Steady State Macroeconomics: (Part 2.2) Neoclassical theories with endogenous growth

 

AK Model of Humand Capital

In this model, there are no decreasing marginal returns on capital as in the models presented in part 2.1.If capital K is consider to reflect the accumulated knowledge and physical capital, this can be consider to provide constant and not reducing returns to scale.

That lead to the following equations for the determinats of the growth of output:

That ultimately means that as long as the technological progress growth is higher than the disccounted dereciation of capital, output will grow at a pace equally to the growth of that general concept of capital (human and physical).

Zero growth conditions

In this model, increases in the productivity t have to be compensated by reductions in the accumulation of capital at the same rate. That would happen if depreciation or saving preferences change in the direction to lower savings and higher depreciation. While here the determinants of growth are engogenous determined, the casual separation between technology developments and accumulation of knowledge and capital seems problematic.

Monopolistic technological change

In this model,technological progress is the result of the aim of firms to get additional rents. In this model, the rate of technological change depends on the amount of investment dedicated to it.

The output will depend by the amount of labor dedicated to production, and the productivity of labor that depends of the state of technology. The distribution of workers and researchers depends on the productivity of each in their respective final and intermediate goods sector.

The time preference affect the amount of investment in researchers, as this provide additional rents but only in the future.

Zero growth conditions

The main condition for long term growth is the investment in research, as this is the only way to achieve long term growth in this model. A sufficiently high discount rate would make investments in research less appealing and therefore growth will stagnate. Another possible condition is to reduce labor supply accordingly with the rate of technological change, so effective labor remains constant. Here the rate of reductions in the supply of labor are not clear as the stock of knowledge affects its productivity.

Replacement or Schumpeterian theories of technological change

In those models the intermediate goods sector is monopolistic and the final goods sector is competitive.  Part of the production of final goods have to be used for the production of the intermediate, which utimately affects its productivity.

To stay as a monopolist, investments are required in new technologies. Those are more or less likely to succeed which more chances the bigger the stock of inventions. 

Zero growth conditions

Constant increases in technological innovations could compensate increases in productivity, as they need a growing fraction of the goods produced. With decreasing returns on such investments that is a likely scenario.

Another option is to reduce labor supply to keep overall output constant. This is particularly relevant for labor augmenting technological change.

Directed Technological change

This models allow us to understand under which circumstances one type of technical change or the other happens. There are two effects determining the direction of technical change, the price and the market size effect. The innovation is focused on the highest profit potential gain. Profits will grow if prices could be increased (price effect) or when the production per unit of input grows (market effect).

In these models, two goods are produced with labor and different  inputs, but both use machines. If the final goods could increase the price, the demand for machines will grow too as it becomes more profitable to use them. Larger supplies of inputs increases the demand for machines too.

The present discounted values of future profits depends on the price of the final goods, as the more profitable they are, the higher the demand for machines (price effect). In the same line, large supplies of the input factors leads to high demand of machines benefiting its owners (market size).

The price effect and the market effects goes in different directions. An increase in the supply of the input would reduce the good's cost, and hence the need for technological investments to increase its effectiveness. Once an input is less costly, its demands grows with respect the others. The need effect depend on the extend that this and the other factor of production are substituable. If they are easily substituted, the demand of the input with lower price will grow sufficiently to compensate for the price effect.  Innovation will be focus on input that increases their supply and cannot be easily substituted, when susbtitution is high higher supply means lower price and hence less incentives for innovation.

Zero growth conditions

Despite the capacity of the model to explain the relationship between substitution elasticities and the incentives for innovation, the condition for the economies without growth remain. The betterment of the technology should be counterbalance by a reduction of labor supply (working hours) or capital.

It is interesting to analyze the case for natural resources and labor. Assuming they are not easily substituted, an exogenous mandated reduction in natural resources will increase the price of input (as the price effect dominate) and hence incentivize increases in natural resource augmenting technologies.

Critical assestment

In the first model presented, the AK, technological change is still exogenous, and capital definition is somehow vague. The reverse causation between savings and investment is also a source of criticism for that model.

Despite increasing our understanding our the sources of growth and the direction of technological change, those models add little insight to the conditions for zero growth and remain supply based.