Question

1. The total cost of producing pizzas for the typical firm in a local town is given by: C(q) 2q+2q2 Thus, marginal cost is MC 2+4g a) Show that the competitive supply behavior of the typical pizza firm is given by: q P/4-1/2. b) If there are 100 firms in the industry each acting as a perfect competitor, show that the market supply curve is, in inverse form, given by: P-2+ Q/25

Answer 1

We see that the total cost of producing pizzas for the typical firm in a local town is given by: C(q) =2q+2q2. In turn, marginal cost is given by: MC = 2 + 4q.

a. Show that the competitive supply behavior of the typical pizza firm is described by: q = P − 1 .
We know that supply curve is the rising portion of MC. Here MC = P = 2 + 4q. Hence q = (P - 2)/4 or q = P/4 - 1/2. This is the supply function by one firm.

b. If there are 100 firms in the industry, each acting as a perfect competitor, show that the market supply curve is, in inverse form, given by: P = 2 + Q/25.

For 100 firms each producing q = P/4 - 1/2, we have Q = 100q = 100*P/4 - 100*1/2

This gives Q = 25P - 50

25P = 50 - Q

P = 2 - Q/25

This is the market supply.