Chapter 3. National Income: Where it
Comes From, Where it Goes
Homework: p. 76-78 #1, 3a c, d; 9
macromodel: equilibrium_interest_rate 1, 3, 7
Link to syllabus
Fig. 3-1 p. 43. Circular Flow
Chapter 3. National Income: Where it
Comes From, Where it Goes
Homework: p. 78-80 1, 4a,c, d; 10
Macromodels: 1, 3, 7 of interest
rate.exe
Fig. 3-1 p. 46. Circular Flow
Lots of formulas and equations. With these formulas, it is
important to know what is assumed. Similarly, which formulas
are important, or just simply illustrative.
Notation: K – capital, L – labor. Production function output Y =
F(K, L)
Y,C,T,S (national saving; stays away from personal saving), I, W,
P, R (rental price of capital), r (real interest rate), (Y-T)
disposable income, etc. W/P.
Ybar means Y is fixed. MP is marginal product, so MPL is
marginal product of labor, etc.
Fig. 3-2 p. 47.The determination of the
earnings of a factor of production.
Fig. 3-2 p. 52.The determination of
factor prices, the earnings of a factor
of production, and hence the (factoral)
distribution of income.
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Fig. 3-3 p. 49. The Slope of the Production Function.
Fig. 3-3 p. 54. The Slope of the
Production Function.
Gives the marginal product
Labor supply and production function
gives aggregate supply. (see chapter 9)
Fig. 3-4 p. 50 The Marginal Product of Labor
Fig. 3-4 p. 56. The Marginal Product
of Labor
Micro principle is MPL = W/P
Similarly, MPK = R/P (p. 53)
Notes definition of constant returns to scale: zY=F(zK, zL) for any
z. States Euler’s equation (p. 57), F(K,L)=MPK xK + MPLxL
doesn’t do much with it.
Cobb Douglas production function: Y =F(K,L) = AKαL(1-α). Has
constant returns to scale. For the US, 1-α=0.7
There is a significant conversation about economic profit, and
accounting profit. Economic profit = Y – MPLxL – MPKxK, so
if CRS, economic profit is zero.
Accounting profit is economic profit plus the return to capital.
Distribution of Factoral Income. With Cobb-Douglas,
MPL=(1-α)Y/L, and MPK= αY/K. So Labor’s share of output =
(1-α), and capital’s is α, and the factorial distribution of income
is fixed.
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Figure 3-5 p. 57. The Ratio of Labor Income
to Total Income
Table 3-1 p. 58. Growth of Labor Productivity and Real Wages
Figure 3-5 p. 61. The Ratio of Labor
Income to Total Income (used to be
in appendix)
Supports Cobb Douglas
Black death as illustration of S&D for
factors.
Table 3-1, p. 60. Growth of Labor
Productivity and Real Wages.
Point is that these two move together,
implying that productivity is the major
determinant of wages.
Look at:
Determination of income, Consumption, investment,
Loanable funds. Crowding out.
Fig. 3-5, p. 53. The Consumption Function
Fig. 3-6 p. 56. The Investment Function
Fig. 3-6, p. 65. The Consumption
Function, where Y-T is disposable
income. C = C(Y-T). Micro/macro
Illustrates MPC, which is typically
constant. Major advance, 30s. Not Y
dist. Doesn’t mention interest rates
Fig. 3-7 p. 66. The Investment
Function
I = (r) where r is the real interest rate
Why I(r )?, Firms borrow money. I
depends on technology, wages, labor
Mention classical investment, retained
earnings.
4
Different text
The prime interest rate and the
Federal funds rate
Other text The Prime interest rate and
the Federal Funds Rate.
Text comments about several different
interest rates, which depend on the
term, the credit risk, tax treatment.
Link to data from the Minneapolis Fed
Model for the determination of income, savings and investment.
Loanable funds market. Crowding out, pp. 72 ff.
Model of loanable funds (pp. 72?ff) in terms of supply and
demand. Assume a closed economy. The only use of funds is for
investment. What about the supply of funds, which comes from
savings? National savings is personal saving (Y-C-T) +
government saving (T-G), or S=Y-C-G.
Now, we can also write the national accounts identity as [AS=AD]
or Y = C + I + G (no NX).
Y – C – G = I, or S = I
where S is total national saving.
which becomes (Y – T – C) + (T – G) = I. (private + public).
Take the classical case, where we assume full employment Ybar.
C = C(Y – T). I = I(r ), G = Gbar, T = Tbar
So Ybar = C(Ybar – Tbar) + I(r) +Gbar.
Now, if G rises and Y-T-C is fixed, then I must fall (1 to 1: 100%.
Give this a loanable funds interpretation: I is use of funds, and S
is supply. If G (and therefore the deficit) increase, the amount of
“loanable” funds declines.
One way to present/illustrate/prove government crowding out.
In the above equation, if G increases, without a corresponding
change in taxes, then something else has to fall -investmentwhich falls if r increases.
Thus, write Y – C(Y – T) – G = I(r)
And Ybar – C(Ybar – Tbar) – Gbar = I(r)
Or Sbar = I(r)
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Thus we have interest rates adjusting for equilibrium of Y.
Fig. 3-7 p. 70. Savings, Investment, and the
Real Interest Rate
Fig. 3-8 p. 62. A Reduction in
Saving
Fig. 3-9 p. 63. Military Spending and Interest
Rates in the U.K.
Fig. 3-8 p. 71.
Savings, Investment, and the Real
Interest Rate.
S&D, where good is loanable funds,
and price is the interest rate.
Fig. 3-9 p. 72. A Reduction in Saving
(caused by increased gov’t spending)
Analysis. Increase in government
purchases: Y is fixed, so S moves to
right. “Y-C (Y-T) – G” falls. So I
must fall. Crowding out.
Would be same for lowered taxes.
Fig. 3-11 p. 73. Military Spending and
Interest Rates in the U.K.
Rough illustration of how an increase
in gov’t spending increased interest
rates.
Fig. 3-10 p. 65. An Increase in Investment Demand:
Fixed Savings
Fig. 3-11 p. 75. An Increase in
Investment Demand: Fixed Savings
Caused by an improvement in
technology.
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Fig. 3-11 p. 65 Increase in Investment Demand
with Savings Responding to Interest Rates
Fig. 3-12 p. 76. Increase in Investment
Demand with Savings Responding to
Interest Rates
Increase in S & I.
Comment that Crowding out is less
than 1 to 1 if S has positive slope.
Comments:
Section on the US financial crisis
Crowding out result doesn’t really depend on assumption that S
is independent of r. But the analysis changes if there is some
unemployment, and in some cases crowding out is minimal.
In addition, inclusion of foreign borrowing – important to the
US today, would also alter the result.
Appendix
Homework problems.
1. Use neo-classical theory to predict impact of: new immigration, earthquake
3a. Suppose Cobb Douglas, with α = 0.3 . a What is labor’s share? C. If K goes up by
10%, what happens to output? R? W?