Steady State Macroeconomics: (Part 2.1) Neoclassical Theories with exogeneous growth

 Foundations

In this theories, two agent types determines the level of production, consumption, investment, labor demand...which are homogeneous firms and homogeneous workers. Firms maximize profits producing more till the point where marginal revenue equals marginal costs. Households are workers decide how much to work given the interest rates and wages, together with their preferences. Their income comes from labor, savings and firm's profits (they are both workers and owners).

Due to the decreasing marginal productivity of the input factors and also consumption in the utility function, more work and consumption ultimately contributes less and less to the utility. Labor supply is positively related to the level of wages (the opposite happens with labor demand). Consumption decisions over time depend on the interest rates, as higher interest rates makes more appealing saving.

In this context there is no unemployment, as all labor is used and adjusted to the productivity levels on their payments. Shortages or excesses are manage via adjustments of the salary rate. The same happens with the capital market.

Without technology, the productive level depends on the amount of capital and labor used. The money market  have little impact on production level, and it solely affects the absolute price following the Fiher equation PY = VM (the level of prices is determined by the money supply (M), the velocity of money(V) and output (Y)). That does not chage the price relantionship between labor, capital and final goods.

Zero growth conditions

As long as preferences does not change and there is no technological progress, output is not changing over time. Changes is preferences affect output only once.

With technological change that increases productivity of all factors equally ( a la Hicks), the supply of factors have to drop proportionally to compensate for increases in productivity.  Households would do that if leisure is value more than additional consumption.

Technological changes that augment the productivity of one factor requires too an opposite change in one or multiple factors to compensate, and this will happen with preferences changes, mainly in favor for leisure or more consumption today instead of capital accumulation.

Solow (1956)

Sollow developed a model where capital accumulates till the marginal contribution equal depreciation rate, and the overall output depends on population/labor growth as well as technological progress. As depreciation limits the amount of capital accumulation, and there are limits on labor contribution to output, it is only technological change that can keep output to grow in the long run.

The homogenous firms face constant returns to scale, so additional inputs do not change the output more than proportionally. Labor supply and technological change are exogenous to the model, while capital accumulation depends on the production function and its inputs, the saving rate (exogenous too) and the depreciation rate (exogenous).

Zero growth conditions

Constant capital, labor and technology will lead to zero growth. If one of multiple factors increase, the other factors will have to decrease in a intensity that is conditional on the output elasticities (depends on the production function, the capital intensity and the level of the production factors. As in the founfational case, with technological change, reductions in the amount of working hours (gl<0) or a redirection of technological change to not being labor augmenting.

Microfoundations : endogenous saving rate

Instead of assuming an exogenous saving rate, the neoclassical growth model could determined endogenously as a function of the utility preferences of households. This ultimately defines how much each consume and work. HH optimize their utilities in a infinite time horizon:

The parameter rho defines the time preference, and how much utility is taken from recent and future conumption. That leads to smoothing in the consumption optimal path.

Firms maximize profits, are homogenous and pay for labor and capital its marginal productivity.

Capital will change depending on the production per unit of capital, its depreciation and consumption:

In this model, it is not possible to determine a single equilibrium as it depends on the initial values of capital and the utility function. What it is possible is determine that the rate at which all key variables evolve in a steady state, which is equal to the rate of technological progress.

Zero growth conditions

In the case without technological progress, it is sufficient that all production is dedicated to the replacement of depreciation and consumption to each zero growth.

With technological progress (labor augmenting), there have to be a counterbalance in the amount of labor supply. Labor would have to drop at the rate of technological change. Capital change does not have concrete conditions as it depends on the production function and all key variables show change equally in the steady state (k,c,y,g).

Discussion

The first observation to be made is that in this theories, zero economic growth is compatible with economic stability. Unemployment simple not exists on those theories, as all labor is employ and paid but their marginal contribution.

The second observation is that long term growth is explained entirely by technology, as there are limits in the marginal contributions of any of the factors of production.

Labor augmenting technology growth would required a reduction on labor supply, and when it shrinks (as it could in a scenario where effective labor goes down without fossil fuels) it will need to grow to compensate for the decrease in overall productivity.

Capital augmenting technology follows the same logic with investments. Lower savings, higher depreciation rates or a reduction of the productivity of capital would require increaes in capital to keep output constant.

Hicks neutral technology (augments equally or input's productivity) would  require proportional decreases of all factors.If only one changes, that would lead to changes it is price and therefore an end to the decay process. 

If the goal is to reduce natural resources usage, and there are little gains from economic growth, technological progress should be redictected towards resource augmenting technologies as far as that can go.

The main criticisms of that theory relate to the causal relationship between savings and investments, as according to keynessian theory is goes the other way around. But most important the assumption of clearing labor market (no unemployment) and freedom to choose the amount of hours (as it depends heavily on the laws and social institutions). Last but not least, the ultimate cause of long term growth in this theories, technological change, it is determine exogenously. 

In the next post, we cover endogeous theories of growth.