Macroeconomics
10th Edition
ISBN: 9780134896441
Author: ABEL, Andrew B., BERNANKE, Ben, CROUSHORE, Dean Darrell
Publisher: PEARSON
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Question
Chapter 3, Problem 5RQ
To determine
The concept of the MPN curve is to be determined along with its relationship with the production function and labor demand.
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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
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?
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.
Chapter 3 Solutions
Macroeconomics
Ch. 3 - Prob. 1RQCh. 3 - Prob. 2RQCh. 3 - Prob. 3RQCh. 3 - Prob. 4RQCh. 3 - Prob. 5RQCh. 3 - Prob. 6RQCh. 3 - Prob. 7RQCh. 3 - Prob. 8RQCh. 3 - Prob. 9RQCh. 3 - Prob. 10RQ
Ch. 3 - Prob. 11RQCh. 3 - Prob. 12RQCh. 3 - Prob. 13RQCh. 3 - Prob. 14RQCh. 3 - Prob. 15RQCh. 3 - Prob. 1NPCh. 3 - Prob. 2NPCh. 3 - Prob. 3NPCh. 3 - Prob. 4NPCh. 3 - Prob. 5NPCh. 3 - Prob. 6NPCh. 3 - Prob. 7NPCh. 3 - Prob. 8NPCh. 3 - Prob. 9NPCh. 3 - Prob. 10NPCh. 3 - Prob. 1APCh. 3 - Prob. 2APCh. 3 - Prob. 3APCh. 3 - Prob. 4APCh. 3 - Prob. 5APCh. 3 - Prob. 6APCh. 3 - Prob. 7AP
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- Consider an economy in which the aggregate production function is given by the equation: Y = 3.6 K0.5 N0.5 where (Y) is aggregate production, (A) measures productivity, (K) is the stock of physical capital and (N) is the amount of labor, measured in millions of workers. Both Y and K are measured in billions of reais. K is given and is 10,000 (i.e., 10,000 billion reais), so K0.5 = 100. The aggregate labor supply is given by the following equation: NS = [(1-t).w]2 where (t) is the income tax rate on labor and (w) is the real wage, measured in reais per hour. t = 0.20 (20%). The equilibrium levels of the real wage (w) and employment (N) are, respectively, [ANSWER] and [ANSWER]. The full employment production level (Y) is [ANSWER]. Finally, the after-tax real wage that workers receive per hour in this economy iarrow_forwardNeoclassical Production Function Please write the production function in its simplest form (human capital being included in TFP) and explain the nature of each factor of production.arrow_forwardState the relationship between the LAC curve and the LMC in economics!arrow_forward
- Assume that we have a Cobb-Douglas type aggregate production function in the form: Y=KaLb a-)Briefly explain why y''≤0 b-) Find the elasticity of substitution between K and L. What does expansion path look like?arrow_forwardExplain the shape of shortrun curves or derive the average long run curve from shortrun curve.arrow_forwardAssume 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?arrow_forward
- 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) 20arrow_forwardWith the Cobb-Douglass production function, the real wage will increase if: A. the supply of labor increases B. total factor productivity increases C. the price of output increases D. the amount of capital decreasesarrow_forwardSuppose the marginal product of labor in the economy is given by MPN = 200 – 0.5N, while the supply of labor is 100 + 4w Find the market-clearing real wage rate What happens if the government imposes a minimum wage of 40? Is there involuntary unemployment? What happens if the government imposes a minimum wage of 60? Is there involuntary unemployment?arrow_forward
- Using "increase" or "decrease", complete this statement:" According to the output effect, a decrease in the wage rate will ______ production costs, so the price of final goods will ______. The quantity of final goods produced will ________, so the demand for labor will ___________."arrow_forwardSuppose the economy's production function is Y=AK0.3N0.7. If K = 2000, N = 100. Calculate the output level of the economy.arrow_forwardPlease help me answer the following question with graphs: Suppose there is a reduction in income taxes. How will this affect the unemployment rate in the short run and the medium run?arrow_forward
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