A firm in a competitive market has the following cost functi

A firm in a competitive market has the following cost function: C(q, beta) = q^beta where beta > 1. Assume that the firm sells its product at a price p. Find q (p.beta) and the indirect profit function Pi (p, beta). What is the economic interpretation of this sign? Find Determine its sign. What is the economic interpretation of this sign? Find Determine its sign. Find Determine its sign. What is the economic interpretation of this sign?

Solution

(a) p = bq^b-1

q* = (p/b)^1/(b-1)

Profit* = p{(p/b)^1/(b-1)} - {(p/b)^1/(b-1)}^b

(b) dq*/dp = 1/b^1/(b-1)[{1/(b-1)}p^b/(b-1)]

(c) dq*/db = - p^1/(b-1)[{1/b^(b-1)}{1/b^b/(b-1)}]

(d) d(profit*)/db = [[{b/(b-1)}p^(b-1)]/b^1/(b-1)] - [{b(b-1)p^1/(b-1)}/b^b/(b-1)]