2. Output and Growth (a) Indicate whether the following statement is true, false, or uncertain and explain your answer using words, graphs and equations as appropriate. (i) If firm's production functions exhibit diminishing marginal product of both capital and labor, then an increase in capital will result in an increase in the marginal product of capital. (ii) If total factor productivity and the number of workers both rise, then real wages will be unchanged. (iii) In the Solow model with technological progress, if the efficiency of labor is increasing at rate g, then in steady state both the real wage and the real rental price of capital also grow at rate g.

2. Output and Growth (a) Indicate whether the following statement is true, false, or uncertain and explain your answer using words, graphs and equations as appropriate. (i) If firm's production functions exhibit diminishing marginal product of both capital and labor, then an increase in capital will result in an increase in the marginal product of capital. (ii) If total factor productivity and the number of workers both rise, then real wages will be unchanged. (iii) In the Solow model with technological progress, if the efficiency of labor is increasing at rate g, then in steady state both the real wage and the real rental price of capital also grow at rate g.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.8P

See similar textbooks

Similar questions

What is the difference between economies of scale, constant returns to scale, and diseconomies of scale?
3. What are the 2 variables that the Production Function is analyzing/graphing? Why does the production function diminish over time?
QUESTION 9 Which of the following best expresses the law of diminishing returns? B. Population growth automatically adjusts to that level at which the average product per worker will be at a D. As successive amounts of O A. Because large-scale production allows the realization of C. Proportionate increases in the inputs one resource (labor) are added to fixed amounts of other resources (capital), beyond some point the resulting extra or marginal output will decline of all resources will economies of scale, the real costs of production vary directly with the level of output result in a less-than- proportionate increase in total output maximum
2. Explain, in words, what is meant by labor augmenting productivity
70,0001 Norway 60,000 United States 50,000- Netherlands Denmark •. Germany France 40,000- :UK South Korea Jарan. Italy" • Spain 30,000- Greece Russia 20,000- Mexico Chile Turkey 10,000- 0. 6,400 6,500 6,600 6,700 6,800 6,900 7,000 7,100 7,200 7,300 7,400 7,500 Average annual hours of free time per worker According to the graph: Select one or more: а. UK workers have more free time than Greek workers. b. UK workers have lower GDP per capita than Spanish workers. O c. The relationship between GDP per capita and free time is downward sloping. d. US workers work longer hours than French workers. GDP per capita (USD PPPS)
12. As a result of a fire, a small business owner loses some of her computers and other equipment. If the property of diminishing returns applies to all factors of production, she should expect to see a. a decrease in the marginal productivity of her remaining capital and an increase in the marginal productivity of her labor. b. an increase in the marginal productivity of her remaining capital and an increase in the marginal productivity of her labor. c. an increase in the marginal productivity of her remaining capital and a decrease in the marginal productivity of her labor. d. a decrease in the marginal productivity of her remaining capital and a decrease in the marginal productivity of her labor.
1. Assume the following Cobb-Douglas production function: Y = 0.5K°.2 10 .8 If L=100, a. What is the marginal product of capital?e b. With your answer in (a), can you prove diminishing marginal product of capital?- c. Estimate real capital incomee
5. A company that produces auto parts has a production function of Q = 300 L-75 K-5. %3D If L= 250 and K= 25, what is the output of auto parts? If L increases to 350, what is the output of auto parts? What does the change in output show regarding labor as a factor of production?
Production function Capital equipment per worker ($ thousands) Which 2 of the following statements are correct? Select one or more: a. The slope of the function is the marginal product of capital. b. The figure shows that higher capital per worker increases output per worker. c. The figure shows that each extra $ of capital per worker raises output per worker by an equal amount. d. The function is "convex" (i.e., it has a slope which increases as capital per worker rises) Output per worker ($ thousands)
Suppose that production function of certain devices is determined by: q = k * L - 0.8 k2 - 0.2 L2 Where q represents annual quantity of devices produced, k represents annual quantity of capital factor, and L represents annual quantity of labor factor. (a) Suppose k = 10; draw a graph with average and total labor productivity. What is level of labor (L) factor at which average productivity reaches a maximum? How many devices are produced at that point? (b) Assuming again that k = 10, plot Marginal Product (MP) curve. At what level do we have that labor (L) factor is MP = 0? (c) Suppose capital (k) factor were to increase to k = 20. How would your previous answers change?
Table 1 - Labor and output data Units of Labor Units of Output 0 0 1 15 2 38 3 62 4 75 In Table 1, which unit of labor starts the law of “diminishing” returns? Include any equation formula if any. Answers: A. 3rd B. 4th C. 2nd D. 1st
13. A firm's only variable factor is labour and it produces a single product, X. It also has fixed costs. The short-run production function is; X-0.1L+ 6L? + 12L. Where X is the output in tons, and L is the number of persons employed. a. How many persons are employed if the average physical product of labour is maximized? b. How many persons are employed if the marginal physical product of labour is maximized? c. What is the quantity of X when average variable cost is minimized?