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南京翻譯公司關鍵字：Assume an economy, its social production function for the traditional Codd-Douglass production function:
Y = KαL1-α. Where Y is output, K and L are the stock of capital and labor. Obviously, this is a no technological progress of the economy. However, the existence of technological progress, is not important for our derivation. In order to derive a further simplicity, we assume that this economy has assumed all the Solow model properties, such as labor force growth rate constant (assumed to be n), the savings rate is exogenous and fixed (set s), depreciation rate δ, there is no economic專業翻譯公司服務最好的 fluctuations, to maintain full employment and so on.
Changes in the production function, by its intensive form: y = kα ... ... ... ... (1)In which y = Y / L, k = K / L. Since both capital and labor grow over time, all variables can be written as a function of time t, so we have k (t) = K (t) / L (t). Both sides of this formula for the derivative of time t to get: dk / dt = sf (k (t))-δk (t)-nk (t) ... ... ... ... (2)
By (2) shows that dk / dt is a function of k, and if k = k * when the economy reaches a balanced growth path, thedk / dt = 0. Therefore, k = k * out of dk / dt = dk / dt (k) for a first-order Taylor series approximation, we obtain:
Because β> 0, then as time goes on, y (t)-y * will become increasingly smaller. When t tends to infinity, y (t)-y * tends to zero. In other words, neo-classical assumption of diminishing marginal returns of capital, that is, α <1, on the implicit assumption that the economy will eventually converge. If that initial period, the average growth rate to t r, then y (t) = erty (0), will be substituted into the equation of (8), there are: erty (0) = e-βt (y (0)-y *) + y *, introduced:
We can see that the lower the initial per capita output, the average growth rate is higher; the other hand, the lower. Below, we will use the 28 provinces in mainland China (excluding Hainan, Chongqing, Tibet) 1952 to 2000 data to test this conclusion.
Assuming the province i in period t per capita GDP for the yi, t, per capita GDP in the initial period of yi, 0, if the period from 0 to t the average growth rate r, then yi, t = ert yi, 0, so the average rate ri = (lnyi, t-lnyi, 0) / T. If there is convergence, which the y value of 0 is lower, the higher the average growth rate. In order to return with feasibility, equation (9) to simplify, we set the regression model:
ri = A + b * lnyi, 0 + ei ... ... ... ... (10)Where A is a constant, ei is the random disturbance. If the regression results show that b is negative, which prove the existence of convergence, and the b-value, the stronger the greater the convergence. Use
And goodness of fit of this model has reached R2 = 0.83. Compared with the previous regression equation, equation (14) an excellent fit to prove the coastal nine provinces in the reform and opening up, economic專業翻譯公司服務最好的 growth has a strong convergence.
Ⅱ. Conclusion
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