Question

Two firms currently comprise the market for chicken sandwiches. One firm has been in the market for 50 years and has considerable market share. The other firm has been in the market for 25 years and is trying to erode the market share of the first firm. Below is the inverse demand function for the market. Each firm also faces marginal costs of $1.

P(Q) = $8 - 0.25Q

MC = $1

How much in profit will each firm earn? How much will the industry earn in profit Draw a supply and demand diagram for this market. How much is consumer and producer surplus in this market?

Answer 1

Since the other firm is trying to erode the market, it is a perfect competition in this case.

Under perfect competition, prices are set equal to the marginal cost of the good, that is, P = MC. This is because, as one firm try to capture the market by setting the price low, another firm sets the price even lower. This goes on, but firms can not set prices less than the marginal cost, or the firms will incur a loss in the market.

So, Equilibrium price will be $1, then equilibrium quantity would be P = 8 - 0.25Q, putting the value of P = 1, 1 = 8 - 0.25Q, such that, Q = 28, this is the equilibrium quantity in the market.

As no firm will achieve profit, profit = 0 for both firms. The industry as well will earn zero profit.

This is a supply and demand diagram for this market, here Blue line shows the demand while Red line shows the supply. On the x-axis, it is the number of chicken sandwiches and on the y-axis, it is the price of the chicken sandwich. Equilibrium is achieved at point (28,1).

There will be no producer surplus in the market. While consumer surplus is the area between the blue and red line till the equilibrium point. Since, it is a triangle, it's area would be, 0.5 * (8 - 1) * 28 = $98. This is the consumer surplus in this market.