Consider a water heater manufacturing company. The number of water heaters manufactured per day, q, is a function of the number of workers per day, L, and the number of square feet of sheet metal per day, S. Specifically, its CES production function is q = (L^-2 + K^-2/40)^-0.5. The hourly wage rate is $20 and the price of per square foot of sheet metal is 50c.

a. What is the marginal productivity of labor? What is the marginal productivity of capital? b. What is the formula needed to draw the expansion path? Draw the expansion path.

c. Derive the long run cost function.

d. Suppose the price of sheet metal decreases to 25C. Draw the new expansion path. Discuss the magnitude of the shift in the expansion path.