1. An improvement in technology shifts
The Sources of Growth
An improvement in technology shifts
the production function up
Output per worker, Y/N
Capital per worker, K/N
F(K/N, 1)
F(K/N, 1) B´ A A´
Growth comes from capital accumulation and technological progress.
Because of decreasing returns to capital, capital accumulation by itself cannot sustain growth.

2. Interactions between Output and Capital
Capital, Output, and Saving/Investment
The amount of capital (K)  amount of output (Y)
The amount of output (Y)  the amount of savings (S) & investment (I = S when G-T=0)  amount of capital (K)
ΔK = I – Depreciation = sY - δK

3. Interactions between Output and Capital
Per worker output and capital accumulation
Capital/worker in t+1 = Capital/Worker in t, adjusted for depreciation and investment Investment/worker = Savings rate x Output/worker in t -
Change in capital from year t to year t+1 =
Invest- ment during year t
depreciation during year t

4. Dynamics of Capital and Output Graphically
Output per worker
f(Kt/N)
Depreciation per worker
Kt/N
Investment per worker
sf(Kt/N)
Y*/N A B
Output per worker, Y/N C
AB = Output/worker
AC = Investment/worker D
AD = Depreciation
AC > AD
(Ko/N)
K*/N
Capital per worker, K/N

5. Steady-State Capital and Output
Steady-State Value of Capital/Worker:
Investment just offsets depreciation
Steady-State Value of Output/Worker

6. The Effects of Different Saving Rate
Investment
s0f(Kt/N)
s1f(Kt/N)
Output per worker, Y/N
Capital per worker, K/N
Depreciation per worker
Kt/N
Output per worker
f(Kt/N) D
Y1/N
K1/N B A
(K0/N)
Y0/N C
I >

7. The Effects of Different Saving Rate
Output per worker, Y/N
Time
(No technological progress)
Associated with saving rate s1 > s0
Y1/N
Y0/N
Associated with saving rate s0 t

8. The Effects of Different Saving Rate
(Technological progress)
Output per worker, Y/N
(log scale)
Time
Associated
with saving
rate s1 > s0
Associated with saving rate s0 t

9. The Savings Rate and the Golden Rule
Does an increase in saving lead to an increase in consumption in the long run?
Two Scenarios:
Saving Rate = 0
Capital = 0
Output = 0
Consumption = 0
Saving Rate = 1
Consumption = 0
Output replaces depreciation

10. Implications of Alternative Saving Rates
Maximum steady state
Consumption per worker:
At Golden Rule Level of Capital
Consumption per worker, C/N
Saving rate, s sG 1

11. In steady-state is constant and the left side = 0 and:
Assume:
(Constant return to scale and decreasing returns to either capital or labor)
Then
In steady-state is constant and the left side = 0 and:
Double s  Quadruple K/N and double Y/N

12. What saving rate that would maximize steady-state consumption?
The U.S. Saving Rate and the Golden Rule
What saving rate that would maximize steady-state consumption?
In Steady-State:
If s < .50: increasing s will increase long-run consumption
In the U.S., s < 20%