1. The effect of a government tax increase of $100 billion on (a) government saving, (b) private saving, and
(c) national saving can be analyzed by using the following relationships:
National Saving =
+ [Government Saving]
= [Y – T – C(Y – T)] + [T – G]
= Y – C(Y – T) – G.
a. Government Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100 billion and, therefore, government saving increases by $100 billion.
b. Private Saving—The increase in taxes decreases disposable income, Y – T, by $100 billion. Since the marginal propensity to consume (MPC) is 0.6, consumption falls by 0.6 ×$100 billion, or $60 billion.
Private Saving = – $100b – 0.6 ( – $100b) = – $40b.
c. National Saving—Because national saving is the sum of private and public saving, we can conclude that the $100 billion tax increase leads to a $60 billion increase in national saving. Another way to see this is by using the third equation for national saving expressed above, that national saving equals Y – C(Y – T) – G.
The $100 billion tax increase reduces disposable income and causes consumption to fall by $60 billion.
Since neither G nor Y changes, national saving thus rises by $60 billion.
d. Investment—To determine the effect of the tax increase on investment, recall the national accounts identity: Y = C(Y – T) + I(r) + G.
Rearranging, we find
Y – C(Y – T) – G = I(r)
National Saving = I(r)
The left-hand side of this equation is national saving, so the equation just says that national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion.
2. a. Private saving is the amount of disposable income, Y – T, that is not consumed:
= Y – T – C(Y – T) = Y – T – MPC(Y – T)
= 5,000 – 1,000 – (250 + 0.75(5,000 – 1,000))
Public saving is the amount of taxes the government has left over after it makes its purchases:
Public (Government) Saving = T – G
= 1,000 – 1,000
Total saving is the sum of private saving and public saving, which will be 750.
b. The equilibrium interest rate is the value of r that clears the market for loanable funds. We already know that national saving is 750, so we just need to set it equal to investment:
750 = 1,000 – 50r
Solving this equation for r we find r = 5%.
c. When the government increases its spending, private saving remains the same as before (notice that G does not appear…