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Competitive firm with the profit function

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Reference no: EM131325810

Please show the steps on how it is solved.

Question: Consider a competitive firm with the following profit function

Π = R-C = PQ-wL-rK

where P = Price of the output

Q = Output

L = Labor input

K = Capital input

w = wage rate for labor input

r = rental rate for capital input

and Q(K,L) = 16K^1/4 L^1/4

(a) Find the input quantities K*and L*that satisfy the first order conditions for the profit maximization. Assume the parameter values P = 4, w = 1, and r = 1.

(b) Compute the profit maximizing output Q*.

(c) Compute the maximum profit Π*.

(d) If the wage rate w changes to w = 2, determine the new L**.

(e) If the rental rate r changes to r = 2, determine the new L**.

(f) If the output price P changes to P = 16, determine the new L**.Hint: All other parameters remain as in the original case in last three parts.

(g) Also compute the profit maximizing output Q** and the maximum profit in each case Π** in each of the last three parts, i.e., (d)-(f).

Reference no: EM131325810

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