Question

On a market with monopolistic competition, a firm meets the demand QD = 400 – 4P. The firm’s marginal cost is given by MC = 40 + 2Q. 

A. Which quantity should the firm produce to maximize its profit? Which is the profit maximizing price on the market?

B. Draw a figure that shows the firm’s profit maximizing quantity and price.

C. What is the firm’s long-term profit?

D. Now instead assume the market is a duopoly, and that the total demand is given by QD = 1600 – 2P. The two firms on the market, Delta and Gamme, have identical cost functions TCD = TCG = 200 + 50Q. The firm’s respective boards have agreed to collaborate to maximize their collective profit. What is the profit of Delta and Gamma if the firms together agree on which quantity to produce?

Answer 1

Solution:

Demand curve: Qd = 400 - 4P

Marginal cost = 40 + 2Q

A) The profit for a monopolistically competitive firm is maximized where the marginal revenue (MR) equals the marginal cost (MC).

Total revenue, TR = P*Q

With demand curve: Q = 400 - 4P, our inverse demand curve becomes: P = 100 - 0.25Q

So, TR = (100 - 0.25Q)*Q = 100Q - 0.25Q²

So, marginal revenue = = 100 - 0.5Q

With the profit maximizing condition of MR = MC, we have

100 - 0.5Q = 40 + 2Q

Q = 60/2.5 = 24 units

Price at this quantity: P = 100 - 0.25*24 = $94

So, profit maximizing quantity is 24 units, sold at price of $94 per unit

B) Following is the required graph:

C) In the long term, due to positive profit earned in the short run, more firms enter the market. As more firms enter, with such increase in supply, prices go down, ultimately lowering the profits to 0 (just like under the perfect competition market structure). So, in long run, all firms under monopolistic competition earn normal profit, that is zero profit. This is one of the features of monopolistic competition.

D) If the market has only two firms, that is if the market structure is that of a duopoly, and both firms plan to collaborate, they will act as a monopoly in the market (and share the profit equally). We know that under monopoly, profit is maximized where the marginal cost equals marginal revenue (same as monopolistic competition, just that under monopoly, firms earn positive profit even in the long run). Let's denote the quantity produced by Delta firm by Q1, and quantity produced by Gamme firm by Q2, then

Total cost of merged firm = (200 + 50Q1) + (200 + 50Q2) = 400 + 50Qm ; where Qm is the total quantity produced by merged firm, so, Qm = Q1 + Q2

So, marginal cost = = 50

With market demand curve: Qd = 1600 - 2P, inverse demand curve: P = 800 - 0.5Qm

So, total revenue = P*Qm = 800Qm - 0.5Qm²

Marginal revenue, MR = = 800 - Qm

With MR = MC, we have

800 - Qm = 50

Qm = 750 units

And price at this quantity, P = 800 - 0.5*750 = $425

So, total profit of merged firm = P*Qm - (400 + 50Qm)

= 425*750 - (400 + 50*750) = $280,850

And individual profits by each firm: 280850/2 = $140,425