1,a) Prove that profit maximization implies cost minimization but not vice versa.b) Consider the...

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1,a) Prove that profit maximization implies cost minimization but not vice versa.b) Consider the problem of maximizing profit
= py – wl subject to the production function y = l^a, a?(0,1). Derive the profit function and confirm that Hotelling’s lemma hold. Explain what happens if a = 1.
2, Long run average costs rise as output increases if and only if the production function is homogeneous of degree p?(0,1). True or false? Explain your answer.

David · Accepted Answer

Answer 1) A) 
Suppose that a firm uses two inputs x1 and x2 input prices are p1 and p2 respectively. The firm 
production function Q = Q = f(x1, x2). The firm chooses quantities of its inputs, x1 and x2 
recognizing that output is determined through the production function Q = f(x1, x2). Thus, the 
profit maximization problem of the firm will be  
Π = p*f(x1, x2) – p1x1 – p2x2 
First order condition:
The above two condition states that a profit maximizing firm will choose its input so that,  
(I) The additional output that the firm get from additional unit of money spent on labour 
equals the reciprocal of market price.

1,a) Prove that profit maximization implies cost minimization but not vice versa.b) Consider the problem of maximizing profit = py – wl subject to the production function y = l^a, a?(0,1). Derive the...

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