Homework Answers
Diminishing returns to Capital occurs when as we hire more capital output will increase at a a diminishing rate and hence MPK should be decreasing.
Diminishing returns to Labor occurs when as we hire more Labor output will increase at a a diminishing rate and hence MPL should be decreasing
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9. Use the Cobb-Douglass production function (Y AK L1-a) to find the general form of MPK...
Consider a firm that faces the following production function: q = f(L, K) = L1/2 K1/2...
Consider a firm that faces the following production function: q = f(L, K) = L1/2 K1/2 where q is output, L is labor, and K is capital. Use this production function to answer the following questions. (a) What is the marginal product of labor (MPL)? (b) Does the MPL follow the law of diminishing returns? How do you know? (c) What is the marginal product of capital (MPK)? (d) Does the MPK follow the law of diminishing returns? How do...
Assume the following Cobb-Douglas production function: Assume the following Cobb-Douglas production function: Y = AK 0.4...
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
Suppose a firm has a production function given by Q = L1/2 K1/2. Therefore, MPL = K1/2 / 2L1/2 and MPK = L1/2 / 2K1/2 Th...
Suppose a firm has a production function given by Q = L1/2 K1/2. Therefore, MPL = K1/2 / 2L1/2 and MPK = L1/2 / 2K1/2 The firm can purchase labor, L at a price w = 36, and capital, K at a price of r = 9. a) What is the firm’s Total Cost function, TC(Q)? b) What is the firm’s marginal cost of production?
#1 (2 points) What are the relationships that the aggregate production function repre- sents? As a...
#1 (2 points) What are the relationships that the aggregate production function repre- sents? As a hypothetical example, describe each part of the function as if the variables represent data from the United States. #2 (2 points) In economics, what is the difference between the short run and long run? Is the aggregate production function a short run or long run model? #3 For this question use this aggregate production function: Y = AK1/4 [3/4 Part A) (2 points) Does...
3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L...
3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L & K represent quantities of labor and capital. Suppose each unit of labor costs $25, each unit of capital costs $100, and the company wants to produce exactly Q=1920. a. Use the method of Lagrangian Multipliers to find the quantity of Land K that meet production requirements at the lowest cost. (5 pts) b. Show that the values found in part (a) satisfy the...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at...
Consider the following production functions Y = AK1/2L1/2 Y=AK+3L a. Fixing total factor productivity (A) at 2 and labor employment (L) at 16 units, what is the marginal product of capital when capital employment (K) is 25, 35, and 45 for each production function? Do these production functions exhibit diminishing returns to capital employment? Explain. b. Are labor and capital complements under these production functions? Explain. c. Is either production function a “Cobb-Douglas” function? Explain. 3. Describe the difference between...
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas...
Problem 1. Suppose that production function for the corporate sector is well presented by the Cobb-Douglas production function: Y = K0.3L0.7 With this production function: MPL(K, L)=0.7K0.3L0.3 and MPK(K, L)=0.3K0.7L0.7 a) Suppose the capital stock of the firm is K¯ =10. Show that the demand for labor is given by: b) Find the amount of labor demanded for W P = 0.1,W P = 0.3, W P = 0.5, W P = 0.7 and W P = 0.9. Plot the...
Use calculus to find the MPK and MPL Find the Slope of the Isoquant Production Function:...
Use calculus to find the MPK and MPL Find the Slope of the Isoquant Production Function: Q=50+6L-.5L^2+22K-.25K^2
1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) =...
1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) = AK of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com pute the marginal product of capital. Does this function satisly the neoclassical assumptions?
Assume that the aggregate production is given by the following: Y stands for output, K stands...
Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between 0 and 1 a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product...
Assume the following Cobb-Douglas production function:
Assume the following Cobb-Douglas production function: Y = AK 0.4 20.6 If Y=12; K=8; and L=95, answer the following questions (SHOW ALL YOUR WORK): - 1. What is total factor productivity? 2. With your answer in (1), assume L=95 and estimate the production function with respect to K 3. Estimate the marginal product of capital and demonstrate diminishing marginal product of capital 4. Estimate real capital income 5. Estimate the share of capital income...
#1 (2 points) What are the relationships that the aggregate production function repre- sents? As a hypothetical example, describe each part of the function as if the variables represent data from the United States. #2 (2 points) In economics, what is the difference between the short run and long run? Is the aggregate production function a short run or long run model? #3 For this question use this aggregate production function: Y = AK1/4 [3/4 Part A) (2 points) Does...
3. Suppose a company's production is given by the Cobb-Douglas function: Q = 60L3K3 Where L & K represent quantities of labor and capital. Suppose each unit of labor costs $25, each unit of capital costs $100, and the company wants to produce exactly Q=1920. a. Use the method of Lagrangian Multipliers to find the quantity of Land K that meet production requirements at the lowest cost. (5 pts) b. Show that the values found in part (a) satisfy the...
1. (The AK Model) Consider an economy with an aggregate production function given by Y=F(K) = AK of capital. The law of motion for capital is just as in the neoclassical model where s and δ are the savings rate and depreciation rate, respectively. a) Show whether F(K) exhibits constant, decreasing or increasing returns to scale. Com pute the marginal product of capital. Does this function satisly the neoclassical assumptions?
Assume that the aggregate production is given by the following: Y stands for output, K stands for the capital stock, N stands for the number of the people employed, L stands for the quantity of land used in production, and A stands for a measure of labour efficiency. a and B are parameters whose values are between 0 and 1 a) Derive an analytical expression for the marginal product of capital (MPK), marginal product of labour (MPN), and marginal product...
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