Suppose that the aggregate production function takes the form y A(SON-0.1A2), where Yis output, A is productivity, and N is total hours worked. Let's suppose A=1.0. Assuming that the supply of labor is given by - 100 + 10w where wis the wage rate. What is the equilibrium level of output and hours worked? (Hint: use the labor market equilibirum condition to find w) OA N-150, Y-2,350 OB N-200, Y-6000 OC N-200, Y-5,000 OD N-50, Y-3,750
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- How is the concept of technology, as defined with the aggregate production function, different from our everyday use of the word?Country A and country B both have the production function Y = F(K, L) = K^0,5L^0,5 A. Does this production function have constant returns to scale? Explain. B. What is the per-worker production function, y = f(k)? C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 20 percent of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Theen find the steady-state levels of income per worker and consumption per worker. D. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator or a computer spreadsheet…Suppose that output is produced according to the production function Y = Kα[(1 - u)L]1-α, whereK is capital, L is the labor force, and u is the natural rate of unemployment. The national savingrate is s, the labor force grows at rate n, and capital depreciates at rate d.a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and thenatural rate of unemployment (u).b. Write an equation that describes the steady state of this economy. Find the steady state capitalper worker and steady state output per worker.c. Does this production function have constant returns to scale? Explain.
- 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.Suppose a country has a production function Y=2K0.5L0.5, where K is the amount of capital and L is the amount of labor. The economy begins with 400 units of capital and 625 units of labor. Find numerical answers to the following. Be sure to show your work. What is the real wage and the real rental price of capital? (Hint: Assume the firms are maximizing profit.) Suppose there is a natural disaster and half of the capital is destroyed. What is the new level of output? What is the new real wage and real rental price of capital? How much output does the economy produce? Please answer all part I will rateWhich is an example of the aggregate production function, Y = F(K, N), that exhibits constant returns to scale? Y= 2 K N Y = 3 K N Y = K/N Y= 2K + 3 N
- Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb 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?Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?
- Ecuador's economy has a production function that is as follows: Y = K2/5L3/5 The men in Ecuador generally stay home performing household chores while women work. Since the Ecuadorian state television stopped airing soap operas, many men decided to join the workforce and thus the labor force increased by 6.5%. However, recent storms have destroyed much of the capital stock of the country and thus the capital stock shrank by 2.5%. A. Assuming there is no change in total factor productivity in Ecuador, how would the output of Ecuador's economy change? B. How would labor productivity (output per worker) be affected by the increase in labor and decrease in capital stock? Explain. C. Assuming instead that Ecuador's economy grew by 4.9%, what would be the change in total factor productivity in the economy?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?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