1. Suppose a single firm has production function q = F(K, L) = 210.510.5. (a) If K = 4, derive the short-run production function, which depicts the relationship between the amount of labor hired and the amount of output produced. (b) Graph the short-run production function. You need not be too precise, as long as the shape is correct. (c) Using your answer from part (a), rearrange to obtain L in terms of q, i.e. rearrange so that L is on the left-hand side, not q. (d) The firm's short-run cost function is C(K, L) = rK + wL. Simplify this cost function by substi tuting in the wage rate, w = 8, the rental rate of capital, r = 8, and the fixed quantity of capital, K = 4. Your cost function should only have one variable left, L. (e) Now substitute in your answer from (c) for L. Your cost function will now be a function of q. Therefore, it will tell us the firm's (short-run) cost of producing any level of output, q. (f) What is the firm's fixed cost, and what is its variable cost? (g) What is the firm's marginal cost function. Hint: the marginal cost function is simply the derivative of the cost function, dq ' (h) Draw the firm's cost function and its marginal cost function (both in terms of q)