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This problem is meant to teach you with a concrete example how to derive the short-run and long-run cost functions

and supply curves for a firm in a competitive market, using the two-step approach.

Suppose the firm in question uses two factors, capital (K) and labor (L) for production, and its production function is given by Q=K1/2L1/2. The rent for capital is r, the wage for labor is w, and the market price of its product is p.

1. a) Assume that the firm's capital stock K is fixed at K=1 in the short run. Derive the firm's short-run cost function.
2. b) What is the firm's fixed cost? What are the total variable cost, average variable cost, and marginal cost of producing Q units of output?
3. c) What is the firm's profit πs of producing Q units of output? What is the firm's short-run supply curve, i.e., the optimal output as a function of output price, Qs*(p)?

Now let's turn to the firm's long run decision, where both capital and labor inputs are variable. We first

When the capital stock of the firm is fixed at 1, we need to simply plug K=1 into the... View the full answer

Date:
Actoline
Page No:
he are given Q= *1 / 2 1/ 2
- visit ne at www actolineproducts.com-
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