Question

Suppose that there are two types of firms in a perfectly competitive market. Firms

of type A have costs given by CA(q) = 30q2 + 10q. Firms of type B have costs given by CB(q) = 50q2 + 10.

( dCA

dq = 60q + 10 and dCB

dq = 100q). There are 60 firms of type A and 100 firms of type B.

(A). [5 Points] Derive the individual firm supply functions for each type of firm qs

A(p) and qs

B(p). What

is the range of prices in which some firms produce but others do not? Are there prices at which no firms

produce? Why?

Answer 1

(a)

(a)

Type A firm

$CA(q) = 30q^{2 }+ 10q$

$MC=60q + 10$

$P=MC$

$P=60q + 10$

$q=\frac{P−10}{60}$

There are 60 firms. Supplyfunction will be

$Q=60q=60\frac{(P−10)}{60}$

$Qs=p-10$

Type B firm

$CB(q) = 50q^{2 }+ 10$

$MC=100q$

P=MC

$P=100q$

$P=\frac{P}{100}$

There are 100 firms. Supply function will be

$Q=100\frac{p}{100}$

$Qs=p$

(b)for firm A

P=60q + 10

For firm b P=100q

There are prices at which no firms

produce because the market exists a large number of buyers and sellers having homogeneous products.