HW4 Solutions Essay

HW4 Solutions Essay HW4 Solutions Essay HW4 Solutions 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 Ãâ€"ï€  $100 billion, or $60 billion. Hence, 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)) = 750. 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 = 0. 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: S =I 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