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)$c=K0\times (v+w\times q^\frac{-a}{b^2})$

derivative function

$c=v+w\times q^\frac{-a}{b^2}$

the marginal cost of the firm

(ii) supply volume will be determined by the point of intersection of the price line with the marginal cost curve:

$p=v+w\times q^\frac{-a}{b^2}$

(iii) $QS=c+d\times p$

$QS=200\times (v+w\times q^\frac{-a}{b^2})+d\times p$