Answer to Question #151810 in Macroeconomics for umar

Question

1Theoretically, and graphically, explain Steady State level of capital and Golden Rule level of Steady State capital as technological progress is occurred in any developing economy in the long run

Answer 1

$$Solution$$

The steady state is a state where the level of capital per worker does not change.

If present capital stock (represented by $k$ ), future capital stock (represented by $k$ ’), the rate of capital depreciation (represented by $d$ ), and level of capital investment (represented by $l$ ) are linked through the capital accumulation equation$k'=k(1-d)+l$ .

The capital accumulation equation in per worker times is given through the following equation: $(1 + g)k’ = (1 – d)k + sy = (1 – d)k + saf(k) = (1 – d)k + sak^b$

Using the Cobb-Douglas production function, $Y = aKbL1-b\ where\ 0 < b < 1$

Therefore, output per worker is given through the following equation: $y = ak^b$  where $y = \frac{Y}{L}$ (output per worker and $k = \frac{K}{L}$ (capital stock per worker)

This can be represented in the graph below.

The steady state is found by solving the following equation$k’ = k => (1 + g)k = (1 – d)k + sak^b$

Golden Rule is the capital stock per-worker that maximizes consumption per-worker. In the Solow Growth Model with technological progress, this can be denoted as $MPK=(n+\delta)$

On the graph below, the golden rule capital stock is the $k$ that maximizes the distance between the production function and total depreciation. This is because the difference between the two lines is consumption; the golden rule capital stock is the

$k$ that maximizes consumption. Mathematically, this is where the slope of the production function (MPK) is equal to the slope of the depreciation line (δ).

The golden rule can be interpreted in terms of marginal product of capital and depreciation. A one-unit increase in k raises output by MPK.

Therefore this explains the progress of a give economy in the longrun.