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Unformatted text preview: Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Homework 3 1. In 1931, Babe Ruth was the highest paid player in Major League Baseball, earning an annual salary of $80,000, an amount that was unheard of at the time. In 2007, the highest paid player in baseball was also a New York Yankee, Alex Rodriquez, who earned $27,000,000 that year. Which salary was higher in real terms? Go to the Fred database and use the Consumer Price Index for All Urban Consumers: All Items (not seasonally adjusted) for June 1931 and June 2007 to determine the value of Babe Ruth’s salary in terms of 2007 dollars. ( http://research.stlouisfed.org/fred2/categories/9 ) Problems 2 ‐ 6 refer to the “Problems and Applications” section at the end of Chapter 12 of Mankiw (p. 270). 2. 3. 4. 5. 6. 7. No. 3 No. 7 No. 8 No. 9 No. 10 Assume that the production function for the country of Longhornstan depends only on capital (K) , where A and labor (L) inputs, and is given by the Cobb‐Douglas production function: is the level of technology in Longhornstan. a. Show that this production function exhibits constant returns to scale by doubling all inputs and demonstrating that output doubles as a result. b. Show that the production function can be written in terms of output per worker (productivity), y = Y/L, and capital per worker, k = K/L. c. Assume that the labor force, L, is fixed at 100, A = 1 and α = 0.7 . Beginning at a capital stock of K = 1000, assume that the government introduces tax incentives for increased saving and investment that increase the capital stock to K = 1200. What is the increase in capital per worker, k? What is the increase in productivity, y, that results? Give an explanation for this result. d. Assume that the poorer country of Draglandia has the same values for the parameters A and α as Longhornstan, as well as the same labor force, but a lower capital stock of K = 200. Assume that the capital stock increases to K = 400. Show the increase in productivity that results. Compare this result to that for Longhornstan. Why is the increase in productivity different for the two countries, given that the increase in k is the same in both? Draw a diagram of the production function for each country on the same graph. Explain the relevance of the changes in productivity in the two countries in terms of the “catch‐up effect.” e. Beginning at the new capital stock of K = 400, assume that population growth in Draglandia increases the labor force to L = 200. Show the effect on productivity. Explain your answer. Show the effect on a diagram of the production function for Draglandia. f. Now assume that a technological breakthrough improves manufacturing methods in Longhornstan resulting in an increase in A. Show the effect of this increase on a diagram of Longhornstan’s production function. ...
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This note was uploaded on 12/17/2010 for the course ECO 33530 taught by Professor Sadler during the Spring '10 term at University of Texas at Austin.
- Spring '10