Macroeconomics
13th Edition
ISBN: 9781337617390
Author: Roger A. Arnold
Publisher: Cengage Learning
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Chapter 17, Problem 5WNG
To determine
Movements of rise in labor along the production function and thereby change in the Long Run
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Using the production function Real GDP = T (L, K), define the term production function and describe what each of the variables (T, L, and K) represents. When graphed with Real GDP on the vertical axis and labor on the horizontal axis, which variable(s) can shift the production function and which variable(s) can cause a movement along the production function?
Suppose the economy's production function is to Y=AKN. If K = 2000, N= 100, and A=1. The calculate Y.
Suppose a country has a population of 120 people, a working-age population of 100 people, its labor force participation rate is 0.5 (50%), and the quantity of output is 60 units. Suppose that the production function of the economy is given by Y=2N, where Y represents the quantity of output and N represents the number of workers needed to produce the output.
I know the answer is 0.4 but I don't understand how to get it. Thank you!
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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 ratearrow_forward0.5 0.5 Given a production function: Y = AK N If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at % ? (Answer in integer only, no decimal place.) Your Answer: Answer Given a production function: Y = AK0.5 N0.5. If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at %? (Answer in integer only, no decimal place.) Your Answer: Answerarrow_forwardAn article in the Wall Street Journal observes: “For 2008, productivity grew an astounding 2.8% from 2007 even as the economy suffered through its worst recession in decades.” How is it possible for labor productivity to increase if output is falling?arrow_forward
- A country has a Cobb-Douglas production function given by: Y = AK0.5H0.1 If total factor productivity is 46, human capital is 1,828, and the capital stock is 2,736, what will this country's GDP be? Do not round until your final answer, when you may round to two decimal places. Country A produces GDP according to the following equation: GDP 5K and has a capital = stock of 13,399. If the country devotes 13% of its GDP to producing or repairing investment goods, how much is this country currently investing? Rounds your answer to two decimal places.arrow_forwardConsider an economy with a Cobb-Douglas production function. Assume that the labour income share parameter is 1/3. The economy is producing 100 units of output and the productivity parameter is equal to 1. f the depreciation rate for capital is 6%, investment rate is 6%, and there are 125 workers in the economy. The growth rate in the economy: Select one: a. is positive because the economy is below its steady state. b. is equal to zero because the economy is at its steady state. C. is negative because the economy is above its steady state. d. cannot be determined.arrow_forwardThe following data give real GDP, Y, capital, K, and labor, N, for the U.S. economy in various years. Units and sources are the same as in Table 3.1. Assume that the production function is Y-AK0.3N0.7 Year 1970 1980 1990 K 5600 8055 10,946 2000 13,131 14,711 137 2010 15,599 17,682 139 ● Y 4951 6759 9365 L 79 99 119 (a) Calculate total factor productivity (A). By what percentage did U.S. TFP grow: between 1970 and 1980? between 1980 and 1990? between 1990 and 2000? between 2000 and 2010? (b) Plot the short-run production function while keeping capital fixed at the 1970 level. (c) What happened to the marginal product of labor between 1970 and 2010? HINT: Calculate the marginal product numerically as the extra output gained by adding 1 million workers in each of the two years. (The data for employment, N, are measured in millions of workers, so an increase of 1 million workers is an increase of 1.0.)arrow_forward
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- 10. As an alternative to the story of Robinson Crusoe, macroeconomists use the "aggregate production function," written as Y = AF(L,K,H,N), to link economy-wide output Y to the number of workers L, the stock of physical capital K, the stock of human capital H, the stock of natural resources N, and stock of technological knowledge A. With reference to this aggregate production function, please indicate whether each of the following statements is true or false. (a) The aggregate production function exhibits "constant returns to scale" if doubling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a doubling of output. (b) The aggregate production function exhibits "constant returns to scale" if tripling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a tripling of…arrow_forwardSuppose China has a production function of the form: GDP per worker = Tx (physical capital per worker)0.4 x (human capital per worker)0.6 Using this production function, which of the following statements are true? (Select all that apply) Unlike physical and human capital, technology (T) is not directly measured GDP per worker will increase if the labor force grows Output per worker will grow more if human capital increases by 1% than if physical capital increases by 1% None of the abovearrow_forwardSuppose the economy's production function is Y=AK0.3N0.7. If K = 2000, N = 100. Calculate the output level of the economy.arrow_forward
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