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1. Suppose that two identical firms produce widgets and they are the only firms in the market. The cost functions of the two firms are given by C1(Q1) = 60Q1 and C2(Q2) = 60Q2. The demand function of the market is given by the function P = 300 - Q where Q=Q1+Q2.

a. Find the Cournot equilibrium output levels and profit for each firm.

b. Suppose the two firms form a Cartel and to maximize joint profit. Calculate how many widgets each firm will produce and their output levels.

c. Suppose firm 1 is the only firm in the market. Determine the output and price that firm 1 will produce and charge. Also, determine the profit level.

d. Suppose firm 2 takes its output decision after firm1 has announced its output decision. Calculate the output levels and profit levels of the two firms. Comparing the output and profit of part (a), which firm is better off and which firm is worse off ? Explain your answer.

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Retselisitsoe Pokothoane
Retselisitsoe PokothoaneLv10
28 Sep 2019

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Related questions

Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q1 and q2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q1 and q2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reaction functions to find q1 and q2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.

Given: Market Demand Curve: Q=100-2P
Industry/ Firm Cost Function: TC=2q
Assumptions:
1. These are only 2 firms in the industry.
2. If the firm are competitive (or seemingly competitive), theyequally share the industry output.
3. If the firms collude, they exercise equal market power (theyequally share the industry output)
Solve for the profit maximizing industry and firm output, price andfirm profits under:
a. Quasi-competitive market
b. Cartel Model
c. Cournot Model

Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. Firm 1 is the leader and firm 2 is the follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

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