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Macroeconomics ECO 403

LESSON 22

ECONOMIC GROWTH (Continued...)

Issues under Consideration

Technological progress in the Solow model

Policies to promote growth

Growth empirics:

Confronting the theory with facts

Endogenous growth:

Two simple models in which the rate of technological progress is endogenous

Introduction

Previously, in the Solow model

· The production technology was held constant

· Income per capita was constant in the steady state.

Neither point is true in the real world

Tech. progress in the Solow model

A new variable: E = labor efficiency

Assume:

Technological progress is labor-augmenting: it increases labor efficiency at the exogenous

rate g:

ΔE

We now write the production function as:

Y = F (K , L × E )

Where L × E = the number of effective workers.

Hence, increases in labor efficiency have the same effect on output as

increases in the labor force.

Notation:

y = Y/LE = output per effective worker

k = K/LE = capital per effective worker

Production function per effective worker:

y = f(k)

Saving and investment per effective worker:

s y = s f(k)

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Macroeconomics ECO 403

(δ + n + g)k = break-even investment:

the amount of investment necessary to keep k constant.

Consists of:

δ k to replace depreciating capital

n k to provide capital for new workers

g k to provide capital for the new "effective" workers created by technological progress

Δk = s f(k) - (δ +n +g)k

Investment, break-even

investment

(δ +n +g ) k

sf(k)

Capital per

worker, k

Steady-State Growth Rates in the Solow Model with Tech. Progress

Variable

Symbol

Steady-Steady growth rate

k = K/ (L ×E )

Capital per effective worker

y = Y/ (L ×E )

Output per effective worker

(Y/ L ) = y ×E

Output per worker

Y = y ×E ×L

Total output

n+g

The Golden Rule

To find the Golden Rule capital stock,

express c* in terms of k*:

= y* - i*

= f(k* ) - (δ + n + g) k*

c* is maximized when

MPK = δ + n + g

or equivalently,

MPK - δ = n + g

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Macroeconomics ECO 403

In the Golden Rule Steady State, the marginal product of capital net of depreciation equals the

population growth rate plus the rate of tech progress.

The Golden Rule Capital Stock

steady state

(δ +n+g) k*

output and

investment

f(k*)

C*gold

i*gold = (δ+ n+g)k*gold

k*gold

steady-state capital per

worker, k*

Policies to promote growth

Four policy questions:

· Are we saving enough? Too much?

· What policies might change the saving rate?

· How should we allocate our investment between privately owned physical capital,

public infrastructure, and "human capital"?

· What policies might encourage faster technological progress?

1. Evaluating the Rate of Saving

Use the Golden Rule to determine whether

our saving rate and capital stock are too high, too low, or about right.

To do this, we need to compare

(MPK - δ ) to (n + g).

· If (MPK - δ ) > (n + g), then we are below the Golden Rule steady state and should increase

· If (MPK - δ ) < (n + g), then we are above the Golden Rule steady state and should reduce

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Macroeconomics ECO 403

To estimate (MPK - δ ), we use three facts about an economy;

1. k = 2.5 y

the capital stock is about 2.5 times one year's GDP.

2. δ k = 0.1 y

about 10% of GDP is used to replace depreciating capital.

3. MPK × k = 0.3 y

Capital income is about 30% of GDP

1. k = 2.5 y

2. δ k = 0.1 y

3. MPK × k = 0.3 y

To determine δ , divided 2 by 1:

0.1

δk

0.1 y

⇒

δ =

= 0.04

2.5

2.5 y

To determine MPK, divided 3 by 1:

MPK × k

0.3 y

0.3

⇒

MPK =

= 0.12

2.5 y

2.5

Hence, MPK - δ = 0.12 - 0.04 = 0.08

Real GDP grows an average of 3%/year,

so n + g = 0.03

Thus, in this economy,

MPK - δ = 0.08 > 0.03 = n + g

Conclusion:

The economy is below the Golden Rule steady state:

if we increase saving rate of this economy, the economy will have faster growth until it

reaches to a new steady state with higher consumption per capita.