For a production function q= f(K, L) = K^1/3 L^1/3 and factor prices w=8 and r=1, answer the following questions: (a) Explain what returns to scale mean and its implication for the cost function. What returns to scale does this production function exhibit? (b) optimal mix and equation of the expansion path. What does it show? (c) Minimized cost function for the technology. (d) Why are the short-run cost curves different from the long-run cost curves? Your answer must include the terms expansion path and optimal input mix.

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