Download Lecture 1 - Economics

Lecture 3
National Income
Production function
Production Function:
Y = F(K, L) = Kα L1-α
Constant Return to Scale:
zY = F(zK, zL)
A country as a whole, K and L are constant. Then the
supply curve is constant.
Production function: scale economy

(1)
(2)
(3)
If double the K and the L:
Output is doubled  constant return to
scale
Output is less than doubled  decreasing
return to scale
Output is more than doubled  increasing
return to scale
Production function: scale economy

Example: STARBUCKS


In the 1990s  probably increasing
return to scale. The company opens a
new store every weekday.
Since 2008  probably decreasing
return to scale. The company has
announced 900 store closure in the US.
Demand for capital and labor
Firms maximize their profits by selecting optimal amount of K
and L:
Max Profit = Revenue – Labor Costs – Capital Costs
=
Y
-- WL
RK
= F(K, L) – WL
RK
α 1-α
=K L
– WL
RK
Demand for capital and labor
First order conditions:

 MPK  R  K  1 L1  R  0
K

 MPL  R  1   K  L  W  0
L
Now we have:
MPK = R, MPL = W
Discussions #1

MPL = W. If Cobb-Douglas function,
1   K  L

W
At the given level of K, a higher number of
workers would lead to a lower wage.
Discussion #1
Wage
wage
MPL, labor
demand
Quantity of labor
demanded
Labor
Discussions #1

Similarly, MPK = R, we have:
K  1 L1  R

Since α – 1 < 0, at any given level of L, a
higher K would lead to a lower interest
rate.
Supply is vertical in the whole country
Two basic predictions of the model



At any given level of L, a higher K would
lead to a lower interest rate.
At any given level of K, a higher number
of workers would lead to a lower wage.
Verifying these two predictions are very
difficult.
Example: the Black Death
The Black Death


The total number of death world wide
are estimated at 75 million.
Approximated 25-50 million in
Europe, about 30% to 60% of
Europe’s population.
The effect of the Black Death on wages
Labor supply after
Labor supply before
wage after
wage before
The Golden Age of British Laborers



Wages did not move much long
before the Black death.
Wages have almost doubled after
the Black death.
It is still controversial.
Example: Mariel Boatlift



Began 4/15/1980, and ended
10/31/1980.
More than 125,000 Cubans arrived at
Southern Florida, mostly in Miami.
50% of them stay in Miami – a 7%
increase of the Miami labor market and
20% increase in Cuban working
population.
Example: Mariel Boatlift
The Mariel Boatlift
The effect of the Mariel Boatlift on wages
Labor supply before
Labor supply after
wage before
wage after
The effect of the Mariel Boatlift on wages


Not much change in wages for both
Cuban workers and for Caucasian
workers.
Why?
The effect of the Mariel Boatlift on wages
Labor supply before
Labor supply after
wage before
wage after
Demand for
labor shift
right since
capital stock
increases
Discussion #2: share of income


1   K  L  W
1   K  L  L  WL
1   Y  WL
Share of labor is 1-α
Share of capital is α.
output
Share of income
Nonwage
benefits, such as
health insurance
etc
Demand for goods and services


GDP =
If NX = 0
GDP =
Consumption (C) +
Investment (I) +
Government Purchase (G) +
Net Exports (NX)
Consumption (C) +
Investment (I) +
Government Purchase (G)
Consumption



Depends on the disposable income:
C = C(Y – T) = a + b * (Y – T)
Example:
C = 250 + 0.75 (Y – T)
Marginal propensity to consume: 0.75
On additional dollar, only 75 cents are
consumed, the rest is saved.
Investment function


A higher cost or rental price of capital
would lead to a lower investment.
Example of investment function:
I = I(r) = 1,000 – 50 r.
Equilibrium of demand and supply




GDP equation:
Y = C + I + G = C(Y-T) + I(r) + G
Rewrite:
Y–C–G=I
Supply of loanable fund:
Y – C – G = Saving
Demand for loanable fund:
I(r)
Equilibrium of demand and supply
Case 1: an increase in government spending, G.
Is this true?
Case 2: Bush’s cut in capital gains tax
Summary

Total output is determined by the
economy’s quantities of capital and labor
(and technology).
Y = F(K, L)

Competitive firms hire both K and L until its
marginal product equals its price.
Summary



Profit is maximized when
MPK = R and MPL = wage.
A closed economy’s output is used for:
Y=C+I+G
In the long run, the equilibrium is reached
when saving and investment are equal.