Question

2. Assume the production function is y 5-30, and the price of r is w 1 (a) Derive the firm's total cost curve C(y), average cost curve AC(y), and marginal cost curve MC(y) (b) Assume that p> min AC(y), derive the firm's supply curve y(w,p)?

Answer 1

a. The production function is:
$\dpi{80} \fn_phv \small y=5x^{\frac13}-30$
Computing the value of x:
$\dpi{80} \fn_phv \small x=(y+30)^3$
The firm's cost function is:
$\dpi{80} \fn_phv \small Cost=wx=x=(y+30)^3$
Average and marginal costs are:
$\dpi{80} \fn_phv \small AC=\frac{(y+30)^3}{y},MC=3(y+30)^2$

b. The firm sets its marginal cost equal to the market price to determine its supply:
$\dpi{80} \fn_phv \small MC=3(y+30)^2=p\rightarrow y=\sqrt{\frac{p}{3}}-30$