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2. Suppose the production function of a firm is given by q=L 1/4 K 2/4 . The prices of labor and capital are given by

2. Suppose the production function of a firm is given by q=L^1/4K^2/4. The prices of labor and capital are given by w = $9 and r= $18, respectively.

a) Write down the firm cost minimization formally.

b) What returns to scale does the production function exhibit? Explain.

c) What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor?

d) What is the optimal capital to labor ratio? Show your work.

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