Dietmar Meyer

Budapest University of Economic Sciences, Dept. of Macroeconomics

H-1093 Budapest, Fõvám tér 8.

- Human factor: division of labour (A. Smith)

- Industrial revolution Þ importance of real capital Þ Solow and Swan (1956)

Solovian approach:

- One-sector-model (homogeneous good) with neoclassical properties

- Growth rate of labour is constant: = const.

- Increase of real capital stock (= investment) is motor of economic development measured with income (Y)

- Investment is financed by savings as a part of income: ; no money!

- Properties of the technology:

* Two factors of production - capital and labour - will be used efficiently in the production process Þ production function

* Decreasing returns Þ production function is concave

* is assumed to be homogeneous of degree one, thus with and .

- From these assumptions:

,

or

.

- Using , one obtain

. (Basic equation)

- This can be solved if is known. The usual Cobb-Douglas function

implies

, the basic equation becomes , a well-known Bernoulli differential equation.

- It can be shown:

* The steady-state (stationary) solution ist stable, thus for one has , with .

From follows , or

Graphic No. 1

If some > , then > , thus < , and if,

on the contrary < , then < , thus > ,

- The dynamics of the simplest model of economic growth imply non-linear differential equations.

Their equilibrium solution proved to be stable.

Generalisations of Solow’s Model: (since 1956)

- Introduction of money

- Introduction of intervention by the state

- Disequilibrium on the labour market

- Saving ratio will change over time

- Growth rate of labour is not constant, it depends on the economic situation (Malthusian approach)

- Taking into account exhaustable natural ressources as factor of production

- Two- or More-Sector-Models

- Problem of optimal growth

- Effects of international trade, etc.,

but - from the present point of view - the most important:

Technical progress, the role of human capital in economic development

- Exogeneous technical progress

- Endogeneous technical progress

* Arrow (1962): Learning by Doing

° Technical progress (= development of knowledge, = development of human capital, etc.) has two parts: an exogenous factor expressing the cultural level (and its development) of economic actors and an part depending on the capital stock (or in an other model: on the wealth accumulated over time),

.

Assuming now and is

homogeneous of degree one, it will be obtained

with and

. Using the basic equation will be

. 

The Lucas-Romer Approach:

- Based on the generalisations of Solow’s model

* More-Sector-Model

* Technical progress - increasing returns Þ problem of financing Þ monopoly Þ redistribution

The Model (Horváth - Farkas - Meyer 1999, Barro - Sala-I-Martin 1995):

Technological conditions:

Production of physical capital

Production of human capital

Increase of physical capital is equal to real capital produced minus consumption minus depreciation:

Since human capital is not used in consumption:

Growth rate of consumption is equal to the difference between the net increase of physical capital and the time preference:

Autonomous system of three non-linear differential equations. Analysis:

- Determination of an equilibrium

- Linearisation in the neighborhood of this equilibrium

- Analysis of the linear system as a good approximation of the original system

Result:

in every equilibrium point there are the same positive, negative and zero eigenvalue of the linearised system Þ L line (the set of all equilibrium points) implies four parts of the K-H-C three-dimentional space (see graphics No. 2-4)

Graphic No. 2

Graphic No. 3

Graphic No. 4

For interpretation is should be assumed:

- return of human capital is slower than that of physical capital;

- (relatively) free capital flows between the two sectors;

- consumption is preferred, i. e., dcreasing consumption is accepted only in the short run;

human capital stock decreases, i. e., its depreciation is higher than its reproduction, the growth of physical capital at the beginning is - at least for a time - enough for the increasing consumption; later the decreasing human capital stock goes parallel with a slower growth of real capital stock which leads to an decreasing physical capital stock;

In this sector the ratio between human capital and real capital is relatively high Þ relatively good skilled labour force is in contradiction to the level of real capital, and can not be used efficiently in the production of human capital Þ low earnings of human capital in this sector Þ moving into sector with higher income, into the sector of consumption goods Þ here this part of human capital is higher skilled Þ its efficiency is higher than the average there before Þ earning higher incomes Þ higher consumption demand; when human capital depreciates physical capital goes down Þ increasing consumption is possible only by using the capital stocks Þ collaps of the economy;

Situation similar as in sector I Þ human capital flow to sector II; difference: now the obviously existing depreciation of human capital doesn’t imply the decrease of real capital, on the contrary: physical capital increases; the basis for the investment in this field is the forgone consumption;

Real capital stock is higher than human capital stock Þ capital flow into the field of human capital; both capital types move in the same direction, thus a mutual stimulation can be expected; but this contradicts the fact of decreasing consumption; one possible interpretation may be that real capital stimulated by human capital is used in an not efficient way; this society may be characterised by "knowledge for nothing", or as a "society of hungry researchers"; some parallels can be seen with the former socialist system: relatively well developed educational system, but no commodities in the shops ...

Final result is the same as in Sector I: higher consumption because of the using of both capital types, human capital and real capital; difference: at the beginning the ratio between real capital and human capital is relatively high, thus there will be a capital flow to the human capital sector; lower returns of human capital and the lower level of real capital stock imply decreasing consumption and low efficiency of human capital, thus both real capital as well as human capital will decrease; that’s why consumption can increase;

Generally accepted that development of human capital is neccessary for succesful transition, thus transition economies have to move into sector I or II; a high level of capital (due to the level of real capital), however, can induce two developments of contrary directions: the collaps of the economy (sector I), or the growing economy (sector II); It could be seen that the main difference between these sectors is the kind of interaction between human capital and real capital: if they are more or less independent, then it is sector I, but if there would be a feedback, a mutual stimulation of both capital types, then it is sector II.

Þ importance of human capital for transition ("transition process is going on in the heads"

Þ institutions must be established for the feedback mentioned above (co-operation between universities and firms, banks, etc.; adjustment of educational programs to the needs of economic practice; etc.)

Þ transition mus be considered - from this point of view also - as a complex problem