Question

3. Consider a price-taking firm that produces widgets with only labour input. Let the relation between widget output and labour input be the function f(n), where n is labour input. Denote the price of widgets by p and the wage rate (the price of labour) by w. "Price taking" means that w and p are beyond the firm's control. Profits are defined to be total revenue less total costs. Write profits as a function of n.p, w: enote the function by r(n, p u Treating p, w as constants, find the first and second dern atives of π with respect to n if f(n)- n1

Answer 1

Production function f(n)

Revenue=Price* output=p*f(n)

Cost=labor cost=wn

Profit=Revenue-Cost=pf(n)-wn

π(n,p,w)=pn^(1/2)-wn

First order condition will be

dπ(n,p,w)/dn=0.5p/n^(0.5)-w

Second order condition will be

d2π/dn2=-0.25p/n^(1.5)