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


Chapter 4

Numerical

1.   Y / Y = C / Y + I / Y + G / Y

       I / Y  = a - .02R

      a)    Y/Y = C/Y + I/Y + G/Y = 1.0
           
Since C/Y does not depend on R, I/Y must adjust enough to offstet the fall in G/Y.   Therefore I/Y must
            rise by 4% of GDP from its original level.

      b)    Since I/Y rises by 2% for every 1% decrease in R, it is necessary for R to fall by 2%.

      c)    The growth accounting formula is given by DY/Y = DA/A + .3DK/K + .7DN/N. If K/Y is initially 2, then
            K = 2Y.   If I/Y increases by 4%, then I/K will have increased by 2%.   Since I =
DK, the increased share
            of investment in GDP leads to an increase in the growth rate of real GDP equal to .3
DK/K = .3(.02) = .006,
           
or .6%.

2.   a)    1000 = [.3(4000) - 4000(.05)]P
                      = (1200 - 200)P
                   1 = P.

      b)    1100 = 1000P
                1.1 = P.
              10% change in M and P.

      c)             1000 = [1200-4000(.10)]P
              1000/800 = P
                      1.25 = P.
            Interest rates increase due to an increase in government spending.

      d)             1000 = [.3(4500) - 200]P
            1000/1500 = P
                        .87 = P.

Analytical.

2.   a)    Output increases due to increased labor input.

      b)    Output increases due to improvement in technology.

      c)    Output is unchanged; only price level changes.

      d)    Output is unchanged initially, but C crowds out some I.

6.   a)    Both the investment spending and nongovernment spending schedules shift down.

      b)    If no other spending component were related to R, then R would fall enough to restore I to its
             original level.

      c)    If the fall in interest rates increases net exports and investment, then the decline in R will crowd
             in some of each.   I will not return to its original level, but X will be higher than it was initially.


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