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Textbook Site for: Economics, Fourth Edition John B. Taylor, Stanford University Parallel Problems Chapter 21: Productivity and Economic Growth The following table shows how output (shaded) depends on capital and labor. Using the table, draw the production function Y = F(L), when the capital stock (K) is 50 and when it is 100. What do you observe? Now draw the same curve when the capital stock is 150 and 200. Do you observe any difference in the resulting increase in output? Are there diminishing returns to labor and capital? Explain. Using the table from problem 1, suppose that the capital stock is 50 and the subsistence level is 8 units of output per unit labor. If the current level of the labor force is 150, explain whether the labor force and output are likely to increase or decrease as the Malthusian equilibrium is reached. If the capital stock was 100 instead of 50, the subsistence level was still 8 units of food per unit labor, and the current level of the labor force was still 150, explain whether the labor force and output would be likely to increase or decrease as the Malthusian equilibrium was reached. What does the Malthusian model implicitly assume about the number of children people will have? Draw a diagram showing the Malthusian equilibrium for an economy that subsists on rice. As a result of the current government being removed from office and replaced by a new, more food conscious government, a new crop is grown. The new crop is more nutritious than rice and so it takes fewer acres of this crop per person to stay alive. Show the new equilibrium point on the diagram and explain the adjustment to the new equilibrium. Suppose you are given the following information about productivity growth and growth of capital per hour of work for two different time periods. How much of the slowdown in productivity was due to technological change? Is there anything that the government could do to reverse this situation? Suppose a country’s capital stock is $14 trillion and a fall in government spending causes a $700 billion increase in investment. Use the growth accounting formula to determine the effect which the change in government purchases has on long-run output growth. (Assume the coefficient on capital in the growth accounting formula is 1/3.) Explain why the discussion about the former Soviet Union illustrates the importance of providing adequate incentives to enable technological change. Suppose a country has no growth in technology, the capital stock is growing at a rate of 4% per year, and the labor force is growing at a rate of 1% per year. What is the growth rate of real GDP per hour of work? Illustrate this situation on a productivity graph. Suppose a country has a capital stock which is growing at 1%, a labor force which is growing at 4%, and the growth of real GDP per hour of work is 2%. What is the growth rate of technology? of real GDP? Illustrate on a productivity graph. Suppose that capital plus depreciation as a share of aggregate income is 1/2 rather than 1/3. How does this affect the importance of the increase of capital per worker on the growth rate of real GDP per hour worked? Use the data from problem 4 to recalculate the change in technology when capital’s share, i.e., the coefficient on capital in the growth equation, is 1/2. Would these new results cause you to worry more or less about technological growth? A bookstore installs a system where customers can scan their own books and then pay by credit card. An employee by the door verifies that customers have paid for their books. An accounting agency does some restructuring which means that half of its work force can now work out of their homes. A firm which used to operate two production facilities consolidates the two operations by running the production facility 24 hours a day instead of only 12. New data has just been released which shows that there has been a drop in the growth rate of technology. Write a short memo which explains what the government can do to improve the situation. What if the data had also showed a drop in capital per hour of work? Which of the following types of government spending are likely to help economic growth? Why? FBI spending on advertising for new recruits. Spending by NASA on research for a new solar panel. Funding to improve the interstate highway system. Spending by the federal government to send all 4 year olds to pre-school. Spending by the federal government on research into alternative fuels to gasoline. Subsidies to place more artwork in public places, such as the cows in Chicago.