What are the Pareto-ecient outcomes?

Instructions: Remember that assignments are to be solved in teams of two students or individually. Assignments with teams of more than two (2) will NOT be accepted. Please make sure that your answers are well-justified and are easy to read. All graphs, if any, should be properly labeled and well drawn.

1 Perfect Competition

1. A business firm is operating in a perfectly competitive industry, with the following cost function,

CT (y) = 40 + 10y + 0.1y2

where y is the number of units produced per day. The current market price is $20 and the marginal cost function is MC(y) = 10 + 0.2y.

a. How many units should the business firm produce in order to maximize its profits?

b. What is the maximum profit per day?

c. Draw a graph with the average cost curve and the marginal cost curve. Show in the graph the maximum profit per day obtained in (b).

2. Draw a short-run diagram showing a U-shaped average total cost curve, a U- shaped average variable cost curve, and a “swoosh” shaped marginal cost curve. On it, indicate the range of output and the range of price for which the following descriptions would be true.

a. The firm shuts down immediately.

b. The firm operates in the short run despite sustaining a loss.

c. The firm operates while making a profit.

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2 Monopoly

1. Using the following total revenue schedule of Cool Watches, Inc., a monopoly producer of sports watches, calculate the answers to the following questions,

a. The demand schedule (use a table).

b. The marginal revenue schedule (use a table).

c. Find the inverse demand linear function.

d. Find the marginal revenue function. (Hint: find the marginal revenue using the same procedure followed in class where we worked with a linear function as an example)

2. A monopolist faces the following market demand, y = 30�p and has a cost function

C(y) = y2

2 , so the marginal cost function is MC(y) = y,

a. Find the quantity (y), and the price (p) that would maximize the monop- olist’s profits (Hint: find the marginal revenue using the same procedure followed in class where we worked with a linear function as an example).

b. Suppose the government imposes a regulation to the monopolist where he can only charge a maximum price of $18 for each unit. How much would the monopolist produce in this case?

c. Illustrate points (a) and (b) with a graph. Make sure to show marginal cost, marginal revenue, and profits.

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3 Game Theory

1. Consider the interaction described by the game payo↵ matrix:

a. What are the Pareto-e�cient outcomes? (Briefly explain your reasoning)

b. Are there any dominant strategies? If so, which?

c. Represent the game in extensive-form.

d. Is there any Nash-Equilibrium?

2. Consider the interaction described by the game payo↵ matrix:

a. Is there a predicted outcome for this game? If so, which? (Briefly explain your reasoning)

b. What are the Pareto-e�cient outcomes? (Briefly explain your reasoning)

c. Are there any dominant strategies? If so, which?

d. What about Nash Equilibrium? Justify your answer