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1. Suppose that the aggregate production function has the Cobb-Douglas form The parameter A is called...
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...
(Growth Accounting) Suppose that the representitive firm's production function is Cobb- Douglas: (a) Show that the...
(Growth Accounting) Suppose that the representitive firm's production function is Cobb- Douglas: (a) Show that the growth rate of total output can be decomposited as (Hint: You may take logarithm to equation (4) on both sides, then use chain rule to take derivative with repect to time t) (b) Suppose in the year 2016, compared to 2015 the total output increases by 3%, and the technology keeps the same (no change in A). Also the labor force inceases by 0.05%...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form,...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to you. It says that output Q is related to inputs K and L as: This production function implies that the cost-minimizing demand for capital will be Ou where w is the wage rate, r is the cost of capital, Q is output level, and α and β are parameters We will assume that α + β 1; this is the constant-returns-to-scale assumption we saw...
The aggregate wage bill in an economy is equal to 60 and output, which is produced...
The aggregate wage bill in an economy is equal to 60 and output, which is produced according to the Cobb-Douglas production function, is equal to 100. The output growth rate was 10 percent and the growth rates of capital and labor were 10 percent and 5 percent respectively. A) What was the overall productivity (TFP) growth rate for this economy? B) Repeat (a) if the wage bill is 80 instead of 60. C) Derive the expression for TFP growth in...
Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α...
Imagine a Solow Growth Model with a standard Cobb-Douglas production function and the following parameters: α = 0.33; d = 0.05; A = 2; s = 0.5; n = 0.25 a) Calculate the rate of capital accumulation (law of motion) b) Calculate the steady state level of capital? c) Calculate the steady state level of real output/income? d) Calculate the steady state level of investment? e) Calculate the steady state level of consumption? f) What effect does a higher productivity...
Consider an economy described by the Cobb-Douglas production function: Y = A, KAH 1/3 H1/12 1/12...
Consider an economy described by the Cobb-Douglas production function: Y = A, KAH 1/3 H1/12 1/12 1/2 If the capital stock and real GDP each grows at 3 percent per year, while labor hours grow at 1 percent per year, and the quantity of human capital and natural capital are both constant, what is the average annual growth rate of efficiency (or total factor productivity)? 1.5 percent per year 2 percent per year 0-1 percent per year O percent per...
For the Cobb-Douglas production function F(L,K) = ALαKβ, a factor-neutral technical change would be represented by:...
For the Cobb-Douglas production function F(L,K) = ALαKβ, a factor-neutral technical change would be represented by: a) an increase in the value of β b) values of α and β for which α + β = 1. c) an increase in the value of A. d) an increase in the value of α.
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and...
Consider a profit maximizing firm that uses a Cobb-Douglas production function Y = AKαL 1−α and hires labor L at wage rate w and capital K at rental rate r. (1) Set up the profit-maximization problem of the firm and derive the first-order condition for the profit-maximizing choice of capital. (2) Show that the marginal product of capital is a decreasing function of capital. (3) Solve for the optimal choice of capital and show that the optimal choice of capital...
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...
(Growth Accounting) Suppose that the representitive firm's production function is Cobb- Douglas: (a) Show that the growth rate of total output can be decomposited as (Hint: You may take logarithm to equation (4) on both sides, then use chain rule to take derivative with repect to time t) (b) Suppose in the year 2016, compared to 2015 the total output increases by 3%, and the technology keeps the same (no change in A). Also the labor force inceases by 0.05%...
Question 2: Production Function and Profit Maxi- mization Consider a production function of Cobb-Douglas form: for some α, β E (0, 1) (a) Plot the isoquant of F (b) Derive that technical rate of substitution of F. Does F exhibit diminishing technical rate of substitution? (c) Does F exhibit diminishing marginal productivity of labor? What about marginal (d) Find out the conditions for α and β such that F is increasing return to scale, (e) Suppose that F does not...
Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume...
All firms produce according to a Cobb-Douglas production function. This production function should look familiar to you. It says that output Q is related to inputs K and L as: This production function implies that the cost-minimizing demand for capital will be Ou where w is the wage rate, r is the cost of capital, Q is output level, and α and β are parameters We will assume that α + β 1; this is the constant-returns-to-scale assumption we saw...
The aggregate wage bill in an economy is equal to 60 and output, which is produced according to the Cobb-Douglas production function, is equal to 100. The output growth rate was 10 percent and the growth rates of capital and labor were 10 percent and 5 percent respectively. A) What was the overall productivity (TFP) growth rate for this economy? B) Repeat (a) if the wage bill is 80 instead of 60. C) Derive the expression for TFP growth in...
Consider an economy described by the Cobb-Douglas production function: Y = A, KAH 1/3 H1/12 1/12 1/2 If the capital stock and real GDP each grows at 3 percent per year, while labor hours grow at 1 percent per year, and the quantity of human capital and natural capital are both constant, what is the average annual growth rate of efficiency (or total factor productivity)? 1.5 percent per year 2 percent per year 0-1 percent per year O percent per...
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