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1、C. A technological advance improves the production function.Problem 2: If a 10-percent increase in both capital and labor causes output to increase by less than 10 percent, the production function is said to exhibit decreasing returns to scale. If it causes output to increase by more than 10 percent

2、, the production function is said to exhibit increasing returns to scale. Why might a production function exhibit increasing or decreasing returns to scale?Problem 3: Suppose that an economys production function is Cobb-Douglas with parameter alpha=0.3. 3.3A. What fractions of income do capital and

3、labor receive?3.3B. Suppose that immigration raises the labor force by 10 percent. What happens to total output （in percent）? The rental price of capital? The real wage? 3.3C. Suppose that a gift of capital from abroad raises the capital stock by 10 percent. What happens to total output （in percent）

4、?3.3D. Suppose that a technological advance raises the value of the parameter A by 10 percent. What happens to total output （in percent）?Problem 4.: Empirically the trend in the real wage closely tracks the trend in labor productivity. Explain why?Problem 5. A. Over the past century, the productivit

5、y of farmers has risen substantially because of technological progress. According to the neoclassical theory, what should have happened to their real wage? B. Over the same period, the productivity of barbers has remained constant. Suppose workers can move freely between farmers and being barbers. W

6、hat does this mobility imply for the wages of farmers and barbers? C. What do your previous answers imply for the price of haircuts relative to the price of food? D. Who benefits from technological progress in farming farmers or barbers?Problem 6.: （Harder） Consider a Cobb-Douglas production functio

7、n with three inputs. K is capital （the number of machines）, L is labor （the number of workers）, and H is human capital （the number of college degrees among the workers）. The production function is:Problem 6A. Derive an expression for the marginal product of labor. How does an increase in the amount

8、of human capital affect the marginal product of labor?Problem 6B. Derive an expression for the marginal product of human capital. How does an increase in the amount of human capital affect the marginal product of human capital?Problem 6C. What is the income share paid to labor? What is the income sh

9、are paid to human capital? In the national income accounts of this economy, what share of total income do you think workers would appear to receive? （Hint: Consider where the return to human capital shows up.）Problem 6D. An unskilled workers earns the marginal product of labor, whereas a skilled wor

10、ker earns the marginal product of labor plus the marginal product of human capital. Using your answers to （a） and （b）, find the ratio of the skilled wage to the unskilled wage. How does an increase in the amount of human capital affect this ratio? Explain.Problem 6E. Some people advocate government

11、funding of college scholarships as a way of creating a more egalitarian society. Others argue that scholarships help only those who are able to go to college. Do your answers to the preceding questions shed light on this debate? THE LABOR MARKET Consider an economy with the following Cobb-Douglas pr

12、oduction function:. The economy has 1000 units of capital and a labor force of 1000 workers.A. Derive the equation describing the labor demand in this economy as a function of the real wage and the capital stock. B. If the real wage can adjust to equilibrate labor supply and labor demand, what is th

13、e real wage? In this equilibrium, what is employment, output, and the total amount earned by workers? C. Assume that a minimum wage of 1 dollar is imposed by Congress. What happens to employment, output, and the total amount earned by workers. D. Did the minimum wage help the working class in this e

14、xample? Suppose that a country experiences a reduction in productivity （A）;A.What happens to the labor demand curve?B.What is the effect on employment, unemployment and the real wage if we assume perfect competition? Assume that the labor supply curve is vertical.C.How would this change in productiv

15、ity affect employment if unions prevent the real wage from falling?TOPICS 1 and 3: GROWTH ACCOUNTING （“TILLVXTBOKFRING”） AND GROWTH RATES In an economy which is characterized by perfect competition in the goods and labor market, the owners of capital get two-thirds of national income, and the worker

16、s receive one-third. Assume a Cobb-Douglas aggregate production function.Problem 1A: The men stay at home in this economy, while the women work in factories. If some of the men started working outside the home so that the labor force increased by 5 percent, what would happen to the measured output o

17、f the economy? Does labor productivity （output per worker） increase, decrease or stay the same? Does total factor productivity （A） increase, decrease, or stay the same?Problem 1B: In year 1, the capital stock was 6, the labor input was 3, and output was 12. In year 2, the capital stock was 7, the la

18、bor input was 4, and output was 14. What happened to total factor productivity between the years? Assume an economy which is characterized by perfect competition in the goods and labor market, in which the owners of capital get one-third of national income, and the workers receive two-thirds. Assume

19、 a Cobb-Douglas aggregate production function.Assume that total output and total capital stock grow at 3.6 percent per year, and that labor input grows by one percent per year. Use the growth-accounting equation to divide output growth into three sources capital, labor, and total factor productivity

20、 how much of output growth would you attribute to each source?Problem 4. If GDP per capita in Sweden （in 1995 prices） in 1995 and 2000 were 194 and 222 thousands of kronor, what was the average annual rate of economic growth during this 5-year period?Problem 5. If a variable during a 30-year period

21、increases by 54 percent, what average annual growth rate does this correspond to?Problem 6. If the growth rate of GDP per capita was 2 percent between 1960 and 1990, and the population growth rate was 3 percent during the same period, what was the growth rate of GDP during this period?Problem 7: Ass

22、ume that GDP per capita in Sweden and Zambia in 2002 were 16000 and 800 USD, respectively, and that the growth rate of GDP per capita in Sweden and Zambia is 1 and 7 percent, respectively.a） How does the absolute difference between the 2 countries develop over time?That is, GDP per capita in Sweden

23、GDP per capita in Zambia.b） How does the relative difference develop over time?That is, GDP per capita in Sweden/GDP per capita in Zambia.You may want to use EXCEL to answer these questions.Problem 8: If your wage is 100 kronor and the growth rate is 5 percent, how many years does it take for your w

24、age to double?TOPIC 4: ECONOMIC GROWTH THEORY: THE SOLOW MODELProblem 00: Show in the Solow-diagram and explain in words:A. The effect of an increased saving rate on the steady-state levels of production per worker （Y/L）, capital per worker （K/L）, and the real wage （W/P）.B. The effect of a lower pop

25、ulation growth rate on the steady-state levels of production per worker （Y/L）, capital per worker （K/L）, and the real wage （W/P）.C. The effect of a better technology on the steady-state levels of production per worker （Y/L）, capital per worker （K/L）, and the real wage （W/P）.Problem 01A. In the long-

26、run equilibrium, assume that the long-run population growth rate is 2 percent （that is, n=0.02）, and the long-run growth rate of A is 0 percent （that is, g=0）, calculate the long-run equilibrium growth rate of Y, （Y/L）, K, （K/L）, and the real wage （W/P）.Problem 01B. In the long-run equilibrium, assu

27、me that the long-run population growth rate is 2 percent （that is, n=0.02）, and the long-run growth rate of A is 2 percent （that is, g=0.02）, calculate the long-run equilibrium growth rate of Y, （Y/L）, K, （K/L）, and the real wage （W/P）.Quantitative questions on the Solow Model: Country A and B has t

28、he production function:A. Does this production function have constant returns to scale?B. What is the per-worker production function, Y/L=f（K/L）C. Assume that neither country experiences population growth or technological progress and that 5 percent of capital depreciates each year. Assume further t

29、hat country A saves 10 percent of output each year, and country B saves 20 percent of output each year. Find the steady state level of capital per worker, the steady-state level of income per worker and consumption per worker.D. Suppose that both countries start off with a capital stock per worker o

30、f 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is gross investment minus depreciation, calculate capital stock per worker, income per worker, and consumption per worker over time. How many years will it be before consumption per worker in Country B is higher than the level of consumption per worker in country A.In the discussion of German and Japanese postwar growth, the text describes what happens when part of the capital stock is destroyed in a war. By contrast, suppose that a war does not affect the capital s