The Solow model is widely considered to be the standard neoclassical economic growth model which serves as the basis for understanding economic growth. I will first introduce the two basic equations that the Solow model is built around, discussing the main assumptions made along the way. I will then present the key equation of the Solow model and discuss its results and implications. I will then address why it is desirable to use log-linearization, and how it can be used to study the dynamics near the steady-state. We will then briefly look into the empirical results of Mankiw et al. (1992) and what they mean for the Solow model. We begin with the aggregate production function of the model. Let us denote output (Y), capital (K), labour (L) and the index of productive efficiency (A). The production function can then be written as:
Y=F(K,AL)
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To the contrary, if a is high then the rate of convergence is low because diminishing returns set in slowly.
The differential equation for output convergence is quite similar. Assuming Cobb-Douglas technology we can show that y=k^a which then implies that y ̇/y=a k ̇/k by taking logs and differentiating with respect to time. Here a is translating a given growth rate of capital into a given growth rate of output. Substituting into the previous differential equation we get a new one for the growth rate of output:
y ̇/y≈-λ[logy-logy^*]
The growth rate in each of these expressions is linear in the gap from the steady-state measured in logarithms.
Solving both differential equations and re-arranging we get: logy(t) =(e^(-λt) )logy(0)+(1-e^(-λt) )logy^* (5) k(t)- k^*=(e^(-λt) )[k(0)-k^*]
11 (TCO 3) What is the LAW OF DIMINISHING RETURNS, and why is this law considered a short-run phenomenon?
Y=A*K, Y is the output, A is the productivity (mainly dependent on technology), K is the capital. From the definition we know the function represents constant return to scales. Therefore there would be no convergence between the growths of developed countries and developing countries, with different starting capital and productivity.
The terminal growth rate is the average growth rates from 2007 to 2011. Combining with previous cash flows of 5 years, the whole future cash flows are:
This research paper is an empirical investigation comparing the economic growth of Australia, China and the United States. It covers four topics which include the production model, the Romer model’s growth rate
Exponential Growth is shaped in a J-form, this type of growth curve occurs when supplies and materials to a specific population are abundant. Since usually environments are not idealized and resources are limited, exponential growth curve doesn’t occur as much as a logistic growth curve. Logistic growth is a type of growth curve,in a S-form, that occurs more often in an environment. Since each environment has a carrying capacity,which is the number of individuals from a population an environment can hold,the logistic growth is the most logical way to represent a population size over time. An example of a population size that could be represented by an exponential growth curve are mice. Since mice reproduce many offspring at the time of reproduction the population size will exponentially grow, however since mice also have a high predation rate the exponential curve starts rapidly decreasing over a period of time. An example of a population size that could be represented by a logistic growth curve are lions. Usually when lions reproduce only a few offspring are created. However, once an environment reaches its carrying capacity, the population size decreases as the environment can’t sustain the entire population and the “fittest” survive.
Economic growth is a common term used by economists to describe in increase in production in the long run. According to Robinson (1972) economic growth is defined as increases in aggregate product, either total or per capita, without reference to changes in the structure of the economy or in the social and cultural value systems. The basic tool of measuring the economic growth includes the real GDP. It provides some quantitative measures in terms of the production volume.
5. Growth rate of the industry: It is related to the speed at which a company goes through the phases of evolution and revolution. When it is a fast growing industry, the evolution period tends to be shorter than in a slow growing industry.
In the specific case of healthcare and marginal product, this would be the quantity of medical services divided by change in the variable input. With productivity rising to its optimal level, marginal productivity will then equal average productivity and thus average productivity is maximized. An example of this would be purchasing units of hospital beds. The more bed in inventory the more production will be realized at a certain point. Then productivity would be diminished at a rate specified above.
Exponential growth and decay are modeled in many real-world processes. Populations of people, and a growing population of anything, can be modeled as a function showing exponential growth. The growth of a savings account collecting compound interest is another example of an exponential growth function. But in conclusion Exponential growth is a mathematical change that increases without limit based on an exponential function. The change can be in the positive or negative direction. The important concept is that the rate of change continues to
In Stage two, the birth rates take a very minor dip in the graph, but maintains its birth rate. The death rate is decreasing due to increasing amounts of knowledge towards medicine as time goes by. The total population is increasing due to the death rates decreasing.
However, I=sY implying that investment is financed by savings in the economy. The growth rate of K is therefore KK=sY/K-δ. K can also be written as K=kAL and using the rules of growth rates, we can write the following; KK= kk+A/A+L/L. Denoting the rate of growth of technology A by g and rate of growth of labour by n and using the fact that KK=sY/K-δ, we can derive the growth rate of capital per effective worker as kk=sy/k-(n+g+δ) or k=sfk-n+g+δk. This is the fundamental equation of the neoclassical growth model. The economy reaches a steady state when the rate of change of capital per effective per worker equals zero. In other words, sf(k)=(n+g+δ)k. That is investment per effective worker equals the break even investment. This can be graphed as follows:
This empirical study is being presented in three sets of possible future population growth outcomes. Having Series B as a
The Solow model indicates that countries with high population growth (with no change in capital) will have lower levels of output per person. In the model therefore, population growth capital per worker and output per worker are constant. Correspondingly, the aim of the Solow Model becomes clear: it is to show that an economy will incline towards a long-run equilibrium K/L (k) ratio at which Y/L (y) is also in equilibrium, so that Y, K and L all grow at the same rate, that is n. Ultimately the model predicts long run equilibrium at the natural
The old linear economy growth model is no longer suitable for today’s economic system and gradually fall into disuse due to its inability to minimize waste from production process,
The study of economic growth focuses on the long-run trend in aggregate output as measured by potential Gross Domestic Product (GDP). Increasing the growth rate of potential GDP is key to raising the level of income, the level of profits, and the living standard of the population.