Chapter 3 National Income: Where It Comes From and Where It Goes c. If the marginal productivity of barbers is unchanged, then their real wage is unchanged d. The real wage in(c)is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a hair cut e. If workers can move freely between being farmers and being barbers then they must be paid the same wage w in each sector. f. If the nominal wage w is the same in both sectors but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods g. Both groups benefit from technological progress in farming 4. The effect of a government tax increase of $100 billion on(a) public saving, (b)private saving, and(c)national saving can be analyzed by using the following relationship National Saving =[Private Saving]+[Public Saving] TY-T-c(Y-T)+IT-GI Y-C(Y-T)-G a. Public Saving-The tax increase causes a l-for-l increase in public saving. T increases by $100 billion and, therefore, public 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 x $100 billion, or $60 billion. Hence APrivate Saving=-$1006-06(-$1006)=-$406 Private saving falls $40 billion c. National Saving-Because national saving is the sum of private and public sav ing, we can conclude that the $100 billion tax increase leads to a $60 billion increase in national savin 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 bil lion. 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-⑦)-G=I(r). The left-hand side of this equation is national saving, so the equation just says the national saving equals investment. Since national saving increases by $60 billion investment must also increase by $60 billionc. If the marginal productivity of barbers is unchanged, then their real wage is unchanged. d. The real wage in (c) is measured in terms of haircuts. That is, if the nominal wage is in dollars, then the real wage is W/PH, where PH is the dollar price of a hair￾cut. e. If workers can move freely between being farmers and being barbers, then they must be paid the same wage W in each sector. f. If the nominal wage W is the same in both sectors, but the real wage in terms of farm goods is greater than the real wage in terms of haircuts, then the price of haircuts must have risen relative to the price of farm goods. g. Both groups benefit from technological progress in farming. 4. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c) national saving can be analyzed by using the following relationships: National Saving = [Private Saving] + [Public Saving] = [Y – T – C(Y – T)] + [T – G] = Y – C(Y – T) – G. a. Public Saving—The tax increase causes a 1-for-1 increase in public saving. T increases by $100 billion and, therefore, public 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. Hence, ∆Private Saving = – $100b – 0.6 ( – $100b) = – $40b. Private saving falls $40 billion. c. National Saving—Because national saving is the sum of private and public sav￾ing, 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 bil￾lion. 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). The left-hand side of this equation is national saving, so the equation just says the national saving equals investment. Since national saving increases by $60 billion, investment must also increase by $60 billion. Chapter 3 National Income: Where It Comes From and Where It Goes 13