3. Suppose the production function takes on the following form: Q = aK2L 2 a) What...
3. Suppose the production function takes on the following form: Q = aK2L 2
a) What is the marginal productivity of labor? Evaluate it at L = 2 and K = 4.
b) What is the marginal productivity of capital? Evaluate it at L = 2 and K = 4.
c) What is the Marginal Rate of Technical Substitution, and what does it mean? (Provide two interpretations of the MRTS) Evaluate the value of the MRTS at L = 2 and K = 4?
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3. Suppose the production function takes on the following form:
Q = aK2L 2
a) What...
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal...
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal productivity of labor? Evaluate it at L = 5 and K = 7. (5 points) b) What is the Marginal Rate of Technical Substitution? Evaluate it at L = 5 and K = 7. (5 points)
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently...
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSx) (Round to the nearest fwo decimal places if necessary) Answer Suppose the production function for a firm is given by: q-4L K 25 If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal...
4. Consider the production functions given below: a. Suppose that the production function faced by a...
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
6. Suppose the production function takes on the following form: a) What is the marginal rate...
6. Suppose the production function takes on the following form: a) What is the marginal rate of technical substitution? Evaluate it at L5 and K 7. (5 points) b) What are the returns to scale for this production technology? (5 Points)
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently...
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer:
2. Suppose the production function of a firm is given by q=L1/4K2/4. The prices of labor...
2. Suppose the production function of a firm is given by q=L1/4K2/4. The prices of labor and capital are given by w = $9 and r= $18, respectively. a) Write down the firm cost minimization formally. b) What returns to scale does the production function exhibit? Explain. c) What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor? d) What is the optimal capital to labor ratio? Show your work.
Suppose the production function for automobiles is ? = ?? where Q is the quantity of...
Suppose the production function for automobiles is ? = ?? where Q is the quantity of automobiles produced per year, L is the quantity of labor (man-hours) and K is the quantity of capital (machine hours). a) What is the total product (number of automobiles) if the firm uses 25 man hours and 2 machine hours? b) Sketch the isoquant corresponding to a quantity of Q=50. c) What is the general equation for the isoquant corresponding to any level of...
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently...
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer
Practice Questions: Firm Cost Minimization The production function of computers takes the following form: Q= K02L...
Practice Questions: Firm Cost Minimization The production function of computers takes the following form: Q= K02L 1. Based on the production function, find MRTS LK a. b. Mathematically show that MRTS,K diminishes as the firm uses more labor. Suppose currently the company uses 3 units of K, and 2 units of L What is MRTS? What does the number tell you? c. Suppose the wage rate W= $8/hour and the rental rate of capital R $4/hour. Write an equation for...
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor.
Given production function Q=f(K, L) = 8KL + √L where K is capital and L is labor. a. Find marginal product of labor and marginal product of capital.b. Define what is marginal rate of technical substitution, MRTS. Calculate the MRTS for the above case.c. When K = 10, L = 16, what is the total output? Sketch this isoquant function on a diagram where K is the vertical axis and L is the horizontal axis.
6. Suppose the production function takes on the following form: Q=K’L? a) What is the marginal productivity of labor? Evaluate it at L = 5 and K = 7. (5 points) b) What is the Marginal Rate of Technical Substitution? Evaluate it at L = 5 and K = 7. (5 points)
Suppose the production function for a firm is given by: q-2L *4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSx) (Round to the nearest fwo decimal places if necessary) Answer Suppose the production function for a firm is given by: q-4L K 25 If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal...
4. Consider the production functions given below: a. Suppose that the production function faced by a milk producer is given by Q = 40.5 20.5 = 4VK VL, where MPx = 2K-0.5 20.5 = 2 and MP, = 2 K0.5L-05 = 2 * i. Do both labor and capital display diminishing marginal products in the short run? ii. Find the marginal rate of technical substitution for this production function. (Hint: The MRTS = 1) iii. Does this production function display...
6. Suppose the production function takes on the following form: a) What is the marginal rate of technical substitution? Evaluate it at L5 and K 7. (5 points) b) What are the returns to scale for this production technology? (5 Points)
Suppose the production function for a firm is given by: q=2L +4K. If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer:
0.5,,0.25 Suppose the production function for a firm is given by: q-4L If the firm currently has 20 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTS). (Round to the nearest two decimal places if necessary.) Answer
Practice Questions: Firm Cost Minimization The production function of computers takes the following form: Q= K02L 1. Based on the production function, find MRTS LK a. b. Mathematically show that MRTS,K diminishes as the firm uses more labor. Suppose currently the company uses 3 units of K, and 2 units of L What is MRTS? What does the number tell you? c. Suppose the wage rate W= $8/hour and the rental rate of capital R $4/hour. Write an equation for...
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