Questions and Answers on Managerial Economics

Managerial Economics HW #4 (Chapter 5)

1.A firm can manufacture a product according to the production function
Q F(K, L) K3/4L1/4

a. Calculate the average product of labor, APL, when the level of capital is fixed at 16 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 81 units of labor?
Saat (Capital) K = 16
(Labour) L = 16

Q = (16)0,75(16)0,25
Q = (8)(2) = 16

APL =Q/L =16/16=1.

Saat K= 16
Q= 81
Q = (16)0,75(81)0,25
Q = (8)(3) = 24
APL =Q/L =24/81= 0,296

b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 16 units. Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.

(Marginal Product Labor) MPL = 2(L)-3/4
Saat L= 16,
MPL = 2(16)-3/4 = 0.25= 1/4.
Saat L= 81,
MPL = 2(81)-3/4 = 0,037 =2/27

Jumlah Labor yang di perlukan akan bertambah , Sehinga Marginal Product Labor berkurang..
MPL = (16)= 1/4.>2/27= MPL (81) menjaga tingkat Modal tetap.

c. Suppose capital is fixed at 16 units. If the firm can sell its output at a price of $100 per unit and can hire labor at $25 per unit, how many units of labor should the firm hire in order to maximize profits?
VMPL = (P)(MPL)
= ($100) [ 2(L)-3/4]
= 200(L)-3/4

$25 = 200(L)-3/4
L = 200/25 x 2
L = 16 units labor to maximize Profits.

4. An economist estimated that the cost function of a single-product firm is
Based on this information, determine:
C(Q) = 50+25Q+30Q2+5Q3

a. The fixed cost of producing 10 units of output.
FC = 50
b. The variable cost of producing 10 units of output.
VC (10) = 25 (10) + 30(10)2 + 5 (10)3
= 250 +3000 + 5000
= $ 8250.

c. The total cost of producing 10 units of output.
C(10) = 50+25(10)+30(10)2+ 5(10)3
= 50 + 250 + 3000 + 5000
= $ 8300.

d. The average fixed cost of producing 10 units of output.
AFC(10) = $50/10 =$5.

e. The average variable cost of producing