A competitive producer has a production function given by

q=f(k,L) = 8k^(¾)L^(¼)

Where k denotes the quantity of capital, and L denotes labor hours. The factor prices are v, and w.

1. Write down the producer’s cost minimization problem and find the contingent factor demands and cost function.

2. From now on assume that the factor prices are fixed at w = $16, and v = $.25. Suppose that, in the short run, the capital stock is fixed at k = $81. Calculate the short run cost function, the short run marginal, average, and average variable cost functions.

3. Plot the short run marginal, and average variable cost functions

4. Suppose now that, in the short run, the capital stock is fixed at k-bar. Calculate the short run cost function as a function of q and k-bar

5. On one diagram, plot the short run cost functions for k-bar= 16, 81, 256 and the long run cost function (for w=16 and v=.25). Show that the long run cost function envelopes the short run cost functions.