Uzawa-Lucas model

The Uzawa-Lucas model is a model of the endogenous growth theory . It's a two-sector model. The first sector looks at physical capital and the second at human capital . It was first presented in 1988 by Robert E. Lucas . It arose from the criticism z. B. the AK model , in which capital was considered regardless of its characteristics. Lucas leans heavily on a model by Hirofumi Uzawa (1965).

Sector consideration

Scheme of the Lucas model

The model is based on a neoclassical production function in which unskilled labor has been replaced by human capital ( H ):

{\ displaystyle Y = F (K, H)}

with = physical capital and = human capital. ${\ displaystyle K}$ ${\ displaystyle H}$

Physical capital sector

For a Cobb-Douglas production function under the assumption that only a part of the human capital ( u ) flows into the production of real capital, the result is

{\ displaystyle Y = AK ^ {\ alpha} (uH) ^ {1- \ alpha}}

where A represents the constant technology parameter.

Human capital sector

{\ displaystyle {\ dot {H}} = B (1-u) H- \ delta H}

where corresponds to the part of the working time that remains for employment in the education sector; is the depreciation of human capital per period and B is the “technology parameter” of the education sector. As long as is greater than δ, the increase in human capital for the economy is all the greater: ${\ displaystyle (1-u)}$ ${\ displaystyle \ delta \ cdot H}$ ${\ displaystyle B \ cdot (1-u)}$

the higher the productivity B of the education sector
the lower the depreciation rate δ is
the higher the initial stock H of human capital
the smaller u , i.e. the working time for the formation of physical capital.

Results

The lower their preference for contemporary consumption (i.e. the lower their rate of time preference ), the more time the workers invest in building up human capital .

Empirical Findings

The model helps to explain why countries react differently to real capital inflows. After the Second World War , real capital was transferred to the destroyed Federal Republic of Germany and the economic miracle occurred . Similar transfers of capital in kind to developing countries show little to no impact. The reason is that there was plenty of human capital in Germany, while in many developing countries the lack of human capital means that physical capital inflows are ineffective.

literature

Robert E. Lucas : On the Mechanics of Economic Development . 1988 in the Journal of Monetary Economics , vol. 22, pp. 3-42.
Hirofumi Uzawa : Optimum Technical Change in an Aggregative Model of Economic Growth . 1965 in International Economic Review , vol. 6, pp. 18-31.
Michael Frenkel, Hans-Rimbert Hemmer : Foundations of the growth theory . Verlag Vahlen, Munich 1999, ISBN 3-8006-2396-X .

Web links

Uzawa-Lucas model (complete) - detailed description and solution of the problem (University of Leipzig)