Question2 Imagine you work for a firm that only utilizes labor and capital as inputs and ha CES production function: q = f(L, K) = [aLº + BK²] Where a = B=0.5.y = 1.p = 2. a. What is the MPL ? What does this mean economically? b. What is the MPK? What does this mean economically?
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- What is an aggregate production function?Suppose you are a worker in the construction industry in the state ofToronto, Canada. The MPL in this industry is (see attached image) where Kc and Lc are the amounts of labor and capital, respectively, in the indus-try. If Toronto has 30,000 construction workers and 120,000 units ofconstruction capital, what is your MPL)? Note: Attached is the formula.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 rate
- Suppose a firm’s hourly marginal product of labor is given by MPN = A (200 – N) If A = 0.2 and the real wage rate is $10 per hour, how much labor will the firm want to hire? Suppose the real wage rate rises to $20 per hour. How much labor will the firm want to hire? With the real wage rate at $10 per hour, how much labor will the firm want to hire if A rises to 0.5?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?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?
- prove that dMRTS/dL<0 when FKL > 0 where MRTS =MPL/MPK MPL= marginal product of labor MPK - marginal product of capitalSuppose the marginal product of labor is MPN = 200 – 0.5N where N is aggregate employment. The aggregate quantity of labor supplied is 300 + 8w, where w is the real wage. What is the equilibrium real wage? (a) 5 (b) 10 (c) 15 (d) 20Consider an economy in which the marginal product of labour is given by MPN = A(150 − N), where N is the amount of labor used. The amount of labour supplied is given by 60 + 5(1 − t)w, where w is the real wage and t is the tax rate on labour income. (a) Suppose A = 2 and t = 20%. Calculate the equilibrium levels of real wage and employment. (b) Suppose that the economy experiences an adverse supply shock and A = 1. Everything else remains the same as before. Calculate the equilibrium levels of real wage and employment in this case. (c) Suppose that the government lowers the labour income tax by 50% following the adverse supply shock, i.e., A = 1 and t = 10%. Calculate the equilibrium levels of real wage and employment in this case. (d) Use the labour market diagram to illustrate the adjustments from the original equilibrium in part (a) to the equilibrium in part (b) and then the adjustments from the equilibrium in part (b) to the equilibrium in part (c). Explain the adjustments from…
- How does the graph look for the effect of a temporary but persistent increase in total factor productivity on current output. I know that the x axis is quality of labour (employment) and the y axis is level of current output but im not sure how the graph should look. Could you show me what the graph should look like?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.How does the graph look for the effect of a temporary but persistent increase in total factor productivity on current prices. I know that the x axis is the quantity of output and the y axis is the price level but im not sure how the graph should look. Could you show me what the graph should look like?