# AK model

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3.1. The AK growth model
The models described so far all have the implication that changes in government policies, such as subsidies to research or capital investment, have level effects but no long-run growth effects. That is, these policies raise the growth rate temporarily as the economy grows to a higher level of the balanced growth path. But in the long run, the growth rate returns to its initial level.
There are two meanings of the phrase endogenous growth:
[1] Long-run growth is not driven by some exogenous process, like exogenous technological progress. Instead the long-run growth rate depends on the economic decisions of economic agents (households and firms).
[2] Public policy is potentially capable of affecting the long-run growth rate.

3.1.1. A simple model
The simplest endogenous growth model is a straightforward extension of the Solow model. In the Solow model the production function reads Y = A K a L1-a . If we set a = 1 and assume A = const. we get
Y = AK

with

A = const. > 0

For simplicity, we assume that the savings rate s is exogenously given. The capital accumulation equation hence is
°
K =sAK -dK
`
and the growth rate of capital turns out to read K = s A - d . In addition, the growth rate of output is equal to the growth rate of capital
` `
Y = K =sA-d
Since we assume that there is no population growth, overall output is equal to per capita output. Assuming that s A > d
`
(i.e. the growth condition holds), we have Y > 0. The explanation for this perpetual growth is immediatley seen by comparing the two diagrams below. The neoclassical convergence mechanism (i.e. the average product of capital falls as the capital stock increases) is absent in the AK model since the production function is linear in capital
4
2 s Y

3

Y

1.5

2

δ K

1

δ K
1

s Y

0.5

5

10
The AK model

15

20

K

2

4

6

8

10

12

14

K

The Solow model

KEY IMPLICATIONS:
[1] Growth is

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