Written Problems:

Monopolistic Competition

1. Suppose a firm operates in a monopolistically competitive market. Suppose the demand for their product is given by d = q = 180 - 4P + 2A where A is the amount of money spent on advertising.  Also suppose the firm's total cost function is given by TC (q) = 2q² + 20 + A.

a. What type of costs are advertising costs for the firm.

b. Suppose the firm does not advertise, what level of output should they produce to maximize profits?

c. Suppose now that the firm adds $18 in advertising.  How much output should they produce to maximize their profits?

d. How are the profits different when they do not advertise and when they do advertise?  What do you suggest they do?

e. Show graphically the profit and output choices before and after the advertising. Fully label and explain your graph.

2. When would it not be beneficial for a firm to advertise in the monopolistically competitive market if their objective is to maximize profits?

a. What are some typical advertising outlets for firms?

b. How have the advertising outlets changed over the past several years for firms?

c. How do advertising outlets different across products and demographics?

Oligopoly:

3. Consider an oligopoly market with two firms. Now suppose two firms compete by each setting output simultaneously treating the other's output as given.Firm 1's total cost is 2q₁²  and firm 2's cost is given by 2q₂².

a. Suppose market demand is given by Q = 30 - (1/2)P find the profit maximizing output for both firms when they firms choose output simultaneously treating the other's output level as given.

b. What will the price of the product be?

c. Find the profit for each firm.

4. Consider an oligopoly market with two firms that compete by choosing output at the same time.  This time they have different costs functions.  Let the market demand be given by Q = 25 -(1/2)P.  And the cost function of Firm 1 is given by TC(q₁) = 10 + 2q₁ and the cost function of Firm 2 is given by TC(q₂) = 12 + 8q₂.

a. Which firm's total cost of production is higher?

b. Which firm's marginal cost of a specific level of production is higher?

c. Solve for each firm's profit maximizing level of output.

d. Solve for the price of the output in the market.

e. Solve for each firm's profit.

f. How are each firm's output levels and profits related to their relative costs?

5. Now consider an oligopoly market in which two firms set the price of their product simultaneously, treating the other firm's price as given.

a. If both firms sell identical products, and both firms have identical cost functions, what will the price of the product be?  Explain why this will be the case.

b. What will happen to the price of the product if Firm 1's costs are higher than Firm 2's costs?

c. Suppose the products are now differentiated.  Firm 1 faces the following demand curve q₁ = 120 - 4P₁ + 2P₂.  Firm 1's cost function is given by 10q₁ .  Firm 2 faces the following demand curve q₁ = 200 - 4P₂ + 2P₁.  Firm 2 also has a cost function given by 20q₂.  What will the prices of the products be? 

d. How much of the product will be produced by each firm?

e. What is each firm's profit?

6. Under an oligopoly market structure, suppose two firms set their output to maximize profit, however, Firm 1 sets its output first.

a. Suppose market demand is given by P = 30 - (1/3)Q. Firm 1 has a cost function given by 2q₁ and firm 2 has a cost function given by 2q₂.  How much of the product does each of the firms produce?

b. Find both firms' profit.

c. Which firm is better off?

Consider the firm that operates in a monopolistically competitive firm.

a. Explain the shape of each firm's demand curve.

b. Explain the long run outcome for each firm in this market.  Use a graph to support your answer.

c. Given the "total welfare" definition of efficiency, how does the efficiency in a monopolistically competitive market compare to perfectly competitive and monopoly?

Give a real world example of when "total welfare" does not completely measure consumer well-being since consumers in this market are better off when the product is sold in a monopolistically competitive market compared to a perfectly competitive