2. The Longheel Press produces memo pads in its local shop. The company can rent its equipment and hire workers at competitive rates. Equipment needed for this operation can be rented at $52 per hour, and labor can be hired at $12 per worker hour. The company has allocated $150,000 for the initial run of memo pads. The production function using available technology can be expressed as: Q=0.25K 0.25 0.75 where Q is memo pads (boxes per hour), K is capital input (units per hour), and L is labor input (units of worker time per hour). The marginal products of labor and capital are as follows: MPL = (0.75)(0.25)K 0.25-0.25 a. Construct the isocost equation. and MPK = (0.25)(0.25)K-0.750.75 b. Determine the appropriate input mix to get the greatest output for an outlay of $150,000 for a production run of memo pads. Also, compute output. c. Explain what would happen in the short-run (keeping capital fixed) to the appropriate input mix if production were changed to 1,500 units per hour. Would the input combination be different in the long-run? If so, how would it change? Explain.

The Mini-Case "Economies of Scale at Google describes economies of scale for Google Cloud Storage. The cost function for this service is well-approximated by K C(q)-F+cq where C is total cost, F is fixed cost, c is a constant and q is output. What is marginal cost for this cost function? What are the average fixed cost, average variable cost, and average cost? Over what range of output does Google have economies of scale? The marginal cost function (MC) is The average fixed cost function (AFC) is AFC- The average variable cost function (AVC) is AVC- MC-C The average cost function (AC) is AC- (Property format your expressions using the tools in the palette. Hover over tools to see keyboard shortcuts. Eg, a fraction can be created with the character) Time Remaining: 02.09.09

Suppose a firm has the following production function  Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total cost function TC = wL + rK The rental cost of capital is 2 euros per hour and the labor wage is 4 euros per hour. Suppose also that in the short-run, the firm uses 8 machines in the production process. (a) Show that the firm’s short-run average cost (SRAC) is SRACK=8  = (16/Q)+ 4√?  (b) Draw the SRAC curve(c) By solving the first order conditions that the global minimum of production is 4(d) Show that the firm’s long-run average cost (LRAC) is 12. Hint: Start by obtaining the firm’s long-run expansion path(e) Draw both the SRAC and the LRAC and explain why the SRAC is always equal or above the LRAC.

4. Ikea Inc., a home remodeling business. The number of square feet they can remodel in a day is described by the Cobb-Douglas production function Q= F (L,K)= 4K5L0.5 where L is their number of workers and K is units of capital. The wage rate is $5 a day, and a unit of capital costs $20 a day. What is their minimum cost input combination for remodeling (Q=200) 200 square feet a day? What is the total minimum cost level? (15p)