respect to Q. If you do not know how to do this or your calculus skills are rusty, then here is the firm's MC curve: MC = 8. On a graph illustrate the Demand curve, Average Total Cost curve, Marginal Cost Curve, and Marginal Revenue Curve for this firm.

b) The government decides to regulate this market using marginal cost pricing. That is, the firm is told to produce that level of output where MC is equal to P for the last unit produced. Calculate the minimum amount of subsidy that will be necessary in order to keep this monopolist in business.  

c) Suppose the government decides to use average cost pricing regulation. That is, the government tells the monopoly to produce that level of output where the firm earns zero economic profit. Identify in your graph the equilibrium price and quantity that corresponds to this type of regulation (don't compute the values, just mark what the Pac and Qac are in your graph). Is this price and output combination allocatively efficient?

4. Price discrimination:

A monopolist faces demand from two groups of consumers.

Demand from class 1 is given by: Q₁ = 20 - P

Demand from class 2 is given by: Q₂ = 22 - (1/2)P

A monopolist has costs given by: 

TC = 10 + 0.5Q²

MC = Q

The firm is able to price discriminate between the two markets.

a) Which group of customers has the more elastic demand curve?

b) Which group do you expect will pay a higher price under 3rd degree price discrimination?

c) What is the equation for Marginal Revenue for each class of consumers?

d) What quantities will the monopolist sell in the two markets?

e) What price will the monopolist charge in each market? Are the optimal prices in each class consistent with your prediction in part (b)?

f) Which class generates the highest revenue for the monopolist?

5. Game theory:

Now consider Julia and Peter. Peter likes Julia, but Julia doesn't like Peter that much, only a little. Each knows this, and neither wants to call the other before deciding what to do this weekend: stay at their respective homes or go to the econ party.

Here is the payoff matrix providing a measure of the benefits that Julia and Peter receive depending upon whether they stay home or go to the party. In each cell the first number refers to Julia's benefit while the second number refers to Peter's benefit.  

a)  Is there any strictly dominant strategy for Julia? Explain your answer.

b) Is there any strictly dominant strategy for Peter? Explain your answer.

c) What is the equilibrium you can predict from this game?

6. Short Essay: I can't wait for Econ 101 to end! (Any answer gets full credit.) Take a breath and write a short essay about 1) what you found interesting in econ 101; 2) what you found challenging in econ 101: or 3) what surprised you most about econ 101. If you write about grades and/or exams make sure your essay is more than just a complaint that there are grades or that the exams are difficult (or, fail to measure what you know-this essay topic needs to fully explicate what you know and why the exams failed to measure it). Use standard English (sentences need a subject, a verb, punctuation and capitalization) and make sure you write an essay and not just talking points! Have a good time with this one. (Suggested length-one good paragraph: does not need to be a long discussion!)