Managerial Economics 12th Edition by Christopher Thomas,Charles Maurice

Exercise 4

Let the long-run total cost function be LTC = (1/12) Qw 0.5 r 0.5.
a. Demonstrate that a doubling of input prices causes LTC to double.
b. Find the elasticity of total cost. This long-run total cost function is characterized ________ by scale.
c. Let w = $16 and r = $25, and find LMC and LAC. Graph the LMC and LAC curves. Are these curves consistent with part b?
d. Is your answer to part b consistent with your answer to part d in Mathematical Exercise 4 in Chapter 9?
Exercise 4 in Chapter 9 for Reference:
For the production function in exercise 3:
a. Find the long-run expansion path.
b. Derive the efficient input-usage functions for labor and capital.
c. Derive the long-run cost functions: LTC, LAC , and LMC.
d. Graph the LAC and LMC curves.
e. What level of output is the minimum efficient scale of production ( MES )?
Exercise 3 for Reference:
The production function for a firm is Q = 24 L.5 K.5. In the short run, the firm has a fixed amount of capital,
The price of labor is $10 per unit, and the price of capital is $20 per unit.
a. The short-run production function is Q = _________.
b. The marginal product of labor is MP L = _________. Show that the marginal product of labor diminishes for all levels of labor usage.
c. Write the equation for the short-run expansion path.
d. Derive the short-run TVC, TFC , and TC functions.
e. Derive SMC, AVC, ATC , and AFC.