## Saturday, October 19, 2019

### Golden Rule of Capital Accumulation and Macroeconomic Policy Essay

Golden Rule of Capital Accumulation and Macroeconomic Policy - Essay Example But this steady state rate of growth can vary across economies (Solow, 1994, pp.45-46). In this context the Golden Rule of capital accumulation determines the optimal level of capital per capita that produces the optimal sustained level of per capita consumption in the economy (Mankiw, 2006, pp.110-115). This paper discusses this Golden Rule of capital accumulation and explains implications for macroeconomic policies in this context. Steady state level of capital and output per capita: The Solow Growth model determines the Ã¢â‚¬Ëœsteady state level of capital stockÃ¢â‚¬â„¢ per capita and the steady state level of output per capita. But the Golden Rule of capital accumulation determines the maximum level of consumption per capita at the Ã¢â‚¬Ëœsteady state level of capital stockÃ¢â‚¬â„¢ (Blanchard, 2006, p.230). This is called the sustainable level of consumption per capita. Here sustainable means that the present generation of the economy saves exactly that amount which is consistent with the replacement of the loss of capital stock that happened due to depreciation of that capital stock, no more and no less. In this sense this Golden Rule of capital stock provides the optimal level of consumption, savings and investment per capita at each period. Before deriving the Golden Rule capital stock let us first determine the steady state level of per capita capital and per capita output (Arnold, 2011, p.340). Assumptions and observations: Suppose that the aggregate production function is given by Y = F (K, L), where, Ã¢â‚¬Å"YÃ¢â‚¬  =aggregate output level Ã¢â‚¬Å"F ( )Ã¢â‚¬  = aggregate function Ã¢â‚¬Å"KÃ¢â‚¬  =aggregate level of capital stock Ã¢â‚¬Å"LÃ¢â‚¬  = aggregate stock of labour (Solow, 1994, pp.45-54). Let, Ã¢â‚¬Å"nÃ¢â‚¬  be the constant and exogenous rate of growth of labour force. By dividing the aggregate production function by the stock of labour Ã¢â‚¬Å"LÃ¢â‚¬ , we get the per capita production function as, y = f (k, 1), where, Ã¢â‚¬Å"yÃ¢â‚¬  = per capita output Ã¢â‚¬Å"f ( )Ã¢â‚¬  =per capita function Ã¢â‚¬Å"kÃ¢â‚¬  = per capita capital stock Ã¢â‚¬Å"1Ã¢â‚¬  is the number. Or this per capita production function can be written as y = f (k). The production function in this economy is assumed to describe the assumption of diminishing marginal productivity, i.e. rate of change in output per capita declines with the increase level of capital stock per capita. That is why the per capita production function is upward sloping and concave. The production function may exhibit constant returns to scale, i.e. one unit increase in the per capita capital raises output per capita by one unit (Baumol, 1986, pp.1072-1101). Ã¢â‚¬Å"?Ã¢â‚¬  is assumed to be the constant rate at which capital stock depreciates in each period. Hence, the total depreciation of capital per capita is: (?+n)*k. Assuming Ã¢â‚¬Å"sÃ¢â‚¬  as the constant rate of saving per capita, the total level of savings in the economy will be: s*y = s*f (k) As savings rate equals i nvestment, EconomyÃ¢â‚¬â„¢s investment is given as s*f (k) (Jones, 2002, pp.97-104). Ã¢â‚¬Å"dk/dtÃ¢â‚¬  measures the rate of change of capital stock per capita and is computed as dk/dt = s*y - (?+n)*k, where Ã¢â‚¬Å"tÃ¢â‚¬  = time element (for simplicity writing the Ã¢â‚¬Å"tÃ¢â‚¬  notation is avoided in each function). Hence, the Ã¢â‚¬Ëœsteady state level of capital stockÃ¢â‚¬â„¢ is achieved for that level of capital stock per capita where the change in capital stock is zero, i.e. , where dk/dt = 0. The steady state capital stock is denoted by k*