Economics 302 Spring 2007 Answer Key: Homework 3 1. a. Y = 2000. C = 1375. S = 2000-1375-700 = -75. Using the condition S=I implies r=21.5. The graph is the standard one used in section: national savings is a vertical line, the investment demand function is linear, downward sloping and crosses the y-axis at I =1000. b. In an open economy, the domestic interest rate will equal the world interest rate. The assumption needed to get this is that of perfect capital mobility. Under perfect capital mobility and a world interest rate r*, domestic firms would never pay a domestic investor more than r*, since it could always get a cheaper loan on the international capital market. At the same time, a domestic investor would never lend to a firm at less than r*, since it could always lend its money to a foreign firm and earn return r*. Thus, the equilibrium domestic interest rate with a small open economy must have r=r*. The appropriate graph should demonstrate that it is the interest rate r=5% which is fixed first. Given this, you can find I(r) from the investment demand curve. Compare this with national income, S, to get the trade balance. c. National savings will be S = Y-C-G = -75. (Under the assumptions of our Classical model, national savings is unaffected by the real interest rate.) d. Given r=5%, I(5) = 750. so I=750>-75=S. This means that the country is investing domestically more than it is saving domestically. Thus, capital must be flowing in from somewhere else. Also NX=S-I=-825<0. e. A world war causes a significant fraction of world governements to spend more and save less (run deficits). Thus, world savings falls. Assuming that the world demand for investment is unchanged (or perhaps increases) then the world interest rate will increase. The “shock” thus has the affect of moving Cowtopia’s domestic interest rate to 10%, as it was in part a. Thus, its trade balance is -575. So it is still negative, just less so. f. In part d, NX=-825=250 – 250 ε, so ε=4.3. In part e, NX= -575 = 250 – 250 ε, so ε=3.3. 2. a. The natural rate of unemployment is s/(s+f) = 4.76%. b, c and d. (see the spreadsheet below). The formula simply calculates the employment rate next period given that fraction s of all employed workers lose their job, thus fraction (1-s) of all employed workers stay employed. At the same time, fraction f of all unemployed find a job. Thus, the formula tells the number of workers who will be employed at the beginning of the next period. As seen in the “unemployment rate” column below, the unemployment rate “converges” to the natural rate of unemployment. Converge is just a fancy way of saying that the numbers get closer and closer to the value to which they are “converging”. Notice that, given the rates s and f fixed, the unemployment rate, starting from some arbitrary level, changes each period by some amount. However, the amount that it changes by diminishes as it gets closer and closer to the steady state. In fact, if it started at the steady state, it wouldn’t change at all. Thus, the name steady state.Year Labor force Employed UnemployedUnemployment rate 0 10,000 8,000 2,000 20.00%1 10,000 8320 1,680 16.80%2 10,000 8572.8 1,427 14.27%3 10,000 8772.512 1,227 12.27%4 10,000 8930.2845 1,070 10.70%5 10,000 9054.9247 945 9.45%6 10,000 9153.3905 847 8.47%7 10,000 9231.1785 769 7.69%8 10,000 9292.631 707 7.07%9 10,000 9341.1785 659 6.59%10 10,000 9379.531 620 6.20%11 10,000 9409.8295 590 5.90%12 10,000 9433.7653 566 5.66%13 10,000 9452.6746 547 5.47%14 10,000 9467.6129 532 5.32%15 10,000 9479.4142 521 5.21%16 10,000 9488.7372 511 5.11%17 10,000 9496.1024 504 5.04%18 10,000 9501.9209 498 4.98%19 10,000 9506.5175 493 4.93%20 10,000 9510.1488 490 4.90%21 10,000 9513.0176 487 4.87%22 10,000 9515.2839 485 4.85%23 10,000 9517.0743 483 4.83%24 10,000 9518.4887 482 4.82%25 10,000 9519.6061 480 4.80%26 10,000 9520.4888 480 4.80%27 10,000 9521.1861 479 4.79%28 10,000 9521.737 478 4.78%29 10,000 9522.1723 478 4.78%30 10,000 9522.5161 477 4.77%31 10,000 9522.7877 477 4.77%32 10,000 9523.0023 477 4.77%33 10,000 9523.1718 477 4.77%34 10,000 9523.3057 477 4.77%35 10,000 9523.4115 477 4.77%36 10,000 9523.4951 477 4.77%37 10,000 9523.5611 476 4.76%38 10,000 9523.6133 476 4.76%39 10,000 9523.6545 476 4.76%40 10,000 9523.6871 476 4.76%41 10,000 9523.7128 476 4.76%42 10,000 9523.7331 476 4.76%43 10,000 9523.7491 476 4.76%44 10,000 9523.7618 476 4.76%45 10,000 9523.7718 476 4.76%46 10,000 9523.7798 476 4.76%47 10,000 9523.786 476 4.76%48 10,000 9523.7909 476 4.76%49 10,000 9523.7948 476 4.76%50 10,000 9523.7979 476
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