Suppose that we have an economy whose production can be represented by a Cobb Douglas production function with parameter α=0.3. You may assume that there is no depreciation (i.e. δ=0). a. What fractions of income do capital and labor receive? b. For the following parts, describe what happens to output (in percent), the rental price of capital and the real wage from: i) Suppose that immigration increases the labor force by 10 percent. ii) Suppose that a gift of capital from abroad raises the capital stock by 10 percent. iii) Suppose that a technological advancement raises the value of the parameter A by 10 percent. Type out the correct answer ASAP with proper explanation

Suppose that we have an economy whose production can be represented by a Cobb Douglas production function with parameter α=0.3. You may assume that there is no depreciation (i.e. δ=0). a. What fractions of income do capital and labor receive? b. For the following parts, describe what happens to output (in percent), the rental price of capital and the real wage from: i) Suppose that immigration increases the labor force by 10 percent. ii) Suppose that a gift of capital from abroad raises the capital stock by 10 percent. iii) Suppose that a technological advancement raises the value of the parameter A by 10 percent. Type out the correct answer ASAP with proper explanation

Principles of Microeconomics (MindTap Course List)

8th Edition

ISBN:9781305971493

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter18: The Markets For The Factor Of Production

Section: Chapter Questions

Problem 9PA

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Suppose that an economy’s production function is Cobb–Douglas with parameter = 0.3 a. What fractions of income do capital and labor receive? b. Suppose that immigration increases the labor force by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage? c. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output (in percent)? The rental price of capital? The real wage ?
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.
Q 1. Given the following production function Where; Y is the total output of the economy K is the amount of land, and L is the labor force of the economy Assume A=1 and  = 0.5 The initial values of K and L is 100 units. a. How much output does the economy produce? b. What are the wage and rental price of land? c. What share of output does land receive? d. If a flood damaged half of the land, what is the new level of output in the economy? e. What is the new level of wage and rent? f. What share of output does land receiving now? Q 2. Suppose in an economy, people hold currency worth of 10,000 Rs and 4000 Rs worth of demand deposits in the only bank. The reserve-deposit ratio is 20%. a. What is money supply, monetary base and money multiplier? b. Suppose the economy only bank is a simple bank. It takes deposits and make loans and has no capital. Show the balance sheet of the bank. c. The central bank wants to increase the money supply. Should it buy or sell the Govt bonds in the…
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?
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Problem 4 Consider the following production function: Y, = AKÇH!-"L where Kr is capital, H;is human capital, Leis the amount of workers and A is the (constant) level of technology. • (1) Does this production function satisfy all the neoclassical properties. Discuss the meaning of each property INTUITIVELY. Imagine that parents invest in the human capital of their children up to the point where the MARGINAL PRODUCT OF PHYSICAL CAPITAL, K, is equal to the MARGINAL PRODUCT OF HUMAN CAPITAL, H:. 2 • (ii) What is the relation between K:and H:? Use this relation to write down total output as a function of Kronly. Imagine that the number of people in this economy, Nr, is different from the number of workers because some people do not work. Let l =4 be the number of workers per capita (the fraction of the population that works). Let y; be output per capita and Kt be capital per capita. Finally, let n be the rate of population growth and y, be the growth rate of labor. (iii) Using the…
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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?
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Consider a hypothetical economy that has the production function Y = F(K, LE) = K¹/3 (LE) 2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%. a. Solve for the per-effective-worker production function. b. At what rate (%) do the following grow in the steady state? i. Total output ii. Output per worker iii. Output per effective worker iv. Real rental price V. Real wage
Consider an economy that produces two goods, an agricultural good and a manufacturing good. An amount YA of the agricultural good can be produced using the following equation: YA = LA where LA is the amount of labor used in this sector. An amount of YM of the manufacturing good can be produced using the following equation: YM = KθLM 1-θ where K is capital stock and LM is the amount of labor used in such sector. So, this economy’s total output (i.e. GDP) is: Y = YA + YM. This economy has zero population growth rate (i.e. n = 0) and the depreciation rate is δ. The total number of workers in the economy is L and of course, L = LM + LA. Let P = LA/L. Furthermore, define: y = Y/L, k = K/L and c = C/L. As usual, we have: ∆k = sy – (δ+n)k. Please use the above information to derive the key equation for this version of Solow model. Show the steady state of the economy is a diagram with k as the x-axes. Label k* , y* and c* in your diagram.