A water heater manufacturer produces q water heaters per day, q, using L workers and S square feet of sheet metal per day, using a constant elasticity of substitution production function, q = (L-2 + S-2/40)-0.5. The hourly wage rate is $20, and the price per square foot of sheet metal is 50¢.
a. What is the marginal product of labor? What is the marginal product of capital?
b. What is the expansion path equation? Draw the expansion path.
c. Derive the long-run cost function.
d. Suppose the price of sheet metal decreases to 25¢. Draw the new expansion path. Discuss the magnitude of the shift in the expansion path due to this price decrease?