AK model

The AK model or Rebelo model is an endogenous growth model that goes back to the Portuguese economist Sérgio Rebelo  (1992).

Model and statements

The production function of the model was used before and later expanded in many ways. It is linear and explains the production result (Y) via the use of capital (K) and a macroeconomic technology parameter (A) that is greater than zero:

${\displaystyle Y=A\cdot K}$.

This is basically a variant of the Cobb-Douglas function for which the parameter is one. Both physical and human capital are summarized under the concept of capital . Unskilled work, on the other hand, does not matter, which is plausible for modern production techniques. ${\displaystyle Y=AK^{a}L^{1-a}}$ ${\displaystyle a}$

Increasing the technology parameter, for example by adapting external knowledge, leads to an increase in the long-term growth rate. The AK model also explains permanent differences in the growth of economies.

criticism

Failure to observe unskilled work is criticized. In industrialized countries this may be plausible, but for less developed countries, this is problematic. The aggregation of human and physical capital is not problematic either. The capital accumulation rate must now be related to both physical and human capital. Capturing investment in human capital seems difficult because national accounts record relevant expenditure such as teacher salaries, student living expenses, etc. as consumption expenditure. The entirety of these expenditures needed to build human capital is often referred to as productive consumption .

Economic Policy Implications

The AK model shows that an increase in per capita income can be achieved by:

1. Investments in physical and human capital, e.g. B. Expansion of infrastructure or expansion of the education sector
2. Facilitating access to (external) knowledge
3. on the one hand: protection of property rights in order to increase the incentive for research
4. on the other hand: not protecting property rights too much so that research results can disseminate
5. Support for foreign capital inflows
6. Curbing population growth

Consideration with an open economy

The AK model in the case of an open economy has been analyzed by various scientists.

In the case of equal interest rates at home and abroad, there would be no movement of capital, i.e. the equilibrium would not differ from that of the closed economy . It is different in the case of different interest rates. These arise from different time preference rates in households. Capital would now flow from the land with the lower interest rate to the one with the higher rate. However, the model does not assume decreasing marginal utility of capital. As a result, with full capital mobility, the capital would flow entirely into the country with the higher interest rate. This is a fact that cannot be determined empirically . This fact could only be explained through limited capital mobility, so that an outflow cannot be infinitely high.

literature

• Lutz Arnold: Growth Theory . Verlag Vahlen, Munich 1997, ISBN 3-8006-2242-4
• Michael Frenkel, Hans-Rimbert Hemmer : Foundations of the growth theory . Verlag Vahlen, Munich 1999, ISBN 3-8006-2396-X
• Sérgio Rebelo : "Long-Run Policy Analysis and Long-Run Growth", in the Journal of Political Economy , 1991 Vol. 99, pp. 500-521
• Sérgio Rebelo : "Growth in Open Economies", 1992, Carnegie-Rochester Conference Series on Public Policy , vol. 36 pp. 5-46