Mathematical explanation of Classical Growth Theory

Size: px

Start display at page:

Download "Mathematical explanation of Classical Growth Theory"

Brittney Houston
6 years ago
Views:

1 Classical Growth Theory Classical economist refers growth process in terms of technological progress along with population growth. With regards to their point of view the technological progress have leading role in economy for a certain period of time and eventually disappears when the accumulation of capital is restricted by the falling rate of profit. At this period the economic attain the position of inactiveness (stagnation). In broader sense, classical theory of economics can be defined as: For an expected gain or increased of profit will brings the increment in the investment, which in turn increases the existing capital stock and it will create a gradual improvement of technology. The increased capital stock will lead to the increment of rent of the labor. Higher wage rate lead to induction of higher accelerated population growth rate, which in turn increase the demand of goods (food). Production is directly related to the number of labor, so that with the increase in the demand of food there is demand of more labor and capital in the market. On contradict, the diminishing return on land brings the rise in labor cost and as a result labor cost increases and the price of good get increases. With the increase in the price the rent increases, thereby lead to reduction in profits. Reduction in profit refers to the reduction in the investment, retardation of technology, diminution (decrease) in the wage rate, and slowing down of population growth and capital accumulation. In classical model, the final result in the capitalist development is to the point of stagnation. This stagnation resulted from the natural tendency of profit to falls down and consequently cut-off the capital accumulation. At this point when all this happens the capital accumulation ceases (stops), population becomes constant and stationary economy sets in. Mathematical explanation of Classical Growth Theory Explaining with the help of mathematics the classical growth theory will tends to get easier to understand and relatively simple. The classical models in break down to several position from which we evaluate the change and final result. The following position are relevant for ease understanding: Position 1: the Production function As the classical theory, the total productivity/output of an economics is dependent of factors as size of labor force, the capital stock in economy, and the

2 availability of natural resources and technology. The theory can be expressed in the functional relationship or mathematical equation form of dependent and independent variables as: Where, Q=f (L, K, N, T) Q= Total output L=Size of labor K=Capital Stock N=Amount of natural resource T= Technology The amount of natural resource cannot the changed to increase or decrease, but only can be improved through the advance technology. So the total out ultimately depends upon labor size, stock capital, and technology. Position 2: Technological progress depends on investment The relationship between the technology and investment is given as T=f (I) i.e. technological progress is directly and proportionally related linked with investment level. This the primary reason of classical economist stressing in the increment of capital accumulation and saving, as it will ultimately result in progress of technology. Position 3: Investment depends on profit The capitalist makes their investment to increase only when they find the profitability from the production. As per the classical point of view, as being a ration personal not person will tends to invest more when they cannot achieve any profit. And here by investment we can determine the addition in the stock of capital which is Where, I= ΔK= f(r)

3 K=net addition to capital stock R= Return on capital investment or profit. Position 4: Profit depends upon labor supply and level of technology Classical economists believes that profit is function of labor size and technological progress. As with the improvement of technological factor can raise productivity and ultimately profits as well. Thus, we can say that profit is not only dependent on the technological progress but also on the labor size. R=f (T, L) As we have made analysis that technology is dependent on the level of investment and investment depends upon profit. Profit in turns dependent on the technological progress. This analysis provide the ground for interdependence of variables. T=f (I) T=f {I(R)} T=f {R (T, L)} The base of this circular argument is that level of technological progress is one of the key vital necessity of economic development. Position 5: The size of labor depend on size of wage fund This position defines the core law of wages that with the rise in wage fund there is get increased consequently and vice-versa. People it the past were not adequately informed or had idea regarding the stander of living and the consequences brought by population growth. Under this circumstance the classical economist gave a relation between the labor size and wage fund. L=f (W) L=Size of Labor W=Wage fund Position 6: Size of labor depends on investment

4 The classical economist have belief that the wage fund depends upon the saving of capitalists and that particular saving will ultimately finds its ways in the market as investment. So that, wage fund is a function of investment or say investment determines the wage fund, i.e. Here, W=f (I) W= Wage fund I=Level of investment Position 7: Closing equation From the equations above this, so we cannot determined value due to higher number of variables easily. So we determined by the system of determination and equates it to a functional forms: Q= W+R Q= Total output level W= Wages R=Revenue/ Profit i.e. the output is the sum of profits and wage together So that, the closing equation of classical theory is as under; Q= f (L, K, N, T) T= f (I) I= ΔK = f (R) R= f (T, L) L= f (W) W= f (I)

5 Q= R+W The circular model can be said to be, the economic development that implies in the level of output. This is all possible due to the development in the technological factor which is depended on the level of investment. The investment fact is depended on the profit, which is determined by the size of the wage fund. And on addition wage fund is determining factor for the size of labor force and population growth. And population growth will necessitate the development of technology through new inventions for increasing the total output level in the economy. The circular system can be represented as: L Q T W R I In the classical model, the final result of development activities is at the stationary state, which according to the classic economist is the concept of the economy getting mature, so that, it should not be undermine as the under development. The classical growth theory can be explained in simpler form, given a certain amount of labor, at certain level of production, wage will be paid to each labor according to the level of subsistence and any surplus( i.e., Total Surplus= TP- TC) accumulated by the capitalist. With increase in such accumulation there is significant increase in demand of labor, and in context of saturate population, wage tends to rise.

6 As wage surpass the substance level, the resultant would be growth in the population according to the Malthusian Theory of Population. With the growth of population the supply of labor would be fulfilled which decreases the wage to the subsistence level. The dynamics of growth ends as the law of diminishing sets up and wages eats up the whole production. As the result of which there no accumulation of surplus which creates wage rate to become at subsistence level and reduction of population growth rate. The magnificent dynamics does not end with a bang rather grumble as the given figure: TP E 1 E 2 E W P TP TP W 2 W 1 O N 1 N 2 L In the figure above we measure TP in vertical axis, size of labor in horizontal axis and OW line is the subsistence wage line. At the ON 1 number of labor, the level of output is OP. At point OP the wage per unit is N 1 W 1 and the surplus or profit is N 1 E 1, when TP=wage +profit. The emergence of surplus in the economy will leads to an increase in the demand of labor. Wage rise to N 1 E 1, and due to the increase in demand for L with accumulated population, and, at constant supply of labor in the market at ON 1 level. But as the wage rate lies above the subsistence, i.e. N 1 E 1 > N 1 W 1+, growth of population simulated to ON 2. Here when the population is at ON 2 level a surplus emerges again, i.e. W2E2, as wages are driven back to subsistence level and the process went on loop(repetition form) until it reaches to the point E where it reaches the stationary position. As at this point W=TP, there no surplus and the day of doom (portion/equilibrium) is reached. At this point if technological progress is gained,

7 only then the subsistence wage shift upwards (TP to TP! ) signifying the postponed of day of doom but not elimination.

The Production Function and Theories of Growth. Production Function and Promoting Growth. Describing Production Functions

Production Function and Promoting Growth The Production Function and Theories of Growth The production function shows the relationship between the quantity of inputs used in production and the quantity