MORE EXERCISES.
1.
Consider the following long-run model:
Real GDP (Y) = 1,000 Consumption (C) = 100 + 0.8 (Y-T)
Investment (I) = 300 -40r  where r is the real interest rate.
Taxes (T) are 120 and government spending (G) is 130

a) Compute consumption, private savings, public savings, national savings, investment, the real interest rate.
b)  If government expenditure increases to 150, what are the new equilibrium values for consumption, private savings, public savings and national savings?
c)  If taxes are reduced to 100 (and G=130), would your answers be the same in (b) since the effects on public savings is the same?
 

2. Use the same model as in (1), except let C= 130 + .8(Y-T) - 5r
a) Derive an equation for private savings showing how private savings depend on disposable income and the real interest rate.
b) Derive an equation for national savings (in the same way as in (a)).
c) Compute consumption, private savings, public savings, national savings, investment, the real interest rate.
d)  If government expenditure increases to 150, what are the new equilibrium values for consumption, private savings, public savings and national savings?
e)  If taxes are reduced to 100 (and G=130), would your answers be the same in (b) since the effects on public savings is the same?
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ANSWERS:
1. a)  C=804, Spr=76, Spu=-10, Snat=66, I=66, r=5.85%
    b) C=804, Spr=76, Spu=-30, Snat=46, I=46, r=6.35%
    c) C=820, Spr=80, Spu=-30, Snat=50, I=50, r=6.25%.  Note that despite the effects on the public savings being the same in this case compared to (b), consumption and private savings change because of changes in disposable income (since taxes were changed).  Since private savings increase now (but not in (b)), the reduction in national savings is not as great, which means the interest rate doesn't increase by as much.  In this case, the interest rate changes by 0.4% (from 5.85 to 6.25) whereas in (b) the change was 0.5% (from 5.85 to 6.35).

2.  a) Since Spr = (Y-T)-C, substitute the Consumption function in for "C" and you'll get:  Spr = -130+0.2(Y-T) + 5r
     b) Snat = Spr + Spu => Snat = (T-G) + Spr  or Snat = -140 + 0.2(Y-T) + 5r
     c)  C=804.7, Spr=75.3, Spu=-10, Snat=65.3, I=65.3, r=5.87%
     d)  C=802.4, Spr=77.6, Spu=-30, Snat=47.6, I=47.6, r=6.31%   (r changes by .44, from 5.87 to 6.31).
            Note that consumption decreases since the real interest rate is increasing (r is in the consumption function).
     e)  C=818.9, Spr=81.1, Spu=-30, Snat=51.1, I=51.1, r=6.22%   (r changes by .36, from 5.87 to 6.22).
           In this case (compared to (d)), the real interest does not increase by as much since tax cuts increase private savings.