Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=WKr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ).

Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=WKr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ).

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 7E

See similar textbooks

Similar questions

Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ?
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=W.Kr.L1-r where : W=technology and r is standard share parameter of Cobb-Douglas production function. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from previous question (Question-1) (Y=Ka.Lb) ? (Question 1: Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lb )
Consider a competitive, closed economy with a Cobb-Douglas production function with parameter α = 0.25. The parameter A is equal to 60. Assume also that capital is 100, labor is 100. Calculate GDP (Y) for this economy. Does the production function exhibit constant returns to scale? Demonstrate with examples. Determine if the production function exhibits diminishing marginal returns to capital. Demonstrate with calculus What is the real wage in this economy? What share of GDP will go to labor in this economy?
QUESTİON: Assume that we have a Cobb-Douglas type aggregate production function in the form: where : W=technology and r is standard share parameter of Cobb-Douglas production function.a. Find Marginal Rate of Technical Substitution (MRTS) between K and L. b. Why does (or does not) technology affects MRTS? Explain. c. Find output per effective labor; capital per effective labor (y=Y/WL and k= K/WL ). d. Find elasticity of substitution between K and L. Why does (or does not) the result different from the previous question (Question-1)?
Suppose that production function is Y=K1/3(AN)2/3 and competitive firms hire capital and labor to produce output. Let r be the return paid to capital and w be the real wage paid to labor. Which of the following is true? Group of answer choices A) a profit-maximizing firm hires capital and labor until average products equal factor prices B) labor income share is 1/3 C) real return to capital r grows at the rate of productivity growth D) real wages w grows at the rate of productivity growth
Consider a Cobb-Douglas production function, Y=zKα(Nd)1−α, with 0< α <1. (a) Show that this production function exhibits constant returns to scale. (That is, show that when K becomes xK and Nd becomes xNd, Y becomes xY for x > 0. (b) What is MPN? Is it increasing or decreasing in Nd?
Suppose that the production function is given by Y=AK0.4N0.6. What is the percentage change in output if both capital and labor rise by 42%? Write the answer in percent terms with up to two decimals (e.g., 10.22 for 10.22%, or 2.33 for 2.33%).
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=Ka.Lba. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or y- or dy/dk ? c. Briefly explain why y’>0 or =dy/dk >0 . Is it possible that dy/dk>0 ? Why? d. Briefly explain y’’ < 0 e. Find the elasticity of substitution between K and L. What does expansion path look like?
In 2000, the country of Cobra Island has an initial level of capital set at 10 units. The population of Cobra Island is unknown, but we do know that it grows each year at some constant rate. The level of total income is 500 cobra dollars. Finally, the total production function of Cobra Island can be described as Y=10*L1/2k1/2 What is the initial population of Cobra Island? Let the wage of labor is 0.4, and the rental rate of capital is 0.6. The capital to labor ratio after two years (in 2002) is 50 while the amount of workers is 1000. The growth rate of capital is 6,970%. The growth rate of labor is 100%. Find the GDP of Cobra Island. How much labor is there in Cobra Island one year after the initial year (or in 2001)? The growth rate of income is 1,089%. Find the Solow Residual. Do not give the answer as a percentage. Zackland, a developing country, can be described using the Harrod-Domar Model. The ICOR of Zackland is 0.8. Assume that the economy is stable. In other…
Suppose the production function is given by Y = K0.4 L0.6, where K is amount of land and L is amount of labor used in the production process. In the beginning, the economy has equal amount of labor and land (K = L = 100 units). Answer the following questions: How much output does the economy produce with the given inputs? What are the real rental price of land and the real wage of labor at the optimum? What is the share labor income (WL/PY) in the economy? If a plague kills one-half of the population (i.e., labor), how much does the output of the economy, the rental price of land and the wage of labor change? Answer all four.
Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?
Consider the production function Y = z * K^1/3 * N^1/3 * L^1/3 where Y is output, z is a parameter capturing technology, K is capital, N is labour and L is the area of land. Question text If we double the technology factor, z, then output will double. Question 17Select one: True False Question text If we increase the population, and therefore the workforce, then if nothing else changes, the average product of labour must increase. Question 18Select one: True False Question text We would need to increase capital input by a factor of 8 to double output. Question 19Select one: True False Question text Increasing technology will increase labour productivity. Question 20Select one: True False