0. National Income: Where it Comes From and Where it Goes
Topic 3:
National Income: Where it Comes From and Where it Goes
(chapter 3) revised 9/21/09
These are three of the most important economic statistics. Policymakers and businesspersons use them to monitor the economy and formulate appropriate policies. Economists use them to develop and test theories about how the economy works. Because we’ll be learning many of these theories, it’s worth spending some time now to really understand what these statistics mean, and how they are measured.

1. Introduction
In the last lecture we defined and measured some key macroeconomic variables.
Now we start building theories about what determines these key variables.
In the next couple lectures we will build up theories that we think hold in the long run, when prices are flexible and markets clear.
Called Classical theory or Neoclassical.

2. The Neoclassical model
Is a general equilibrium model:
Involves multiple markets
each with own supply and demand
Price in each market adjusts to make quantity demanded equal quantity supplied.

3. Neoclassical model The macroeconomy involves three types of markets:
Goods (and services) Market
Factors Market or Labor market , needed to produce goods and services
Financial market
Are also three types of agents in an economy:
Households
Firms
Government

4. Three Markets – Three agents
Labor Market
hiring
work
Financial Market
borrowing
borrowing
saving
Households
Government
Firms
production
government
spending
consumption
investment
Goods Market

5. Neoclassical model
Agents interact in markets, where they may be demander in one market and supplier in another
1) Goods market:
Supply: firms produce the goods
Demand: by households for consumption, government spending, and other firms demand them for investment

6. Neoclassical model 2) Labor market (factors of production)
Supply: Households sell their labor services.
Demand: Firms need to hire labor to produce the goods.
3) Financial market
Supply: households supply private savings: income less consumption
Demand: firms borrow funds for investment; government borrows funds to finance expenditures.

7. Neoclassical model
We will develop a set of equations to charac-terize supply and demand in these markets
Then use algebra to solve these equations together, and see how they interact to establish a general equilibrium.
Start with production…

8. Three Markets – Three agents
Labor Market
hiring
work
Financial Market
borrowing
borrowing
saving
Households
Government
Firms
production
government
spending
consumption
investment
Goods Market

9. Part 1: Supply in goods market: Production
Supply in the goods market depends on a production function:
denoted Y = F (K, L)
Where
K = capital: tools, machines, and structures used in production
L = labor: the physical and mental efforts of workers

10. The production function
shows how much output (Y ) the economy can produce from K units of capital and L units of labor.
reflects the economy’s level of technology.
Generally, we will assume it exhibits constant returns to scale.

11. Returns to scale Initially Y1 = F (K1 , L1 )
Scale all inputs by the same multiple z:
K2 = zK1 and L2 = zL for z>1
(If z = 1.25, then all inputs increase by 25%)
What happens to output, Y2 = F (K2 , L2 ) ?
If constant returns to scale, Y2 = zY1
If increasing returns to scale, Y2 > zY1
If decreasing returns to scale, Y2 < zY1

12. Exercise: determine returns to scale
Determine whether the following production function has constant, increasing, or decreasing returns to scale:

13. Exercise: determine returns to scale

14. Assumptions of the model
Technology is fixed.
The economy’s supplies of capital and labor are fixed at
Emphasize that “K” and “L” (without bars on top) are variables - they can take on various magnitudes. On the other hand, “Kbar” and “Lbar” are specific values of these variables. Hence, “K = Kbar” means that the variable K equals the specific amount Kbar.
Regarding the assumptions:
In chapters 7 and 8 (Economic Growth I and II), we will relax these assumptions: K and L will grow in response to investment and population growth, respectively, and the level of technology will increase over time.

15. Determining GDP
Output is determined by the fixed factor supplies and the fixed state of technology:
So we have a simple initial theory of supply in the goods market:

16. Three Markets – Three agents
Labor Market
hiring
work
Financial Market
borrowing
borrowing
saving
Households
Government
Firms
production
government
spending
consumption
investment
Goods Market

17. Part 2: Equilibrium in the factors market
Equilibrium is where factor supply equals factor demand.
Recall: Supply of factors is fixed.
Demand for factors comes from firms.
Recall from chapter 2: the value of output equals the value of income. The income is paid to the workers, capital owners, land owners, and so forth. We now explore a simple theory of income distribution.

18. Demand in factors market
Analyze the decision of a typical firm.
It buys labor in the labor market, where price is wage, W.
It rents capital in the factors market, at rate R.
It uses labor and capital to produce the good, which it sells in the goods market, at price P.

19. Demand in factors market
Assume the market is competitive:
Each firm is small relative to the market, so its actions do not affect the market prices.
It takes prices in markets as given - W,R, P.

20. Demand in factors market
It then chooses the optimal quantity of Labor and capital to maximize its profit.
How write profit:
Profit = revenue -labor costs -capital costs
= PY WL RK
= P F(K,L) - WL RK

21. Demand in the factors market
Increasing hiring of L will have two effects:
1) Benefit: raise output by some amount
2) Cost: raise labor costs at rate W
To see how much output rises, we need the marginal product of labor (MPL)

22. Marginal product of labor (MPL)
An approximate definition (used in text) : The extra output the firm can produce using one additional labor (holding other inputs fixed):
MPL = F (K, L +1) – F (K, L)

23. The MPL and the production functionY
output 1
MPL
As more labor is added, MPL  1
MPL
Slope of the production function equals MPL: rise over run
MPL 1 L
labor

24. Diminishing marginal returns
As a factor input is increased, its marginal product falls (other things equal).
Intuition: L while holding K fixed
 fewer machines per worker
 lower productivity
Tell class: Many production functions have this property.

25. MPL with calculus We can give a more precise definition of MPL:
The rate at which output rises for a small amount of additional labor (holding other inputs fixed):
MPL = [F (K, L +DL) – F (K, L)] / DL
where D is ‘delta’ and represents change
Earlier definition assumed that DL=1.
F (K, L +1) – F (K, L)
We can consider smaller change in labor.

26. MPL as a derivative As we take the limit for small change in L:
Which is the definition of the (partial) derivative of the production function with respect to L, treating K as a constant.
This shows the slope of the production function at any particular point, which is what we want.

27. The MPL and the production functionY
output
MPL is slope of the production function (rise over run)
F (K, L +DL) – F (K, L)) L
labor

28. Derivative as marginal productY 9 6 3 L 1 4 9
fL:
F(L): L:
0.5
0.75
1.5 9 6 3 4 1

29. Return to firm problem: hiring L
Firm chooses L to maximize its profit.
How will increasing L change profit?
D profit = D revenue - D cost
= P * MPL - W
If this is: > 0 should hire more
< 0 should hire less
= 0 hiring right amount

30. Firm problem continued
So the firm’s demand for labor is determined by the condition:
P *MPL = W
Hires more and more L, until MPL falls enough to satisfy the condition.
Also may be written:
MPL = W/P, where W/P is the ‘real wage’

31. Real wage Think about units: W = $/hour P = $/good
W/P = ($/hour) / ($/good) = goods/hour
The amount of purchasing power, measured in units of goods, that firms pay per unit of work

32. Example: deriving labor demand
Suppose a production function for all firms in the economy:

33. Labor demand continued

34. Labor market equilibrium

35. Three Markets – Three agents
Labor Market
hiring
work
Financial Market
borrowing
borrowing
saving
Households
Government
Firms
production
government
spending
consumption
investment
Goods Market

36. MPL and the demand for labor
Units of output
Units of labor, L
Each firm hires labor up to the point where MPL = W/P
MPL, Labor demand
Real wage
Let L* be the value of L such that MPL = W/P.
Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker.
Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits.
When L = L*, then firm cannot increase its profits either by raising or lowering L.
Hence, firm hires L to the point where MPL = W/P.

37. Determining the rental rate
We have just seen that MPL = W/P
The same logic shows that MPK = R/P :
diminishing returns to capital: MPK  as K 
The MPK curve is the firm’s demand curve for renting capital.
Firms maximize profits by choosing K such that MPK = R/P .
In our model, it’s easiest to think of firms renting capital from households (the owners of all factors of production). R/P is the real cost of renting a unit of K for one period of time. In the real world, of course, many firms own some of their capital. But, for such a firm, the market rental rate is the opportunity cost of using its own capital instead of renting it to another firm. Hence, R/P is the relevant “price” in firms’ capital demand decisions, whether firms own their capital or rent it.

38. How income is distributed:
We found that if markets are competitive, then factors of production will be paid their marginal contribution to the production process.
total labor income =
total capital income =

39. Euler’s theorem:
Under our assumptions (constant returns to scale, profit maximization, and competitive markets)…
total output is divided between the payments to capital and labor, depending on their marginal productivities, with no extra profit left over.
national income
labor income
capital income

40. Mathematical example
Consider a production function with Cobb-Douglas form:
Y = AKL1-
where A is a constant, representing technology
Show this has constant returns to scale:
multiply factors by Z:
F(ZK,ZY) = A (ZK) (ZL)1-
= A Z K Z1- L1-
= A Z Z1- K L1-
= Z x A K L1-
= Z x F(K,L)

41. Mathematical example continued
Compute marginal products:
MPL = (1-) A K L-
MPK =  A K-1L1-
Compute total factor payments:
MPL x L + MPK x K
= (1-) A K L- x L +  A K-1L1- x K
= (1-) A K L1- +  A K L1-
= A K L1- =Y
So total factor payments equals total production.

42. Three Markets – Three agents
Labor Market
hiring
work
Financial Market
borrowing
borrowing
saving
Households
Government
Firms
production
government
spending
consumption
investment
Goods Market

43. Outline of model A closed economy, market-clearing model Goods market:
Supply side: production
Demand side: C, I, and G
Factors market
Supply side
Demand side
Loanable funds market
Supply side: saving
Demand side: borrowing
DONE 
Next 
DONE 
DONE 

44. Demand for goods & services
Components of aggregate demand:
C = consumer demand for g & s
I = demand for investment goods
G = government demand for g & s
(closed economy: no NX )
“g & s” is short for “goods & services”

45. Consumption, C
def: disposable income is total income minus total taxes: Y – T
Consumption function: C = C (Y – T )
Shows that (Y – T )  C
def: The marginal propensity to consume (MPC) is the increase in C caused by an increase in disposable income.
So MPC = derivative of the consumption function with respect to disposable income.
MPC must be between 0 and 1.

46. The consumption function
Y – T
C (Y –T )
The slope of the consumption function is the MPC.
rise
run

47. Consumption function cont.
Suppose consumption function:
C= Y
MPC = 0.75
For extra dollar of income, spend 0.75 dollars consumption
Marginal propensity to save = 1-MPC

48. Investment, I The investment function is I = I (r ),
where r denotes the real interest rate, the nominal interest rate corrected for inflation.
The real interest rate is  the cost of borrowing  the opportunity cost of using one’s own funds to finance investment spending.
So, r  I

49. The investment functionr I
Spending on investment goods is a downward-sloping function of the real interest rate
I (r )

50. Government spending, G
G includes government spending on goods and services.
G excludes transfer payments
Assume government spending and total taxes are exogenous:
Remind students meaning of ‘exogenous’

51. The market for goods & services
The real interest rate adjusts to equate demand with supply.
Note the only variable in the equilibrium condition that doesn’t have a “bar” over it is the real interest rate.
When the full slide is showing, before you advance to the next one, you might want to note that the interest rate is important in financial markets as well, so we will next develop a simple model of the financial system.

52. The loanable funds market
A simple supply-demand model of the financial system.
One asset: “loanable funds”
demand for funds: investment
supply of funds: saving
“price” of funds: real interest rate

53. Demand for funds: Investment
The demand for loanable funds:
comes from investment: Firms borrow to finance spending on plant & equipment, new office buildings, etc. Consumers borrow to buy new houses.
depends negatively on r , the “price” of loanable funds (the cost of borrowing).

54. Loanable funds demand curveI
The investment curve is also the demand curve for loanable funds.
I (r )

55. Supply of funds: Saving
The supply of loanable funds comes from saving:
Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending.
The government may also contribute to saving if it does not spend all of the tax revenue it receives.

56. Types of saving private saving (sp) = (Y –T ) – C
government saving (sg) = T – G
national saving, S
= sp sg
= (Y –T ) – C T – G
= Y – C – G
After showing definition of private saving,
- give the interpretation of the equation: private saving is disposable income minus consumption spending
- explain why private saving is part of the supply of loanable funds:
Suppose a person earns $50,000/year, pays $10,000 in taxes, and spends $35,000 on goods and services. There’s $5000 remaining. What happens to that $5000? The person might use it to buy stocks or bonds, or she might put it in her savings account or money market deposit account. In all of these cases, this $5000 becomes part of the supply of loanable funds in the financial system.

57. EXERCISE: Calculate the change in saving
Suppose MPC = 0.8
For each of the following, compute S :
G = 100
T = 100

58. Answers
First, in the box at the top of the slide, we plug the given value for the MPC into the expression for S and simplify. Then, finding the answers is straightforward: just plug in the given values into the expression for S.

59. digression: Budget surpluses and deficits
When T > G , budget surplus = (T – G ) = public saving
When T < G , budget deficit = (G –T ) and public saving is negative.
When T = G , budget is balanced and public saving = 0.

60. The U.S. Federal Government Budget
Notes:
1. The huge deficit in the early 1940s was due to WW2: wars are expensive.
s: deficit (Reagan tax cut and military spending)
Surplus in 2001
Back in deficit now, not shown in
Source of data: U.S. Department of Commerce, Bureau of Economic Analysis.

61. The U.S. Federal Government Debt
Fun fact: In the early 1990s, nearly 18 cents of every tax dollar went to pay interest on the debt.

62. Loanable funds supply curve
S, I
National saving does not depend on r, so the supply curve is vertical.

63. Loanable funds market equilibrium
S, I
I (r )
Equilibrium real interest rate
Equilibrium level of investment

64. The special role of r
r adjusts to equilibrate the goods market and the loanable funds market simultaneously:
If L.F. market in equilibrium, then
Y – C – G = I
Add (C +G ) to both sides to get
Y = C + I + G (goods market eq’m)
Thus,
This slide establishes that we can use the loanable funds supply/demand diagram to see how the interest rate that clears the goods market is determined.
Explain that the symbol  means each one implies the other. The thing on the left implies the thing on the right, and vice versa.
More short-hand: “eq’m” is short for “equilibrium.”
Eq’m in L.F. market
Eq’m in goods market

65. Algebra example Suppose an economy characterized by:
Factors market supply:
labor supply= 1000
Capital stock supply=1000
Goods market supply:
Production function: Y = 3K + 2L
Goods market demand:
Consumption function: C = (Y-T)
Investment function: I = 1000 – 5000r
G=1000, T = 1000

66. Algebra example continued
Given the exogenous variables (Y, G, T), find the equilibrium values of the endogenous variables (r, C, I)
Find r using the goods market equilibrium condition:
Y = C + I + G
5000 = ( ) +1000
-5000r
5000 = 5250 – 5000r
-250 = -5000r so r = 0.05
And I = 1000 – 5000*(0.05) = 750
C = ( ) = 3250

67. Mastering the loanable funds model
Things that shift the saving curve
public saving
fiscal policy: changes in G or T
private saving
preferences
tax laws that affect saving (401(k), IRA)
Continuing from the previous slide, let’s look at all the things that affect the S curve. Then, we will pick one of those things and use the model to analyze its effects on the endogenous variables. Then, we’ll do the same for the I curve.

68. CASE STUDY The Reagan Deficits
Reagan policies during early 1980s:
increases in defense spending: G > 0
big tax cuts: T < 0
According to our model, both policies reduce national saving:

69. 1. The Reagan deficits, cont.
1. The increase in the deficit reduces saving… r
S, I
I (r ) r2
2. …which causes the real interest rate to rise… r1
3. …which reduces the level of investment. I2 I1

70. Are the data consistent with these results?
variable 1970s 1980s
T – G –2.2 –3.9 S r I
Display the data line by line, noting that it matches the model’s predictions---UNTIL YOU GET TO Investment.
The model says that investment should have fallen as much as savings. Ask students why they think it didn’t.
Answer: in our closed economy model of chapter 3, the only source of loanable funds is national saving. But the U.S. is actually an open economy. In the face of a fall in national saving--the domestic supply of loanable funds, firms can finance their investment spending by importing loanable funds.
T–G, S, and I are expressed as a percent of GDP
All figures are averages over the decade shown.

71. Chapter summary Total output is determined by
how much capital and labor the economy has
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).

72. Chapter summary The economy’s output is used for
consumption (which depends on disposable income)
Investment
(depends on real interest rate)
government spending (exogenous)
The real interest rate adjusts to equate the demand for and supply of
goods and services
loanable funds
A decrease in national saving causes the interest rate to rise and investment to fall.

73. Friendly quiz #1 Write answers to the following 4 questions on a sheet of paper to hand in (each worth 1 point).
Your name
Your TA’s name (hint: Yi = Monday, Mei = Wednesday)
3) Derive the derivative for
4) Does the following production function exhibit constant returns to scale (yes or no)?

74. Exercise: determine returns to scale