production theory – economics

A firm produces using technology Y = min{√x1/2, √x2, √x3/4} based on three inputs.

1. (a)  What type of returns to scale does this technology exhibit?
2. (b)  Obtain the cost function. Discuss if your findings are consistent with (a)
3. (c)  The firm is the only producer in the industry with demand Q = 90−P/12. Find the optimal price and production of the firm if prices of inputs are given by w1 = 2,w2 = 4,w3 = 1. Compare the result with the competitive case.
4. (d)  Explain (in words) the different behaviour of the firm in the Long-Run vs the Short-Run if in the Short-Run x3is fixed at x3 = 10.

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