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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

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


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