Economıc Growth and Development (ENG) — Ünite 4 Soru-Cevap

Unfortunately, the internalization of the consumption-saving tradeoff in the Ramsey framework does not, by itself, explain why the majority of economies experience positive economic growth. In other words, just like the original Solow model, the original Ramsey model is still unable to explain positive economic growth unless an exogenous source, e.g., technological change, is defined.

However, because it solves the optimal time paths of the variables in the particular problem at hand, the Ramsey framework provides a far superior framework than the Solow framework.

The Ramsey model requires the use of an intertemporal utility function and a neoclassical production function.

The elasticity of marginal utility of consumption measures the percentage change in marginal utility in response to a percentage change in consumption. Recall that any elasticity formula is

"%change in Y /% change in X"

The reciprocal of the elasticity of marginal utility is called the elasticity of intertemporal substitution (EIS) or the intertemporal elasticity of substitution (IES).

As θ is a constant in the form of the instantaneous utility function proposed, 1/θ is called the constant elasticity of intertemporal substitution (CEIS)

In the Cobb-Douglas production function, Yt represents the (total) output, Kt physical capital stock, Lt labor force stock, At technology level, and t time. Notably, population and labor force stock are assumed to be identical. The fact that inputs Kt and Lt , output Yt
and technology At are all indexed by time indicates that they are all subject to change in time.

The Cobb-Douglas form of the production function guarantees that it is continuous and twice-differentiable. Finally, one must be aware that technology is not an input. The Cobb-Douglas production function defined above meets what are called neoclassical properties. The first one of these properties is the law of diminishing marginal returns. This law conjectures that the marginal return of any factor of production must be positive and diminishing, given that other factors of production and technology are constant.

This feature, also called homogeneity of degree one, requires a linear relationship between factors of production and output.


There is a very important reason behind the assumption of CRTS. Growth models are long-term equilibrium models. Under the assumption of a perfectly competitive market economy, profit should be zero in the long run, and the CRTS assumption guarantees zero economic profit. Furthermore, the CRTS assumption allows one to make a representative firm assumption, as it is not possible to determine the scale of production by a firm in perfectly competitive markets.

The two other possible returns to scale forms of production function are decreasing returns to scale (DRTS) and increasing returns to scale (IRTS).

For F(γK, γL, A) = γ mγ , it is the DRTS if m < 1 and IRTS if m > 1. The DRTS form implies positive economic profit, which is not possible in perfectly competitive markets, at least in the long run, and therefore, should be avoided. And the IRTS implies negative profit, which does not make any sense at all.

As any general equilibrium model features, there are two alternating approaches for modeling the Ramsey framework, namely, the decentralized and the centralized approaches

While the decentralized solution is based on the idea of equilibrium of demand and supply in markets, the centralized solution replaces markets by an omnipotent power to allocate input(s) and output(s). It is well-known that the latter always yields the Pareto-optimal solution, that is, no other allocation plan can increase the overall welfare of the representative consumer.

The first welfare theorem: Under certain conditions, the market solution is Pareto optimal.

The second welfare theorem: Under certain conditions, the Pareto optimal solution is the market solution.

These two theorems suggest that centralized solution is always Pareto optimal and that, when certain conditions are fulfilled, the decentralized solution can generate Pareto optimal results.

The transitional period characteristics of the system can be demonstrated by

(i) phase diagram analysis,
(ii) linearization, 
(iii) numerical simulation.

The centralized solution proposes an alternative approach to the construction of the Ramsey model, which is Pareto optimal. The distinguishing characteristic of the approach is that there is an omnipotent power, called the social planner, allocating resources and output to maximize the well-being of households. In that respect, it is the social planner dictating hours of work, quantity of physical capital and its accumulation, savings, and consumption. Clearly, there is no need for market prices, such as the real wage rate and the real interest rate, in this command economy. As long as there are no externalities and no distorting taxes and markets are perfectly competitive, the social planner’s solution and the market solution fully coincide. For this reason, given the short-cut nature of the centralized solution, it is often presented.

According to the maximization problem, the social planner maximizes the overall utility of the household subject to the macroeconomic budget constraint, which allocates income to physical capital accumulation after allocating for consumption and depreciation. The problem formulated above yields the same differential equation system we derived from the competitive solution. As the social planner’s solution has an easier setup, it is often preferred in the literature.

Human capital refers to the skills as well as physical and mental integrity of the labor force. It practically refers to the education level and health status of workers. The concept of human capital was introduced into the economics literature by Becker (1962) and Schultz (1960). The role of human capital in economic growth has been studied since the 1960s, e.g., Arrow (1962) and Uzawa (1965). However, the literature has not been able to provide a satisfactory answer to the question of how human capital leads to endogenous growth until Lucas (1988).

After the first endogenous growth model by Romer (1986), the first study on how human capital leads to endogenous growth is shown by Lucas (1988).

To illustrate positive externality, take the public service of salting roads during snowy winter days. It eases traffic on roads and lowers the possibility of accidents. The salt is purchased from the private sector, paid by tax revenues collected from firms and households, and creates a positive externality for the production activities of the private sector using these roads on snowy days. Similar to this, government-provided meteorological services result in positive externalities for private production (such as agriculture), but private firms bear no direct costs.

Suppose that there are three sectors in a model economy: the final-good sector, the intermediate-good sector, and the R&D sector. Human capital and intermediate goods are the model’s two factors of production

Many technological advancements increase the variety of goods that are offered in the market but are not general-purpose technologies in and of themselves and are developed in conjunction with general-purpose technologies. The bulk of these goods are used as intermediate inputs in manufacturing and referred to as horizontal product differentiation since they are examples of technological developments
that broaden the range of available goods. In contrast to horizontal product differentiation, which contends that increasing technological diversity of goods fosters endogenous growth, the literature refers to quality improvements as vertical product differentiation and argues that endogenous growth may also be a result of ongoing quality improvements.

The R&D industry makes use of a portion of human capital and previously created knowledge to generate new information in the form of patents. These patents are purchased by producers of intermediate goods at a fixed cost. Every patent holder has a monopoly since, starting on the day the patent is acquired, only they are allowed to produce the intermediate goods. Despite this, there is a monopolistic competition in the market for intermediate goods, as the intermediate goods are partial substitutes of each other.