1. Ch3: National Income: Where it Comes From and Where it Goes Mankiw: Macro Ch 3 Mankiw: Econ Ch24, Ch26 Varian: Ch10, Ch19, Ch29 Williamson: Ch 7

2. Learning Objectives  what determines the economy ’ s total output/income  how the prices of the factors of production are determined  how total income is distributed  what determines the demand for goods and services  how equilibrium in the goods market is achieved

3. Outline of model A closed economy, market-clearing model Three markets Labor market: MP L =W/P Goods market:Y S = Y d (Financial market) Loanable funds market: S=I Aggregate Supply side AS=Y S =Production function Aggregate Demand side AD=Y d =C+ I + G

4. Aggregate Supply Side: The production function  describe relationship between inputs and output.  Real Output (Y ，這章定義為大寫 )  Inputs: factors of production 生產要素  Y = F(K, L) K =capital: tools, machines, and structures L = labor: physical and mental efforts of workers  F( ● ) reflects the economy ’ s level of technology  Assumes constant returns to scale

5. Returns to scale: Initially Y 1 = F (K 1, L 1 ) Scale all inputs by the same factor z: K 2 = zK 1 and L 2 = zL 1 (e.g., if z = 1.25, then all inputs are increased by 25%) What happens to output, Y 2 = F (K 2, L 2 )?  If constant returns to scale, Y 2 = zY 1  If increasing returns to scale, Y 2 > zY 1  If decreasing returns to scale, Y 2 < zY 1

6. Examples

7. The distribution of national income  determined by factor prices, the prices per unit that firms pay for the factors of production wage = price of L ren tal rate = price of K

8. Notation W = nominal wage Re= nominal rental rate P = price of output W /P = real wage (measured in units of output) Re /P= real rental rate W = nominal wage Re= nominal rental rate P = price of output W /P = real wage (measured in units of output) Re /P= real rental rate

9.  = change in a variable   X = “ the change in X ” Marginal Product of Labor: Marginal Product of Capital: Diminishing marginal returns: diminishing MP L Suppose L while holding K fixed  fewer machines per worker  lower worker productivity

10. Y output Fig 3.3: MP L ( K fixed ) Diminishing marginal returns L labor 1 MP L 1 1 As more labor is added, MP L  Slope of the production function equals MP L

11. Eg,  Which of these production functions have diminishing marginal returns to labor?

12. Determination of factor prices Varian: 19.7-19.9 and Appendix  Factor prices are determined by supply and demand in factor markets.  Assume: Supply of each factor is fixed.  Assume markets are competitive: each firm takes W, Re, and P as given.

13. Demand for labor benefit = MP L cost = real wage A firm hires each unit of labor if the cost does not exceed the benefit.

14. Fig 3.4: MP L = Demand for labor Each firm hires labor up to the point where MP L = W/P. Units of output Units of labor, L MP L, Labor demand Real wage Quantity of labor demanded

15. Labor Market: the equilibrium real wage Units of output Units of labor, L MP L, Labor demand equilibrium real wage Labor supply

16. Determining the rental rate MP K = Re/P :  diminishing returns to capital: MP K  as K   Firms maximize profits by choosing K such that P ． MP K = Re.  MP K curve is firm ’ s demand curve for renting capital. (for one-time decision)

17. Neoclassical Theory of Distribution total labor income = If production function has CRS, total capital income = labor income capital income national income

18. The ratio of labor income to total income in the U.S. Labor’s share of total income Labor’s share of income is approximately constant over time. (Hence, capital’s share is, too.)

19. Taiwan data: labor share

20. Cobb-Douglas Production Function A: the level of technology. (A is exogenous) Each factor ’ s marginal product is proportional to its average product.

21. C-D Production Function  C-D production function has constant factor shares: capital income = MP K x K =  Y labor income = MP L x L = (1 –  )Y  = capital ’ s share of total income 1- = labor ’ s share of total income

22. C-D Production Function Proof that --- Exhaustion of the product --- imply zero profits for competitive firms in the LR. --- Since π=0 for all periods, can ignore intertemporal analysis: profit maximization over-time

23. Aggregate Demand Side: Demand for goods & services Components of aggregate demand: AD = C+I+G+NX = C+I+G C = consumer demand for goods & services I = demand for investment goods G = government demand for goods & services (closed economy: no NX )

24. Consumption, C  Disposable income total income minus total taxes: Yd=Y – T.  Consumption function: C = C(Yd) assume Yd   C   Marginal propensity to consume (MPC)

25. Fig 3.6: Consumption function C Y – T C (Y –T ) 1 MPC The slope of the consumption function is the MPC.

26. Alternative ( 具個體化更完整的設定 ): Household ’ s intertemporal analysis: utility maximization over-time  With micro-foundation: refer to Ch16 and Varian: Ch10 r ＝ the real rate of return for saving (the payment to compensate the deferment of C) = the real cost of borrowing C = C(lifetime wealth, real interest rate) = C (current income, future income, real interest rate)

27. Investment, I  Investment function: I = I ( r ), r :real interest rate, the nominal interest rate corrected for inflation.  Real interest rate 近似 = Nominal interest rate – Inflation rate

28. Real and Nominal Interest Rates  You lend out $100 for one year. P=$1/candy  Nominal interest rate was 10%.  During the year inflation was 6%.  Present $100/$1= 100 units of candies  $100*(1+10%)/[$1*(1+6%)]=103.7 units of candies  Real return= 3.7 units, real rate of return= 3.7%  Real interest rate （ real rate of return ） 近似 = Nominal interest rate – Inflation rate = 10% - 6% = 4% ( r=R-π)

29. Investment function  Real interest rate is the cost of borrowing the opportunity cost of using one ’ s own funds to finance investment spending. (for over-time decision) So,  r  I 

30. Fig 3.7: The investment function r I I (r )I (r )

31. Firm ’ s intertemporal analysis: profit maximization over-time  With micro-foundation: refer to Ch17 and Williamson Ch7 --- over-time decision rule: I=I(r) Cost of investment= r+δ Benefit of investment = MP K  Earlier: one-time period decision rule:

32. Government spending, G  G = govt spending on goods and services.  G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits).  Assume government spending and total taxes are exogenous:

33. Goods market equilibrium  Aggregate demand:  Aggregate supply:  Equilibrium:  The real interest rate adjusts to equate demand with supply.

34. Saving and Investment in the National Income Accounts (1) GDP= Y=total expenditure Y = C + I + G + NX Y = C + I + G + NX closed economy  A closed economy: no international trade Y = C + I + G → Y – C – G =I Y = C + I + G → Y – C – G =I (2) GDP = Y = national income  Y= C + G + S → National Saving ： S= Y – C - G → (3) For the economy as a whole, S = I

35. The Meaning of Saving and Investment  National Saving 國民儲蓄 S = Y – C – G the total income that remains after paying for consumption and government purchases.  Private Saving 私部門儲蓄 Sp ≡ Y – T – C the amount of income that households have left after paying their taxes and paying for their consumption.  Public Saving 公部門儲蓄 Sg ≡ T – G the amount of tax revenue that the government has left after paying for its spending.

36. Gov ’ t budget constraint (Gov ’ t BC):  Surplus and Deficit （預算盈餘與赤字） Sg ≡ T – G >0 if T > G (budget surplus ) Sg ≡ T – G T (budget deficit) Budget Deficit ≡ D ≡ G-T = - Sg Gov ’ t Bond （公債）： Bg Gov ’ t issue new bonds to finance Budget Deficit △ Bg = D ≡ G-T ， 亦即 Gov ’ t BC: G= T + △ Bg

37. Flow vs. Stock The accumulation of past budget deficits =Public Debt （ Gov ’ t Bond ） Flow 流量： I, education, S, D vs. Stock 存量： K, H, wealth, Bg

38. Market for Loanable Funds  Financial markets coordinate economy ’ s saving and investment market for loanable funds. in the market for loanable funds. ( 可貸資金市場， LF)

39. Supply and Demand for Loanable Funds  The supply of loanable funds (S LF ）＝ S (net) The demand for loanable funds （ D LF ）＝ I  The price (of loan) in the LF market is real interest rate. r=R-π r ＝ the real rate of return for saving = the real cost of borrowing

40. Supply and Demand for Loanable Funds  S LF =S ： (+)vely-slpoed ， Q s LF ↑ =S ↑ as r ↑ 其實不一定是正斜率 Varian:Ch10 As r ↑ ， S ↑ ： if Substitution effect >Income effect As r ↑ ， S ↓ ： if SE <IE Here we assume SE >IE, so r ↑→ S ↑ ( 課本忽略 r 對 C 與對 S 的影響，故設 S LF 為垂直線 )  D LF =I ： (-) vely-slpoed ， Q d LF ↓= I↓ as r ↑ r as the opportunity cost of investment.  LF Market equilibrium: the intersection of S LF and D LF determines r*.

41. Fig 3.12 Market for Loanable Funds Loanable Funds (in billions of dollars) 0 Interest Rate Supply Demand 5% $1,200 Copyright©2004 South-Western

42. Alternative setup (FYI) In equilibrium: Sp + Sg = I  You can set up the model as in equilibrium: Sp= I-Sg = I+ △ Bg S LF =S p D LF =I+ △ Bg=I+(G-T)  The following comparative static analysis ( △ S LF ，△ D LF ) would be different, but the result still be the same.

43. Comparative Statics ( 比較靜態 )  S t = Y t -C t -G t = I t  K t+1 =(1-δ)K t +I t δ: depreciation rate( 折舊率 ) S t ↑ → I t ↑ → K t+1 ↑ → Y t+1 ↑  Government Policies that affect S and I ： 1. Taxes on saving （利息所得稅） 2. Tax credits on investment ( 投資抵減 ) 3. Government budget deficits （預算赤字）

44. Policy 1: Saving Incentives  Taxes on interest income ： real rate of return = (1-t ） r  t↑ reduce future payoff from current saving →reduce the incentive to save.  t↓ → increase the incentive to save: Q s LF ↑ =S ↑ at any given r. S LF curve shifts to the right. r* ↓ ， Q d LF ↑= I ↑ → lower interest rates and greater investment.

45. Fig 3.9b An Increase in Supply of Loanable Funds Loanable Funds (in billions of dollars) 0 Interest Rate Supply,S1S1 S2S2 2.... which reduces the equilibrium interest rate... 3.... and raises the equilibrium quantity of loanable funds. Demand 1. Tax incentives for saving increase the supply of loanable funds... 5% $1,200 4% $1,600 Copyright©2004 South-Western

46. Policy 2: Investment Incentives  An investment tax credit （ 1-κ ） r lowers the cost of borrowing and increases the incentive to borrow. κ↑ ： Q d LF ↑ =I ↑ at any given r. D LF curve shifts to the right. → higher interest rates and greater saving/investment.

47. Fig 3.11 An Increase in Demand for Loanable Funds Loanable Funds (in billions of dollars) 0 Interest Rate 1. An investment tax credit increases the demand for loanable funds... 2.... which raises the equilibrium interest rate... 3.... and raises the equilibrium quantity of loanable funds. Supply Demand,D1D1 D2D2 5% $1,200 6% $1,400 Copyright©2004 South-Western

48. Policy 3: Government Budget Deficits and Surpluses I= S = (Y – T – C) + (T – G) = I= S = (Y – T – C) + (T – G) = Sp + Sg T< G ，  Gov’t budget deficit ： T< G ， Sg<0 at any given r, Q s LF ↓ =S↓ < Sp when Sg<0 S LF curve shifts to the left. →r*↑ ， LF*↓ higher interest rate and lower investment. referred to as crowding out effect ( 排擠效果 ): The deficit borrowing crowds out private investments.

49. Figure 3.9: The Effect of a Government Budget Deficit Loanable Funds (in billions of dollars) 0 Interest Rate 3.... and reduces the equilibrium quantity of loanable funds. S2S2 2.... which raises the equilibrium interest rate... Supply,S1S1 Demand $1,200 5% $800 6% 1. A budget deficit decreases the supply of loanable funds... Copyright©2004 South-Western

50. U.S. Federal Government Surplus/Deficit, 1940-2004

51. U.S. Federal Government Debt, 1940-2004 Fact: In the early 1990s, about 18 cents of every tax dollar went to pay interest on the debt. (Today it’s about 9 cents.)

52. Taiwan data: 台灣政府收支淨額

53. Taiwan data: 台灣政府預算盈餘赤字與新增公債

54. Taiwan data ：公債餘額

55. The special role of r r adjusts to equilibrate the goods market and the loanable funds market simultaneously: If LF market is in equilibrium, S=I → Y – C – G = I → Y = C + I + G goods market is in equilibrium Thus, r adjusts to equilibrate the goods market and the loanable funds market simultaneously: If LF market is in equilibrium, S=I → Y – C – G = I → Y = C + I + G goods market is in equilibrium Thus, LF market equilibrium Goods market equilibrium

56. Walras ’ Law (Varian: Ch 29)  If there are markets for k goods, then we only need to find a set of prices where k-1 of markets are in equilibrium.  Here in our macro model, we have 3 markets, we only need 2 prices to assure general equilibrium: real wage and real interest rate

57. Chapter Summary  Total output is determined by the economy ’ s quantities of capital and labor the level of technology  Competitive firms hire each factor until its marginal product equals its price.  If the production function has constant returns to scale, then labor income plus capital income equals total income (output). CHAPTER 3 National Income slide 57

58. Chapter Summary  A closed economy ’ s output is used for consumption investment government spending  The real interest rate adjusts to equate the demand for and supply of goods and services loanable funds CHAPTER 3 National Income slide 58

59. Chapter Summary  A decrease in national saving causes the interest rate to rise and investment to fall. CHAPTER 3 National Income slide 59