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SHORT-RUN COSTS and OPTIMIZATION: Consider the following production function: Q = K1/3 L1/3. Let the price of output be P = $100 and factor prices w = $5 and r = $10.

a) Assume that K is fixed at 64. What are the short-run costs? C=wL + r(64)?. b) Plot cost versus output. Show that costs are accelerating. Why is this the case? (hint. What are the returns to scale?) c) What is the firm's optimization problem? d) What is the supply function for this firm? Eg, what is the relationship between market prices and the firm's optimal choice of output. Hint: look at MC = P. Confirm that higher P leads to higher Q. e) Graph the supply curve. Discuss its shape (eg why does the slope increase?).