Chapter 3
1. a. True.
b. False. Government spending was 18% if GDP without transfers.
c. False. The propensity to consume must be less than one for our model to be well defined.
d. True. e. False.
f. False. The increase in output is one times the multiplier.
2. a. Y=160+0.6*(Y-100)+150+150
0.4Y=460-60
Y=1000
b. YD=Y-T=1000-100=900
c. C=160+0.6*(900)=700
3. a. No. The goods market is not in equilibrium. From part 2a, Demand=1000=C+I+G=700+150+150
b. Yes. The goods market is in equilibrium.
c. No. Private saving=Y-C-T=200. Public saving =T-G=-50. National saving (or in short, saving) equals private plus public saving, or 150. National saving equals investment.
4. a. Roughly consistent. C/Y=700/1000=70%; I/Y=G/Y=150/1000=15%.
b. Approximately -2%.
c. Y needs to fall by 2%, or from 1000 to 980. The parameter c0 needs to fall by 20/multiplier,
or by 20*(.4)=8. So c0 needs to fall from 160 to 152.
d. The change in c0 (-8) is less than the change in GDP (-20) due to the multiplier.
5. a. Y increases by 1/(1-c1)
b. Y decreases by c1/(1- c1)
c. The answers differ because spending affects demand directly, but taxes affect demand through consumption, and the propensity to consume is less than one.
d. The change in Y equals 1/(1-c1) - c1/(1- c1) = 1. Balanced budget changes in G and T are not macroeconomically neutral.
e. The propensity to consume has no effect because the balanced budget tax increase aborts
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the multiplier process. Y and T both increase by on unit, so disposable income, and hence consumption, do not change.
*6. a. The tax rate is less than one. b. Y=c0+c1YD+I+G implies
Y=[1/(1-c1+c1t1)]*[c0-c1t0+I+G]
c. The multiplier = 1/(1-c1+c1t1) <1/(1- c1), so the economy responds less to changes in autonomous spending when t1 is positive.
d. Because of the automatic effect of taxes on the economy, the economy responds less to changes in autonomous spending than in the case where taxes are independent of income. So output tends to vary less, and fiscal policy is called an automatic stabilizer.
*7. a. Y=[1/(1-c1+c1t1)]*[c0-c1t0+I+G]
b. T = c1t0 + t1*[1/(1-c1+c1t1)]*[c0-c1t0+I+G]
c. Both Y and T decrease.
d. If G is cut, Y decreases even more.