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?
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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?
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- 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?Q2) The production function of a small economy is Y=K0.3L0.7, K is the amount of capital (land), L is the amount of labor. The economy starts with 70 units of land and 80 units of labor. a) How much output does the economy produce? b) What are the wage and the rental price of land? C) What share of output does labor receive? d) If a plague kills half the population, what is the new level of output? e) What is the new wage and rental price of land? f) What share of output does labor receive now?Consider an economy that produces goods and services according to the production function F (L, K) = 90L Ki,where L represents the number of workers in an economy and K represents the combined units of physical and human capital. The marginal products of labour and capital are: (登) MPL = 60 30(£) MPK = Question 1 Initially: there are 27 workers and 64 units of capital. Part (a): What is the economy's real GDP and GDP per capita? 1st scenario Suppose L increases to 125 while capital remains constant at 64: Part (b): Calculate the economy's real GDP and GDP per capita. Part (c): Relative to the initial scenario (L = 27 and K = 64), how much did MPL change by? 2nd scenario Now suppose L remained constant at 27 workers and capital increased to 216 units: Part (d): Calculate the economy's real GDP and GDP per capita. Part (e): Relative to the initial scenario (L = 27 and K = 64), how much did MPK change by? 3rd scenario Finally, suppose L = 54 and K = 128. Part (f): Calculate the economy's…
- In the United States economy, there is a great deal of focus on technological advancements. These advances are said to increase worker productivity (like Zoom) or increase the productivity of capital (such as technology that makes the supply chain more efficient).What effect does advancement in technology have on the equilibrium real rental price and capital, assuming that the supply of capital is fixed? Explain, using the terms in the production function, how you know this to be true.Q 1. Given the following production function Y=AKα L 1-α 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?Suppose that land is specific to corn, capital is specific to automobiles, labor is mobile between sectors, and payments are as follows: Sales revenue = 400; payments to labor = 100; payments to capital = 300 Corn:Sales revenue = 300; payments to labor = 250; payments to land = 50. Holding the price of automobiles constant, suppose the increase in the price of corn is 10% and the increase in the wage is 5%. What is the impact of this on the rental of land and the rental of capital?
- The production function in an economy is. Y = 5(4.00N-0.0188N²), where the marginal product of labor is given by: MPN = 5(4.00 -0.0376N). The equation for the labor supply curve is: NS = 48.0 + 8(1 - t)w, where NS is the amount of labor supplied, w is the real wage and t is the tax rate on wage income. The tax rate is t = 0.20. Determine the labor demand function. (Enter your responses rounded to two decimal places); -0-0w ND=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; 0.9Suppose that the economy's production function is given by Y=K²N¹-a where Y is output, K is capital, and N is labor. Assume that a = 1/3. The production function transformed into output per worker is (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with N character.)
- A producer has the following technology.y= 6K^(1/2)L^(1/2) a) Prove formally that the production function exhibits constant returns to scale (use “λ” argument). b) Find analytically MPL and MPK. Is MPL increasing, decreasing, or constant inL? Is MPK increasing, decreasing, or constant in K? c) Short-run: Given stock of capital ̄K= 1 find labor demand (formula) of a competitive firm. Find equilibrium real wage rate if labor supply is given by Ls= 9 (one number). d) Assume again ̄K= 1 and that Ls= 9. The government adopts a real minimum wage of wmin/p=(3/2). Find labor demand (one number) and the unemployment rate (one number). Please depict the equilibrium on a graph with the real wage on the vertical axis and labor on the horizontal axis, indicating the equilibrium quantity of labor, wage, and unemployment, as well as the relevant curves. e) Find the cost function given prices of inputs wK= 4 and wL= 1 (formula). Plot the cost function on a graph, indicating the slope of the cost…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…a) What are the determinants of production? Explain.b) Suppose that an economy’s production function is in the Cobb–Douglas form with parameter α = 0.3. What is the production function equation? What does each component stand for?
