1. Consider a firm's short-run production possibilities. Let q = LzKz, r and w denote, respectively, the prices of K (capital) and L (labor). Suppose K = 100 (fixed) and L is variable. a. Write down the expression for the short-run production function. b. What is the fixed cost (FC), variable cost (VC), average cost (AC) and, marginal cost (MC)? c. Let q* denote the level of output where average costs are the lowest level possible and minimized. Show that MC(q*) = AC(q*). And, when MC(q) AC(q), average costs increase as q increase. Provide some intuition for this result. d. Using the case in parts a and b of this problem, calculate q*(r,w, K = 100). Illustrate this in a figure where q is on the horizontal axis and AC(q) and MC(q) are on the vertical axis. e. Compute the marginal product of labor. In a sentence or two, provide some intuition for why MC = w/MPL