A firm manufactures widgets according to the production function Q = 8L3/4 K1/4, where Q is the number of skis made, K is the amount of capital, and L is the amount of labor employed. The firm is currently producing Q = 120 using L = 15 and K = 15. The factor price of Labor (w) is $10 and the factor price of Capital (r) is $2. The firm suspects that it is not minimizing the cost of producing Q = 120 and has hired you, a student taking a course with the most famous economist in campus, to help it understand the nature of its inefficiency. a) At the current level of production (Q = 120) what are the marginal productivities of Labor and Capital respectively? MPL = Answer MPK = Answer b) What are the current cost of production for the company? TC = $Answer c) In order to minimize the costs of production the company should use more Answer d) In order to miminize costs of production the company should use the following input ration: K = Answer L e) Say the company wanted to continue use the same total costs as to when K and L = 15, and instead produce more output. How much output can the company produce? Q2 = ?
A firm manufactures widgets according to the production function Q = 8L3/4 K1/4, where Q is the number of skis made, K is the amount of capital, and L is the amount of labor employed. The firm is currently producing Q = 120 using L = 15 and K = 15. The factor price of Labor (w) is $10 and the factor price of Capital (r) is $2. The firm suspects that it is not minimizing the cost of producing Q = 120 and has hired you, a student taking a course with the most famous economist in campus, to help it understand the nature of its inefficiency. a) At the current level of production (Q = 120) what are the marginal productivities of Labor and Capital respectively? MPL = Answer MPK = Answer b) What are the current cost of production for the company? TC = $Answer c) In order to minimize the costs of production the company should use more Answer d) In order to miminize costs of production the company should use the following input ration: K = Answer L e) Say the company wanted to continue use the same total costs as to when K and L = 15, and instead produce more output. How much output can the company produce? Q2 = ?
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Consider a firm with production function f(L, K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average cost of producing q units is?
| A | Ā |
AC(q)=24/q+3 |
| B | Ā |
AC(q)=88/q+1/12 |
| C | Ā |
AC(q)=24/q+1 |
| D | Ā |
AC(q)=114/q+9/8 |
| E | Ā |
AC(q)=24/q+q |
Consider a firm with production function f(L, K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the cost of producing q units is?
| A | Ā |
C(q)=88+q/12 |
| B | Ā |
C(q)=24+3q |
| C | Ā |
C(q)=114+9q/8 |
| D | Ā |
C(q)=24+q2 |
| E | Ā |
C(q)=24+q |
Consider a firm with production function f(L, K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average fixed cost of producing q units is?
| A | Ā |
F=100/q. |
| B | Ā |
F=36/q. |
| C | Ā |
F=40/q. |
| D | Ā |
F=120/q. |
| E | Ā |
F=80/q. |
This is due today!! Thank you!!
Consider a firm with production function f(L, K)=2L+6K. Assume that capital is fixed at K=6. Then, the amount of labor necessary to produce q units is?
| A | Ā |
L(q,6)= q-12 |
| B | Ā |
L(q,6)= q/18-5 |
| C | Ā |
L(q,6)= q/2-18 |
| D | Ā |
L(q,6)= 3q/5-2 |
| E | Ā |
L(q,6)= q2/2-12 |
Consider a firm with production function f(L, K)= 4L2/3K1/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=4 and the price of labor w=2. Then, the average cost of producing q units is?
| A | Ā |
AC(q)= 4/q+q1/2/4. |
| B | Ā |
AC(q)= 2/q+1/4q1/3. |
| C | Ā |
AC(q)= 2/3q+1/q1/3. |
| D | Ā |
AC(q)= 1/3q+q1/2. |
| E | Ā |
AC(q)=8/q+2q1/2. |
Consider a firm with production function f(L, K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the cost of producing q units is?
| A | Ā |
C(q)=3+q2/9. |
| B | Ā |
C(q)=10+q3. |
| C | Ā |
C(q)=5+q3/9. |
| D | Ā |
C(q)=2/3+q2/3. |
| E | Ā |
C(q)=1/3+q3/3. |
