6. 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.
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- Give only typing answer with explanation and conclusion The production function in an economy is given by Y = K0.4L0.6, where Y is output level, K is capital input, and L is labour input. The saving rate is 24%, the annual population growth rate is 4%, and annual depreciation rate is 2%.In class we argued that if people could accumulate human as well as physical capital, the production function would look like the “AK” production function. • (a) If the production function is AK and the savings rate is constant at rate “s”, and the rates of depreciation and populati on growth are δ and n respectively, what would the growth rate of the economy be? • (b) What would be the macroeconomic consequences of decreasing the savings rate in this economy? • (c) What would be the consequences of an increase in fertility in this economy? • (d) Would the consequences of decreasing fertility be UNAMBIGUOUSLY GOOD? • (e) Can human capital grow without bounds? Explain why or why not (make sure you discuss the physical nature of human capital). • (f) What is the growth rate of the economy (in the absence of technological progress) if human capital cannot grow without bounds?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…
- 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 the production function is Y = AK0.3N0.7. Suppose in 2010, K = 1000, N = 100, and Y = 199.5. In 2020, capital, labor, and output have doubled, so K = 2000, N = 200, and Y = 399. (a.) By what percentage did productivity grow from 2010 to 2020? (b.) If output had risen to 798 instead of 399, and capital and labor doubled, by what percentage would productivity have grown from 2010 to 2020?please answer the following, I have attached an image of the question for better format. Thanks! 2. Suppose that the production function of a country is given by Y=K3L0.7, where Y is output, L is labour, and K is capital. a)What is the return to scale property of the production function? B)What will happen to output if we double the use of capital and labour? C)Write the production function as a relationship between output per worker and capital per worker.
- 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?37. Which of the following is the interpretation of production function Y = F (K, L)? a.Output depend on K and L b.If K Increases, L also needs to increase c.If K increases, L needs to decrease d.If K and L Increases Y increases as well
- The aggregate production function is y=3KL. If they are 30 units of capital and 40 units of labor, what is aggregate output?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?The aggregate production function is y=3KL. If they are 30 units of capital and 40 units of labor, what is aggregate output? What is labor productivity? What is capital productivity?