Question

The short-run total cost function of a firm that employs labour (L) and fixed capital

is given by c = vKo + wq^1/B × Ko^ -a/B

Where w is the cost of the labour

and v is the cost of capital

(I) Derived the marginal cost of the firm

ii. Assuming that the firm is a price taking one that sells its output at p per unit, derive the short-run supply function of the firm

iii. If there are 200 firms in the industry with similar cost conditions, compute the total market supply.

Answer 1

(i)c = vKo + wq ^ 1 / B × Ko ^ -a / B  

c=Ko(v+wq^-a/b²)

marginal cost of the firm -  derivative function с:

c'=(Ko(v+wq^-a/b2))'=v+wq^-a/b2

(ii)p=v+wq^-a/b2

the marginal cost curve of a competitive firm (or rather, part of it) is at the same time a firm's short-term supply curve

(iii) $S=200\times p\times K=200\times K\times(v+wq^-a/b2)$

p - price

K - quantity of products produced