Solow Model of Economic Growth - Example

The Solow Model – Savings Rate Population Growth and Technological Progress Introduction This paper is aimed at analysing the Solow model of economicgrowth and identifying the impact of population and increase in savings rate on economic growth. Also it explains how the Solow model accounts for technological progress. In order t do this, the paper first defines economic growth. Economic Growth To construct a definition for economic growth is not an easy task. Economic growth is best defined as transformation of an economy from a one in which rate of growth of per capita income is negative or small to one where per capita income has a self sustained and significant increase and is a long-term permanent feature1. That is, it is not GDP growth but growth in GDP per capita. Solow Model Set under the neoclassical economics framework, Solow model (also known as the Solow–Swan model) is a non-monetary economic growth model2. As all economic theories do, Solow model also makes certain simple assumptions. Following are the assumptions made in the Solow model3: Only a single commodity is produced in a economy Labour (L) and capital (K) are the only two production/output factors. Production must always be seen as net output. That is, depreciation has already happened. As there is only one good, stock of capital is equal to the commodity’s accumulation. Saving is denoted by a constant exogenous factor, s. All savings can be transformed into investment. The production will have constant returns to scale. Capital and labour can be substituted with each other. Diminishing marginal return law applies to both factors separately. Wages and prices are flexible Perfect competition Impact of Increase in Savings Rate upon Economic Growth Now let’s see how increase in savings rate impacts economic growth according to the Solow Model. Let’s start with the output function (production) and assume returns are constant. Y=F(K,L) so… zY=F(zK,zL) Per worker function can be created by setting z=1/L, Y/L=F(K/L,1) Therefore, out per worker is a function of capital per worker and can be written as, y=f(k) The marginal product of capital/worker is indicated by the slope of this function, MPK = f(k+1)–f(k). It indicated what happens to output per worker when the capital per worker is increased by 1. Now taking investment and per worker consumption gives us per worker national income accounting identity, y = c+l. Taking savings rate as‘s’ and (1-s) as consumption rate, consumption function can be generated: c = (1–s)y y = (1–s)y + l i = s*y Therefore, savings per worker is equal to investment per worker. y and k are the endogenous variables in the model and when they both are constant, long run equilibrium occurs. s is the exogenous variable. On substituting (y) by f(k), the investment per worker function (i = s*y) becomes a function of capital per worker (i = s*f(k)). A depreciation rate (δ) is defined to augment the model. Following change in capital formula is developed to witness the impact of depreciation and investment on capital: Δk = i – δk Δk = s*f(k) – δk The allocation of (k) was too high, depreciation would exceed investment and hence (k) would decrease. On the other hand, allocation was too low investment would exceed depreciation and (k) would increase. When both (y) and (k) are constant Δk = s*f(k) – δk = 0 …or, s*f(k) = δk. This occurs at k* which is the equilibrium point. At this point investment equals depreciation. Now let’s see the effects of changes in the savings rate. If there was an increase in savings, there would also be an increase in slope of investment resulting in the function to shift up. This means that steady state level of capital would be high. Similarly lower steady state level of capital would be a result of decrease in savings. Therefore, an increase in the savings rate would result in the economy expanding in the short term but in the long term would get back to the steady state growth rate4. According to this model, savings rate in richer countries is higher than that in the poor countries. Impact of Population Growth on Economic Growth Let’s augment the model to see economic growth is affected by population growth. It is important to first understand how the accumulation of capital per worker is affected by population growth in order to understand the effects of population growth on steady state. On adding population growth (n) to the model, we get: Δk = i – (δ+n)k It is evident that capital stock accumulation is negatively affected by population growth. (δ+n)k can be seen as the minimum amount of investment (break-even investment) need to ensure constant capital stock per worker. Now replacing for (i) in the above equation, we get Δk = s*f(k) – (δ+n)k At (y) = constant and (k) = constant, Δk = s*f(k) – (δ+n)k = 0 or s*f(k) = (δ+n)k This happens at equilibrium point k*. At the equilibrium point, break-even investment is equal to investment. Now let’s assume that there is a change in population growth from n1 to n2. This results in the upward shift in the line representing depreciation and population growth as shown in the figure. Therefore at the new equilibrium rate, output per worker and capital per worker are lower. This indicates that as the rate of population increases the income levels and the capital per worker lowers. According to this model, population growth rates are lower in richer countries than in poor countries5. Solow Model and Technological Progress The Solow model accounts for technological progress by replacing depreciating capital by “δk”, At the point where k and y are constants, Δk = s*f(k) – (δ+n+g)k = 0 or s*f(k) = (δ+n)k Technological progress rate, like population growth and depreciation, causes a shrink in capital stock per worker. At equilibrium, break-even investment is equal to investment. Now, let’s assume that there is a change in the worker efficiency growth rate (technological progress) from g1 to g2. This results in a upward shift in the line representing worker efficiency growth, depreciation and population growth. This also results in leftward shift of the equilibrium poi6nt which means that output per worker and capital per worker are lower. According to this model due to the impact of technological progress if there in an increase in the worker efficiency growth rate then this will result in lower levels of income and capital per worker. Hence, according to the Solow model output per effective worker remains constant in the steady state. Technological growth affects the output per worker while total output is dependent on both technological growth and population. Romer Model Romer model is an improvement of the Solow model for a simple reason that it makes technology endogenous unlike Solow model where technology is an exogenous factor. Also in accumulated factor Solow model has diminishing returns while the Romer model has non-diminishing or constant returns. Romer model attempts to make endogenous the drivers of growth. Conclusion This paper has successfully achieved the purpose which was set out in the beginning. Savings rate positively impacts the steady state output per worker while population growth impacts negatively. Romer model is an improvement of Solow Model as it makes technology an endogenous by inserting it into the model rather than keeping it exogenous. Read More