Do you expect to see a pareto improvement? Why or why not?
Homework Answers
No the reason is quite simple. Wage income will rise and capital per worker will fall reducing Y and wN. Thus profit will fall with passage of time
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Do you expect to see a pareto improvement? Why or why not?
Suppose that you are...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U (C,) InC +0.5ln l where C is consumption and 1 is leisure. The household's time constraint is I+N-1 where Ns is the representative household's labour supply. Further assume that the production function is Cobb-Douglas 0.5 0.5 where 2-1 and K = 1 2.1 Assuming that the government spending is G = 0, use the Social Planners problem to solve for Pareto optimal numerical values...
1. Consider the following production functions. In each case determine if: • the function is Cobb...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
3. LaunchPad. In the United States, the capital share of GDP is about 30 percent, the...
3. LaunchPad. In the United States, the capital share of GDP is about 30 percent, the average growth in output is about 3 percent per year, the depreciation rate is about 4 percent per year, and the capital-output ratio is about 2.5. Suppose that the production function is Cobb-Douglas and that the United States has been in a steady state. (For a discussion of the Cobb-Douglas production function, see Chapter 3.) a. What must the saving rate be in the...
Have question about 7 and 8. Could you please explain why both of these are wrong?...
Have question about 7 and 8. Could you please explain why both of
these are wrong?
77. In a competitive market where worker's wage (W), rental rate of capital (R) and the price of output (P) are exogenous any firm will hire workers and capital up to the point where MPL =W/P and MPK = R/P. T8. For a country with a Cobb-Douglas production Y = F(KL) – AK"L" (A > 0,0 <01 1,0 < < 1 being constant parameters),...
Suppose the representative household has the following utility function: U (C; l) = ln C +...
Suppose the representative household has the following utility function: U (C; l) = ln C + 0:5 ln l where C is consumption and l is leisure. The householdís time constraint is l+N=1 where Ns is the representative householdís labour supply. Further assume that the production function is Cobb-Douglas zK0:5 (N)0:5 where z = 1 and K = 1: 2.1 Assuming that the government spending is G = 0; use the Social Plannerís problem to solve for Pareto optimal numerical...
Suppose that instead of having a fixed income I, you have an endowment of y =...
Suppose that instead of having a fixed income I, you have an endowment of y = 12 units of You can sell each of these units of good Y at price Pj and use the proceeds to buy good X, which good Y has a price of P Draw your budget line if P = 3 andP, = 4 Draw what happens to your budget line if P increases from 3 to 4, or if P, decreases from 4 to...
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...
9. Consider a Classical model with the following specifications in Q1, 2019: . Labor Supply: NS-1%,...
9. Consider a Classical model with the following specifications in Q1, 2019: . Labor Supply: NS-1%, Cobb-Douglas Production Function . The Quantity Theory of Money accurately describes aggregate demand, The Theory of Distribution holds, Parameter values: [y, a, A, K, M, V] [30,0.3, 130, 500, 2500,40]. Suppose a reduction in labor law regulations leads to an outward shift in labor supply, represented as an increase in y from 30 to 32 during Q2, 2019. Assume that everything else stays the...
PLEASE HELP!! Clear steps for each part would be much appreciated. thank you! It's not just money that multiplies with time... Suppose the number of bacteria on the surface of a phone screen dou...
PLEASE HELP!! Clear steps for each part would be much
appreciated. thank you!
It's not just money that multiplies with time... Suppose the number of bacteria on the surface of a phone screen doubles every 3 hours. 4. Write a function for the population, p, of bacteria as a function of n where n is the number of 3-hour periods since the bacteria first start multiplying. Call the initial population po a. b. How much will the population grow over...
(a) What do you understand by sensitivity analysis? Why is it important? How can you use...
(a) What do you understand by sensitivity analysis? Why is it important? How can you use the sensitivity ranges to decide whether your recommendations based on the optimal solution of a linear programming problem are robust or not? (b) What is an assignment problem? Briefly discuss the decision variables, the objective function and the constraint requirements in an assignment problem. How do we determine whether a given assignment problem is balanced? Give a real-world example of the assignment problem. (c)...
2 Calculating a Pareto optimal allocation Suppose the representative household has the following utility function: U (C,) InC +0.5ln l where C is consumption and 1 is leisure. The household's time constraint is I+N-1 where Ns is the representative household's labour supply. Further assume that the production function is Cobb-Douglas 0.5 0.5 where 2-1 and K = 1 2.1 Assuming that the government spending is G = 0, use the Social Planners problem to solve for Pareto optimal numerical values...
1. Consider the following production functions. In each case determine if: • the function is Cobb Douglas (Y = AK 11-a). If the function is Cobb Douglas, what is the value of the parameter a? • Do capital and labor exhibit diminishing returns. Explain your thinking using algebra / calculus /a graph etc. (a) F(K, L) = 27K+15VL (b) F(KL) = 5K + 3L (c) F(KL) = K0.5 0.5 (a) F(KL) - VK2 + L2 2. Suppose that the production...
3. LaunchPad. In the United States, the capital share of GDP is about 30 percent, the average growth in output is about 3 percent per year, the depreciation rate is about 4 percent per year, and the capital-output ratio is about 2.5. Suppose that the production function is Cobb-Douglas and that the United States has been in a steady state. (For a discussion of the Cobb-Douglas production function, see Chapter 3.) a. What must the saving rate be in the...
Have question about 7 and 8. Could you please explain why both of
these are wrong?
77. In a competitive market where worker's wage (W), rental rate of capital (R) and the price of output (P) are exogenous any firm will hire workers and capital up to the point where MPL =W/P and MPK = R/P. T8. For a country with a Cobb-Douglas production Y = F(KL) – AK"L" (A > 0,0 <01 1,0 < < 1 being constant parameters),...
Suppose that instead of having a fixed income I, you have an endowment of y = 12 units of You can sell each of these units of good Y at price Pj and use the proceeds to buy good X, which good Y has a price of P Draw your budget line if P = 3 andP, = 4 Draw what happens to your budget line if P increases from 3 to 4, or if P, decreases from 4 to...
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...
9. Consider a Classical model with the following specifications in Q1, 2019: . Labor Supply: NS-1%, Cobb-Douglas Production Function . The Quantity Theory of Money accurately describes aggregate demand, The Theory of Distribution holds, Parameter values: [y, a, A, K, M, V] [30,0.3, 130, 500, 2500,40]. Suppose a reduction in labor law regulations leads to an outward shift in labor supply, represented as an increase in y from 30 to 32 during Q2, 2019. Assume that everything else stays the...
PLEASE HELP!! Clear steps for each part would be much
appreciated. thank you!
It's not just money that multiplies with time... Suppose the number of bacteria on the surface of a phone screen doubles every 3 hours. 4. Write a function for the population, p, of bacteria as a function of n where n is the number of 3-hour periods since the bacteria first start multiplying. Call the initial population po a. b. How much will the population grow over...
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