1. Suppose the production function is zF(K, N) = ZKªN!a and zF(K', N') = 2K°N-a. (a) Set up the firms problem. (b) Show that labor demand curve is downward sloping (c) Show that investment demand is decreasing in interest rate. 2. Use the Keynesian cross to derive the AD curve. Show it is decreasing in r. 3. Use the labor market clearing condition to derive the AS curve. Show it is increasing in r.

1. Suppose the production function is zF(K, N) = ZKªN!a and zF(K', N') = 2K°N-a. (a) Set up the firms problem. (b) Show that labor demand curve is downward sloping (c) Show that investment demand is decreasing in interest rate. 2. Use the Keynesian cross to derive the AD curve. Show it is decreasing in r. 3. Use the labor market clearing condition to derive the AS curve. Show it is increasing in r.

Macroeconomics: Private and Public Choice (MindTap Course List)

16th Edition

ISBN:9781305506756

Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson

Chapter10: Dynamic Change, Economic Fluctuations, And The Ad-as Model

Section: Chapter Questions

Problem 9CQ

See similar textbooks

Similar questions

Question2 Imagine you work for a firm that only utilizes labor and capital as inputs and has a CES production function: q = f(L, K) = [aLº + BK²] 2/2 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? c. What is the MRTS? What does this mean economically? d. Does this CES function have constant, increasing, or decreasing returns to scale?
1) Suppose the marginal product of labor in the economy is given by MPN = 0.005(18,000 005N), while the supply of labor is 2000 rate and level of employment. (b) What happens to the wage rate and employment if wealth rises, reducing the supply of labor to 200 + 1000w? + 1000w. (a) Find the market-clearing real wage
Consider an economy with production function given by Y = AK0:5L0:5 where A is the total factorproductivity (TFP), K is the capital stock and L is the labor input. For simplicity assume capital is xed and equal to 1. Assume A=100.a. Write the rm's problem of choosing labor demand. Derive the demand for labor as a functionof the real wage.b. Assume labor supply is inelastic and xed at L= 100. Find the equilibrium values of the wageand the employment level for this economy. Display graphically the labor supply and the labordemand curves. Carefully label your graph.c. Suppose the economy faces a positive productivity shock and TFP is now A=200. Displaygraphically the new labor demand function. What are the equilibrium values of employment andthe real wage?d. Compute the total output when A=100 and when A=200. What is the output's growth rate?Compare that growth rate with the growth rate in A. How does the growth rate of output percapita compares to the growth rate in A? Explain…
Consider the market for loanable funds. Suppose the demand for loans is given by i= 100-3Q+π, and the supply of loans is given by i= -20+Q+, where π represents inflation. In the case of T-5, what is the equilbrium quantity of loans and what is the corresponsing interest rate? O Q*=30, i*=5 O Q*=30, i*=15 O Q*=35, i*=10 O Q*=35, i*=2
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…
Assume that the economy starts at the natural level of output. Now suppose there is a permanent increase in the relative price of oil. a. Using the wage-setting and price-setting diagram (and explaining the intuition of the curves), show what happens to the unemployment rate in the medium run. Why does this happen? b. Assuming a simple production function, Y=N, where Y is output and N is employment, explain what happens to mediumrun equilibrium output. C. Assume the central bank has an inflation target. In an AS-AD diagram (explaining what lies behind the curves), show what happens to output and inflation in the short run and the medium run.
8. Suppose 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. 20
Consider an economy with 3 sectors and labour is the only primary input. The primary inputs vector is: |' = (0.1, 0.6, 0.25) What is the employment multiplier when there is a change in the demand for good 2? Select one: a. 10 b. 1.6667 c. 4 d. 1 e. 3.3333
4. Suppose the input coefficients matrix is: (0.4 0.2 0.2 A = 0 0.1 0 0.3 0.3 (1) Find (1-A) 1. (i1) Suppose labour is the sole primary input vector. Identify the direct and indirect effects on the value of employment following a1 unit drop in final demand for the third product. What is the employment multiplier? (ii) How is your answer to (ii) altered if in fact only half the (iv) payments to primary inputs are spent on labour? Suppose in fact that for every £ paid to primary inputs in (v) sector 1, only half is paid to labour and in sector 2 none is paid to labour while in sector 3 all payments to primary inputs go to labour. How is your answer to (ii) altered now? How is your answer to (ili) altered? (Hint: think about how the labour; instead of all primary inputs, vector will look now).
Consider an economy with the Cobb-Douglas production function: Y = 3K0.2L0.8 K = 140000; L=8000 Round answers to two places after the decimal when necessary. c. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 9 percent above the current equilibrium wage. Assuming that Congress cannot dictate how many workers are hired at the mandated wage, calculate what happens to the real wage, employment, output, and the total amount earned by workers. Real wages = $ Total output = d. Does Congress succeed in its goal of helping the working class? O Yes, Congress does succeed in its goal of helping the working class. units No, Congress does not succeed in its goal of helping the working class. Employment = Total earned by workers = $ workers e. Does this analysis provide a good way of thinking about a minimum-wage law? O No, this analysis does not provide a good way of thinking about a minimum-wage law. Yes, this analysis does…
Consider 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…
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.