Economıc Growth and Development (ENG) — Ünite 3 Soru-Cevap

The foundations of modern economic growth theory were laid by the studies of Solow (1956) and Swan (1956), which are often labeled as the Solow model.

The Solow framework has two big successes and one big failure.

The first success of the framework is to show that investing in physical capital stock is not sufficient for an economy to generate positive growth rates in the long run.

The second success of the model is its fit to empirical growth studies. After almost six decades, it is still the only framework for revealing empirical regularities in the economic growth performance of economies.

Its big failure is that the framework does not essentially allow one to study the endogenous mechanisms that drive economic growth in an economy, and in particular, how technology changes endogenously

In this economy, there is only one representative household, Robinson Crusoe, who behaves both as a consumer and producer in the economy.

The Solow-Swan model relies on two basic equations: a neoclassical production function and a capital accumulation equation

We further assume that there is neither government nor foreign trade in this economy.

The Solow model is also a Robinson Crusoe economy. The model assumes a single good, which is either consumed or saved. Savings add to physical capital stock, which is used in the production of the next period’s output. There is no market and no price in the economy and Robinson Crusoe is both the producer and the consumer. The basic version of the model also assumes no government and no foreign trade.

The model assumes a single good, which is either consumed or saved.

Savings add to physical capital stock, which is used in the production of the next period’s output.

The production function is assumed to satisfy the following properties:

(i) The law of diminishing marginal returns: The law of diminishing marginal returns states that the marginal output of an increase in an input is smaller by each additional unit, given that the other factors of production and technology are constant.

(ii) Constant returns to scale: The constant returns to scale (CRTS) feature of a production function implies that a proportionate increase in factors of production results in an equivalent increase in output.

(iii) Inada (1963) conditions: Inada conditions state that the marginal return of a factor of production approaches infinity for the very first infinitesimal unit and approaches zero when the factor of production approaches infinity.

The law of diminishing marginal returns states that the marginal output of an increase in an input is smaller by each additional unit, given that the other factors of production and technology are constant.

The mathematical implication of this statement is that while the
first partial derivative of output with respect to an input is positive, the second partial derivative of output with respect to the same input is negative.

The constant returns to scale (CRTS) feature of a production function implies that a proportionate increase in factors of production results in an equivalent increase in output.

As an example, suppose that a cookware factory produces 10,000 pots per year using 25 units of machinery (physical capital) and 50 workers (labor). Under CRTS, if capital and labor are doubled, then the production of pots also doubles, given technology.

In the Solow model, the fundamental equation of growth shows the dynamics of physical capital over time and is represented as a one-variable differential equation.

One of the most important characteristics of the Solow model is that both the labor force (total population) and technological progress
are exogenously defined in the model.

Endogenous variable: A variable whose value is obtained from the solution of the model. For example, Kt (physical capital)and Yt (total output/production) are endogenous variables in the Solow model.

Exogenous variable: A variable whose value is given.The Solow model assumes that the time paths of labor stock and technology are exogenous; i.e, they are known.

Stock variable: A variable that can accumulate. For example, Kt , At and Lt are stock variables in the Solow model.

Flow variable: A variable that takes a new value at each point in time. For example, Yt , Ct and lt are flow variables in the Solow model.

A stable equilibrium is the situation where the variable (and the model) returns to the same equilibrium point when the variable (or the model) is exposed to a shock. In cases where the equilibrium is unstable, the variable (and the model) cannot return to the same equilibrium point after a shock.

It studies how the long-run equilibrium and the transitional dynamics of a model change in response to a change in a parameter or an exogenous variable.

It involves taking the partial derivative of the long-run equilibrium or transitional dynamics equation of a variable with respect to a parameter or an exogenous variable.

Under the Solow framework, comparative dynamics allow us to investigate the impact of changes in the key parameters (or exogenous variables) on the long-run equilibrium and the transitional dynamics of the economy. In this way, comparative dynamics provides a valuable tool to examine and test changes in government policy or external shocks.

If the savings rate is above the golden rule, s2 > sgold , then there is oversaving in the economy, which ensures high levels of capital k2> kgold in the steady state but does not deliver higher consumption c!2 < c!gold due to higher effective depreciation of physical capital. Hence, consumption per unit of effective labor can be raised by lowering the savings rate from s2 to sgold.

Therefore, a savings rate above the golden rule is dynamically inefficient, as the path of consumption per unit of effective labor always lies below the path implied by sgold.

The Solovian growth theory has also led to the rise of another huge empirical literature, namely the income convergence literature. If you recall, one of the important results of the theoretical analysis was that per capita income would always end up at its long-run value, given the fundamentals, cf. Figure 3.3. And the main driving force behind this result was the diminishing returns to the physical capital feature of the production function.

If we apply this result to a group of countries having similar fundamentals, namely, similar saving rates and population growth rates, it implies that their per capita incomes will converge to a common value in the long run.

In other words, given that they have similar fundamentals, poor (rich) countries that are below (above) their steady states will grow faster (slower) as the marginal contribution of capital to output will be higher (lower) in these countries. This phenomenon is referred to as income convergence or β-convergence.

There are two types of β-convergence: unconditional (absolute) and conditional.

The unconditional β-convergence hypothesis assumes that a country’s growth rate only depends on how far its initial level of per
capita income is from its long-run equilibrium value. For a group of countries, this hypothesis assumes that all of these countries have the same steady states. However, over time, the growth literature has shown that only countries that have similar population growth rates, savings rates, and technology levels can converge to a common steady-state level of per capita income in the long run. Hence, rather than unconditionally, the per capita income levels of countries converge conditionally.

The conditional β-convergence hypothesis also suggests that a country’s growth rate may depend on policy variables. In this regard, a large number of studies in the literature have revealed that the conditional convergence hypothesis applies to various groups collected under incomesuch as high-income and low-income, geography,;Middle East or East Asia, political unions, the European Union, economic unions, the OECD, and military unions, NATO, etc.