Mpl and Apl

HW 2
Managerial Economics, ECON 601

1. Consider the following short-run production function (where L = variable input, Q = output): Q = 6L2 – 0.4L3
|a. |Determine the marginal product function (MPL). (5 points) |
|b. |Determine the average product function (APL). (5 points) |
|c. |Find the value of L that maximizes Q. (5 points) |

a. MPL=△Q/△L=12L-1.2L2 b. APL= 6L-0.4L2 c. MPL=0 12L-1.2L2=0 L=10

2. Consider the following short-run production function (where L = variable input, Q = output): Q = 10L – 0.5L2

Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit.
|a. |Determine the marginal revenue product function. (5 points) |
|b. |Determine the marginal factor cost function. (5 points) |
|c. |Find the optimal value of L, given that the objective is to maximize profits. (5 points) |

a. MPL=△Q/△L=10-L MRQ = 10 MRPL= MPL* PQ= 100-10L b. MFCL= △TC/△L= △TC/△L = 20 c. MRPL= MFCL 100-10L=20 L=8 Maximal profits = 10(10L-0.5L²)-20L=480-160=320

3. Suppose that a firm’s production function is given by the following relationship (where L = labor input, K = capital input, Q = output):

Q = 2.5L0.5K 0.5
|a. |Determine the percentage increase in output if labor input is increased by 10 percent (assuming that capital input is held |
| |constant). (6 points)