Question

Reference the following information about the market demand function for questions 1 to 15. These questions are on different types of market structures – monopoly, perfect competition, Cournot oligopoly market, and the Stackelberg oligopoly market.

The market demand function is given the following equation: P = 1600 – Q where Q is the industry’s output level.

Suppose initially this market is served by a single firm. Let the total cost function of this firm be given the function C(Q) = 80Q. The firm’s marginal cost of production (MC) is equal to the firm’s average cost (AC): MC = AC = 80.

1) What is the output level produced by the profit-maximizing firm in this industry?

2) What will be the market price charged by the monopolist at the profit-maximizing level of output?

3) What will be the profit earned by the monopolist at the profit-maximizing level of output?

4) What would be the industry output level if this was a perfectly competitive industry instead?

5) Now that you have calculated the monopoly equilibrium output level and the perfectly competitive industry output, can you calculate the numerical value of the inefficiency loss (deadweight loss) generated in the economy if the market is served by the monopolist?

6) Can you calculate the consumer surplus generated in the monopoly market?

7) Now suppose two firms supply this market instead of one firm. Thus, Q = Q1 + Q2 where Q1 is output produced by firm 1 and Q2 is output produced by firm 2.

What are the levels of equilibrium output produced by firm 1 and firm 2 in the Cournot model equilibrium?

The right-hand side (RHS) of the marginal profit function of firm 1:   1520 - 2Q1 - Q2

The right-hand side (RHS) of the marginal profit function of firm 2: 1520 - Q1 - 2Q2

8) What will the total industry output produced when firms engage in Cournot market competition?

9) What will be the equilibrium market price in the Cournot model?

10) What will be the profit earned by each of the symmetric firms in the Cournot market equilibrium?

11) Now suppose the two firms engage in the Stackelberg market competition instead. Assume firm 1 is the leader (first-mover) and firm 2 is the follower firm (second-mover).

What will be the equilibrium output level produced by the Stackelberg leader (first-mover) firm?

The right-hand side (R.H.S.) of the Stackelberg leader's marginal profit function is 760 - Q1

12) What will be the equilibrium output produced by the Stackelberg follower (second – mover) firm?

13) What will be the market price in this Stackelberg market?

14)Can you calculate the profit earned by the Stackelberg leader and the Stackelberg follower?

15) Can you identify the results we learned from solving this problem on market structure?

Answer 1

According to HomeworkLib policy, i will answer the first 4 subparts. Please post the question again, asking for the rest, Thanks.

1) To determine the output level produced by the single profit-maximizing firm

Revenue for the firm= PQ=(1600-Q)Q=1600Q-Q²

Costs for the firm= 80Q

So profits= 1520Q-Q²

For maximum profits, d(Profits)/dQ=0

1520=2Q

Q=760

2) Market price charged by the monopolist=P= 1600-Q=1600-760=840

3) Profit earned by the monopolist at the profit-maximizing level of output= Revenue-Costs=PQ-80Q=(1600-Q)Q-80Q=1520Q-Q²= 577,600 (Inserting Q=760)

4) For a perfectly-competitive industry, the Price will be equal to the Marginal cost.

1600-Q=80

Q=1600-80=1520

Therefore the industry output level will be Q=1520 in a perfectly competitive industry.

Hope it helps. Do ask for any clarifications required.