Question

In: Economics

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]1/3 if L≥3...

The technology available allows to produce a good according to the production function F(L,K)=[(L-3)K]^1/3 if L≥3 and K≥0, and F(L,K)=0 if L<3. The market demand for this good is D(p)=90/p. The prices of labor and capital are w=1 and r=9, respectively.

A. (12 points) Describe the cost minimization problem of a firm with this technology, and calculate its conditional factor demands. Also, calculate the firm's total, average and marginal cost functions.

B. (10 points) Calculate la supply of a competitive firm. Calculate also the market supply and the short run competitive equilibrium assuming that there are 6 firms in the market with this technology.

C. (6 points) Calculate price, total output and number of firms in the long run competitive equilibrium.

Expert Solution

Part (A)

substituting in the production function

Part (B)

marginal cost curve is the short run supply curve for the firm

short run equilibrium at point where market demand equals market supply

Part (C)

at long run equilibrium, each firm operates at efficient scale where marginal cost equals average cost

therefore at long run equilibrium 10 firms would be operating in the market

Rahul Sunny answered 2 years ago

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