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### Assignment 4

Course: ECON 3140, Fall 2006
School: Cornell
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Word Count: 337

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314 Macroeconomics Assignment 4 Numerical Problems: 3. a. Year 1 2 3 4 K 200 250 250 300 N 1000 1000 1250 1200 Y 617 660 771 792 Capital-Labor Ratio 0.2 0.25 0.2 0.25 Output/Worker 0.617 0.66 0.617 0.66 Although the total output increases from year 1 to year 3, the capital-labor ratio and output per worker remain constant. The same holds true for year 2 and year 4. Production function per worker: b. Year 1 2 3 4...

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314 Macroeconomics Assignment 4 Numerical Problems: 3. a. Year 1 2 3 4 K 200 250 250 300 N 1000 1000 1250 1200 Y 617 660 771 792 Capital-Labor Ratio 0.2 0.25 0.2 0.25 Output/Worker 0.617 0.66 0.617 0.66 Although the total output increases from year 1 to year 3, the capital-labor ratio and output per worker remain constant. The same holds true for year 2 and year 4. Production function per worker: b. Year 1 2 3 4 K 200 250 250 300 N 1000 1000 1250 1200 Y 1231 1316 1574 1609 Capital-Labor Ratio 0.2 0.25 0.2 0.25 Output/Worker 1.231 1.316 1.259 1.341 y=(K^0.3*N^0.7)/N The total output increases from year 1 to year 3, and the capital-labor ratio and output per worker slightly increase. The same holds true for year 2 and year 4. Production function per worker: y=(K^0.3*N^0.8)/N 5. a. y=f(k)=3k^.5 S=0.3Y s=0.3 n=0.05 d=0.01 (n+d)k=0.15k=sf(k)=0.3*3k^.5 k=36 y=18 c=f(k)-(n+d)k=12.6 b. .15k=.4*3k^.05 k=64 y=24 c=14.4 c. .18k=.3*3k^.05 k=25 y=15 c=10.5 d. .15k=.3*4k^.05 k=64 y=32 c=22.4 Analytical Questions: 1. a. In the long run consumption per worker would be unaffected, because it is a one time loss of capital. b. Consumption decrease, would because more output must be invested in capital for the new workers. c. Consumption would decrease, because productivity would be decreased. d. Long run consumption would increase due to increased capital-stock. e. Consumption would remain constant, because the working population growth rate remains constant despite the one time increase. 3. a. b. Consumption would rise in the short run. However, its steady state along with those of capital per worker and output per worker would fall, due to the lower saving rate. This implies that the optimal level of government purchases is zero. However, this does not account for purchases that lead to productivity growth. 5. Assuming that both countries have capital-ratios below the steady state, the country with the lower capital-ratio will have a faster growing total output. If either of the countries reaches a steady state its output growth will stop. If the two countries are allowed to trade with each other, the country with the lower capital ratio will experience an increase its rate of output growth, because it offers higher returns on investment in capital.
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