DETAILED ANSWERS

In the matrix below, each coefficient refers to the number of units of product j produced in country i in one person-day of labor. aij Shoes Wheat U.S. 4 6 Spain 2 2 (a) Assume both economies are at full employment so that producing more of one good requires reallocating labor from the other good. In a world without trade, if the U.S. wants four more shoes, how many bushels of wheat will it have to give up? If Spain wants four more shoes, how many bushels of wheat will it have to give up? (b) Calculate a trade proposal in which the U.S. offers X bushels of wheat to Spain in exchange for 4 shoes. Your calculated offer should be such that the U.S. loss of wheat is less than if it produced the 4 extra shoes domestically and that Spain is left with at least as many shoes and at least as much wheat as it had before trade?i.e. both countries are better off. (c) In the spirit of the Simon chapter, develop a parallel example where humans and machines take the place of the U.S. and Spain and show how specialization increases total output in the economy. 2. In Table 2 of Alan Krueger's article "Have Computers Changed the Wage Structure?" he shows that, after controlling for the effects of age, education, etc., persons who work with a computer earn a premium of about .18 in the natural log of their wage (the dependent variable of the regression). This translates into about a 20% premium in their actual wage. (a) How would the advertising people who develop Dell commercials like to interpret this coefficient? (b) Give several reasons why the Dell interpretation in (a) may be wrong. (c) Explain why, in Table 2, the coefficient on "uses computer at work" drops in value from .276 (in column 1) to .17 (in column 2) when controlling for things like education, experience, gender, etc. (d) Given plenty of resources, how would you design an appropriate experiment to estimate the correct value of the coefficient (i.e. the causal parameter) Krueger has estimated? 3. Since you have all done at least a little programming, you know it is reasonable to think of a computer as a machine that executes rules. ? Some of these rules are arithmetic rules - i.e. 6x3 = 18. ? Others are logical rules - i.e. If [x(i) ? 15.0] Go to 35. (a) Using rules, write out as completely as you can the process of issuing an airline boarding pass to a passenger - in other words, the software that drives the kiosks for self-service check-in at most airports. (b) In footnote 6 of "The Corporation.....", Simon writes: "This example will seem entirely fanciful only to persons not aware of some of the research now going on into the possible automation of psychiatric processes." The most famous example of a computerized psychiatrist is Eliza, a program to mimic a Rogerian psychoanalyst written in the 1970s by Joe Weizenbaum, now an emeritus professor in Course VI. Go to: http://www.manifestation.comeurotoys/eliza.php3 and have a 10 or 15 line conversation with Eliza. Based on your conversation describe as well as you can the structure of Eliza's software. Then think about what you know about psychotherapy - what you have read, any first hand experience - and describe the information processing done by a human psychotherapist likely differs from the information processing in Eliza. 4. Consider the following definition of skill: "The more years of training an occupation requires, the more skilled it is." For the occupations listed below, do the following: (a) Classify them as "high-skill" or "low-skill" based on this definition. (b) Write down another definition of skill (you can pick one discussed in class) and re-classify these occupations according to that definition. Does the classification change?

3. Solow Growth Model with Technological Progress State the basic assumptions of the Solow model with technological change and derive expression for income per worker y(t) in the steady state of this model. Use the Solow diagram to explain why the economy converges to its steady state. 7. In the Solow growth model of an economy with population growth but no technological change, if population grows at rate a, then capital in the steady state grows at rate and output grows at rate in the steady state. A) n; n B) n; 0 C) 0; 0 D) 0; n 8. In the Solow growth model, capital exhibits growth model, capital exhibits returns. A) constant; diminishing B) constant; constant C) diminishing; constant D) diminishing; diminishing returns. In the basic endogenous MORE EXERCISES 1. Transition dynamics: What is the principle of transition dynamics in the com- bined Solow-Romer model? 2. Long-run growth: Growth in the combined Solow-Romer model is faster than growth in the Romer model. In what sense is this true? Why is it true? 3. Balanced growth: Suppose we observe the following growth rates in various economies. Discuss whether or not each economy is on its balanced growth path. (a) A European economy: gy/L = 0.03, gKIL = 0.03. (b) A Latin American economy: gy/L = 0.02, gKIL = 0.01. (c) An Asian economy: gy/L = 0.06, gKIL = 0.15. 4. Transition dynamics in the combined Solow-Romer model: Consider the com- bined model studied in this appendix. Suppose the economy begins on a bal- anced growth path in the year 2000. Then in 2030, the depreciation rate d rises permanently to the higher level d'. (a) Graph the behavior of output per person over time, using a ratio scale. (b) Explain what happens to the growth rate of output per person over time and why. 5. The combined Romer-Solow model (1): Make one change to the basic combined model that we studied in this appendix: let the production function for outputMORE EXERCISES 1. Transition dynamics: What is the principle of transition dynamics in the com- bined Solow-Romer model? 2. Long-run growth: Growth in the combined Solow-Romer model is faster than growth in the Romer model. In what sense is this true? Why is it true? 3. Balanced growth: Suppose we observe the following growth rates in various economies. Discuss whether or not each economy is on its balanced growth path. (a) A European economy: gy/L = 0.03, gKIL = 0.03. (b) A Latin American economy: gy/L = 0.02, gKIL = 0.01. (c) An Asian economy: gy/L = 0.06, gKIL = 0.15. 4. Transition dynamics in the combined Solow-Romer model: Consider the com- bined model studied in this appendix. Suppose the economy begins on a bal- anced growth path in the year 2000. Then in 2030, the depreciation rate d rises permanently to the higher level d'. (a) Graph the behavior of output per person over time, using a ratio scale. (b) Explain what happens to the growth rate of output per person over time and why. 5. The combined Romer-Solow model (1): Make one change to the basic combined model that we studied in this appendix: let the production function for outputHuman Capital: Our textbook points out that human capital is not included in the simple model of production but that it could be an important factor in explaining why the marginal product of capital differs among countries. 1. Consider a Cobb-Douglas production function with three inputs: Y = KiLiHi, (1) where K is capital, L is labor, and H is human capital. What is the marginal product of capital (MPK) implied by this production function? 2. Is MPK increasing in human capital or decreasing? 3. Use this model to explain why capital may flow from poor to rich countries. 4. Is the return to education higher or lower in countries with scarce capital