## Finding the Golden Rule Level of Capital per Effective Worker

The golden rule level of capital per effective worker, k*_gold, can be found using the Cobb-Douglas production function: Y = K^(a)*(AL)^(1-a). With a = 0.3, delta (the depreciation rate) equal to 0.3, s (the fraction of output that is saved) equal to 0.3, population growing at a rate 0.1 and technology growing at a rate 0.3, the golden rule level of capital per effective worker is:

k*_gold = (s/(n+delta+g))^(1/(1-a))

## Calculating the Steady State of Capital per Effective Worker

The steady state of capital per effective worker, k*, can be found using the Cobb-Douglas production function: Y = K^(a)*(AL)^(1-a). With a = 0.3, delta (the depreciation rate) equal to 0.3, s (the fraction of output that is saved) equal to 0.3, population growing at a rate 0.1 and technology growing at a rate 0.3, the steady state of capital per effective worker is:

k* = (s/(n+delta))^(1/(1-a))

## Calculating the Factor Shares

The factor shares, which are the shares of national income received by capital and labor, can be found using the Cobb-Douglas production function: Y = K^(a)*(AL)^(1-a). With a = 0.3, the factor shares for capital and labor are:

Share of national income received by capital = a = 0.3

Share of national income received by labor = (1-a) = 0.7

## Calculating the Steady-State Growth Rate

The steady-state growth rate, which is the rate of growth of output per effective worker in the long-run, can be found using the Cobb-Douglas production function: Y = K^(a)*(AL)^(1-a). With a = 0.3, delta (the depreciation rate) equal to 0.3, s (the fraction of output that is saved) equal to 0.3, population growing at a rate 0.1 and technology growing at a rate 0.3, the steady-state growth rate is:

Steady-state growth rate = g = n + delta + g = 0.1 + 0.3 + 0.3 = 0.7

Related Questions:

• What is the Cobb-Douglas production function?
• What is the steady-state growth rate?
• What is the golden rule level of capital per effective worker?
• What is the factor share for capital?
• What is the factor share for labor?
• What is the steady state of capital per effective worker?
• What is the depreciation rate?
• What is the fraction of output that is saved?
• What is the population growth rate?
• What is the technology growth rate?