Suppose that the production function is V=5 With this production function, the marginal product of labor is MPN 45K/NAS The labor supply curveis NS-105x1-xwf where wis the real wage rate is the tax rate on labor income, and hence (1-fix is the after-tax real wage rat The capital stock is K-25 Assume that the tax rate on labor income, tequals zero The equilibrium level of the real wage is (Round your answer to two decimal places) :
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- Assume that an economy's production function is Y=1,000L1/2,so that when the marginal product of capital is equated to the real wage the labor demand curve is L = 250,000(P/W)2. The labor supply curve is L = 31,250(W/P). The real wage that solves these equations is W/P = 2. Assume that the expected price level is 10, so that a nominal wage contract setting the wage at 20 is agreed to, making the expected real wage 2. If the price level turns out to be 10, 62,500 workers will be hired and output will be 250,000. If the actual price level turns out to be 20, what will the actual real wage be?b. According to the labor demand curve, how much labor will be demanded if the actual real wage is at the level given in part a?c. According to the production function, if the amount of labor given in part b is actually hired, how much will production be?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?The production function is Cobb-Douglas: Y = AK^αL^1−α, where K = 1000, and L = 100. α=0,365 A=2,3 a) How much output does the economy produce?b) What is the real wage rate equal to in equilibrium? c) What is the real rental rate of capital equal to in equilibrium?
- 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?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.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
- An economy has an aggregate production function to produce goods and services Y = AK1/3L 2/3 where Y represents total output (i.e GDP), K is capital, L is labor, and A is total factor productivity (TFP). This economy devotes a share of 30% of its output to gross investment. Capital depreciates at a rate of 10% per period. The TFP level is one and there are 2 units of labor available for production. • Suppose the economy starts with a capital stock at time t = 1 equal to 1 unit. Write down the values of gross investment, net investment, capital, consumption, and output observed during the subsequent 10 periods • What is the steady state level of capital, assuming A = 1 and L = 2? • Suppose that the economy is at its steady state and there is an increase in the depreciation rate from 0.10 to 0.15. What is the new steady state value for capital? Discuss your results.in an economy with production function Y = 1.5 × K^0.3L^0.7, K = 343, and L = 512. If factor markets are in equilibrium, then the rental price of capital is (approximately) ________, and the real wage is (approximately) ________. A) 0.5; 0.8 B) 7; 8 C) 0.9; 1.35 D) 1.4; 0.4 E) 0.6; 0.9In an effort to stop the migration of many of the automobile manufacturing facilities from the Detroit area, Detroit’s city council is considering passing a statute that would give investment tax credits to auto manufacturers. Effectively, this would reduce auto manufacturers’ costs of using capital and high-tech equipment in their production processes. On the evening of the vote, local union officials voiced serious objections to this statute. Outline the basis of the argument most likely used by union officials. (Hint: Consider the impact that the statute would have on auto manufacturers’ capital-to-labor ratio.) As a representative for one of the automakers, how would you counter the union officials’ argument?
- In an effort to stop the migration of many of the automobile manufacturing facilities from the Detroit area, Detroit’s city council is considering passing a statute that would give investment tax credits to auto manufacturers. Effectively, this would reduce auto manufacturers’ costs of using capital and high-tech equipment in their production processes. On the evening of the vote, local union officials voiced serious objections to this statute. Outline the basis of the argument most likely used by union officials. (Hint: Consider the impact that the statute would have on auto manufacturers’ capital-to-labor ratio.)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. Assume that in this economy consumption (C) is given by the equation C = 600 + 0.6(Y – T). Investment (I) is given by the equation I = 2,000 – 100r, where r is the real rate of interest in percent. Taxes (T) are 500 and government spending (G) is also 500. (Hint: use the GDP obtained in part a). What are the equilibrium values of C, I, and r? What are the values of private saving, public saving, and national saving?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) ?