Two price setting firms have the same price and marginal revenue functions but face different cost functions. These functions are provided below.
P = 165 - 0.025Q
MR = 165 - 0.05Q
Firm 1: TC = 4,000 + 15Q
Firm 2: TC = 3,000 + 22Q
a. Assuming that both firms are profit-maximizers, compute the output that each firm should produce.
b. Compute the price that each firm should charge at their respective output levels you computed above.
c. Compute the economic profit or loss of each firm at their respective output levels.
d. Suppose these firms operate in monopolistically competitive market. What will happen to economic profit or loss in the long run? Please briefly explain your answer.
a. To determine the output that each firm should produce, we need to find the quantity where marginal revenue (MR) is equal to marginal cost (MC).
For Firm 1:
MR = 165 - 0.05Q
MC = d(TC)/dQ = 15
Setting MR = MC:
165 - 0.05Q = 15
Solving for Q1:
150 = 0.05Q1
Q1 = 3,000
Therefore, Firm 1 should produce an output of 3,000 units.
For Firm 2:
MR = 165 - 0.05Q
MC = d(TC)/dQ = 22
Setting MR = MC:
165 - 0.05Q = 22
Solving for Q2:
143 = 0.05Q2
Q2 = 2,860
Therefore, Firm 2 should produce an output of 2,860 units.
b. To compute the price that each firm should charge at their respective output levels, we can substitute the corresponding quantities into the price function.
For Firm 1:
P = 165 - 0.025Q1
P1 = 165 - 0.025(3,000)
P1 = 165 - 75
P1 = $90
Therefore, Firm 1 should charge a price of $90.
For Firm 2:
P = 165 - 0.025Q2
P2 = 165 - 0.025(2,860)
P2 = 165 - 71.5
P2 = $93.50
Therefore, Firm 2 should charge a price of $93.50.
c. To compute the economic profit or loss of each firm at their respective output levels, we need to subtract total cost (TC) from total revenue (TR).
For Firm 1:
TR1 = P1 * Q1
TR1 = $90 * 3,000
TR1 = $270,000
TC1 = 4,000 + 15Q1
TC1 = 4,000 + 15(3,000)
TC1 = 4,000 + 45,000
TC1 = $49,000
Economic Profit (or Loss) for Firm 1:
EP1 = TR1 - TC1
EP1 = $270,000 - $49,000
EP1 = $221,000
Therefore, Firm 1 has an economic profit of $221,000.
For Firm 2:
TR2 = P2 * Q2
TR2 = $93.50 * 2,860
TR2 ≈ $267,001
TC2 = 3,000 + 22Q2
TC2 = 3,000 + 22(2,860)
TC2 ≈ 3,000 + 62,920
TC2 ≈ $65,920
Economic Profit (or Loss) for Firm 2:
EP2 = TR2 - TC2
EP2 ≈ $267,001 - $65,920
EP2 ≈ $201,081
Therefore, Firm 2 has an economic profit of approximately $201,081.
d. In a monopolistically competitive market, firms have some degree of market power but face competition from similar products. In the long run, if firms are making economic profit, new firms will enter the market, increasing competition. This will lead to a decrease in demand and prices for individual firms.
As prices decrease, the economic profit for each firm will diminish. If firms are making losses, some firms may exit the market, reducing competition. This will lead to an increase in demand and prices for the remaining firms.
In the long run, economic profit or loss in a monopolistically competitive market tends to converge towards zero as firms adjust their output and prices to reach equilibrium. Therefore, if these two firms operate in a monopolistically competitive market, their economic profit or loss is likely to decrease or even reach zero in the long run.