CALIFORNIA STATE UNIVERSITY, SACRAMENTO
Department of Economics

Economics 100A
Prof. Yang

Solutions to Homework Problems                     Chapter:  1  2  3  4  5   6  7  8  9  12


Chapter 12

Numerical

1. a) Endogenous: Y, C, I, X, R, E
        Exogenous: G, M, P, Pw.

    b) Y = C + I + G + X
            = (220 + .63Y) + (400 - 2000R + .1Y) + G +
                [600 - .1Y - 100(.75 + 5R)]
            = 1145 + .63Y - 2500R + G, or,
        IS: R = .458 - .000148Y + .0004G.
            Also, as before,
        LM: R = .0001583Y - .001M/P.
            Solving the IS and LM equations for R and Y gives
        AD: Y = 1495.2661 + 1.30591G + 3.26477M/P.
            So, if G = 1200, M = 900, and P = 1, then
        Y =  6000.65, C = 4000.41, R = .0499 = 4.99%, I = 900.25, X = -100.02, E = .9995.

    c) Use the already derived AD equation above.  When G = 1200 and M = 900, the AD equation becomes

        Y = 3062.3581 + 2938.293/P.

    d) If G decreased by $10 billion, according to the AD equation, national income Y will decrease
        by $13.059 billion. So the new level of nationa income will be Y = $5987.59.  Using the LM equation and
        the new value of Y adn remembering that M/P = 900, the new value of R can be found.  R = .0478 = 4.78%.
        Using the new values of Y and R, the new values of C, I, X, and E can be obtained. C = 3992.18, I = 903.09,
        X = -97.59, and E = .9892.  Notice that the sum of C, I, G, and X is $5987.68, which is approximately equal
        to Y = $5987.59.
        If money supply M increase by $20, then Y would increase by $65.30 billion; the new value of Y would
        be $6065.95 billion.  The value of the remaining endogenous variables can also be calculated.
        C = 4041.55, R = .0402 = 4.02%, I = 926.12, E = .9512, and X = -101.71.  Notice that
        C + I + X + G = 6065.95, which is the same as the value of new Y.

5.    a) This economy is more open because net exports are more sensitive to the terms of trade, and terms
           of trade are more sensitive to domestic interest rates, so adjustments heppen more quickly.

        b) First derive the IS, LM and AD equations:
            Y = C + I + G + X
                = (220 + .63Y) + (400 - 2000R + .1Y) + G +
                = [900 - .1Y - 400(.50 + 10R)]
                = 1320 + .63Y - 6000R + G, or
            IS: R = .22 - .00006167Y + .000167G
                Also, as before,
            LM: R = .0001583Y - .001M/P
                Solving the IS and LM equations for R and Y gives
            AD: Y = 1000.1515 + .75769G + 4.54614M/P

            Usng the new equations of IS, LM, AD, and the Phillips curve gives the following result for the case when
            the money supply increases by $10 billion to $910 billion:

                    Year                     0                     1                 Long Run

                    M                     900                 910                       910
                    G                     1200               1200                      1200
                    P                      1.000              1.000                     1.011
                    Y                     6000.91         6046.37                 6000.91
                    R(%)                 4.99                 4.71                     4.99
                    C                     4000.57         4029.21                 4000.57
                    I                         900.20          910.36                   900.20
                    X                     -100.03            -93.20                  -100.03
                    E                       .9994              .9714                     .9884

            And, when government spending increases by $10 billion to reach $1210 billion, the following will result:

                    Year                     0                     1                 Long Run

                    M                     900                 900                       900
                    G                     1200               1210                      1210
                    P                      1.000              1.000                     1.002
                    Y                     6000.91         6008.49                 6000.91
                    R(%)                 4.99                 5.11                     5.16
                    C                     4000.57         4005.35                 4000.57
                    I                         900.20          898.42                   896.87
                    X                     -100.03            -105.42                  -106.53
                    E                       .9994              1.0114                     1.0142


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