# UW-Madison ECON 302 - Answer Key (3 pages)

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- Pages:
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- School:
- University of Wisconsin, Madison
- Course:
- Econ 302 - Intermediate Macroeconomic Theory and Policy

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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 so 4 3 In part e NX 575 250 250 so 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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 Labor force 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 10 000 Employed 8 000 8320 8572 8 8772 512 8930 2845 9054 9247 9153 3905 9231 1785 9292 631 9341 1785 9379 531 9409 8295 9433 7653 9452 6746 9467 6129 9479 4142 9488 7372 9496 1024 9501 9209 9506 5175 9510 1488 9513 0176 9515 2839 9517 0743 9518 4887 9519 6061 9520 4888 9521 1861 9521 737 9522 1723 9522 5161 9522 7877 9523 0023 9523 1718 9523 3057 9523 4115 9523 4951 9523 5611 9523 6133 9523 6545 9523 6871 9523 7128 9523 7331 9523 7491 9523 7618 9523 7718 Unemployed 2 000 1 680 1 427 1 227 1 070 945 847 769 707 659 620 590 566 547 532 521 511 504 498 493 490 487 485 483 482 480 480 479 478 478 477 477 477 477 477 477 477 476 476 476 476 476 476 476 476 476 Unemployment rate 20 00 16 80 14 27 12 27 10 70 9 45 8 47 7 69 7 07 6 59 6 20 5 90 5 66 5 47 5 32 5 21 5 11 5 04 4 98 4 93 4 90 4 87 4 85 4 83 4 82 4 80 4 80 4 79 4 78 4 78 4 77 4 77 4 77 4 77 4 77 4 77 4 77 4 76 4 76 4 76 4 76 4 76 4 76 4 76 4 76 4 76 46 47 48 49 50 10 000 10 000 10 000 10 000 10 000 9523 7798 9523 786 9523 7909 9523 7948 9523 7979 476 476 476 476 476 4 76 4 76 4 76 4 76 4 76

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