economics help

1) Output per worker = , the saving rate is 30 percent, and the depreciation rate is 13.3 percent. Calculate the steady-state values of capital per worker and consumption per worker.

Given Info:

saving rate (s) = 30% = = 0.30

depreciation rate (δ) = 13.3% = = 0.133

production function () =

Calculation of Steady State Capital per Worker:

δk = sy = s*4k1/3

→ k/k1/3 = 4s/δ

→ (k1/3)3 = (4s/δ)3

→ k = (4*.3/.133)3 = 734.5

k = 734.5

Calculation of Steady State Consumption per Worker:

c = (1-s)y = (1-s)4k1/3 = (1-0.3)4 (734.5)3 = 25.3

c = 25.3

2) In a steady-state economy with no population growth, capital per worker is 86, the saving rate is 25 percent, and the depreciation rate is 11 percent. The level of output per worker is ________.

Given Info:

Capital per worker (k) = 86;

savings rate (s) = 0.25;

depreciation rate (δ) = 11% = = 0.11

Calculation of Steady State Output per Worker:

δk = sy

→ y =

So, y =

Hence,

Steady State Output Per Worker, y = 37.84

3) If output per worker in a steady state is $30,000, depreciation rate is 13%, the population growth rate is 2%, and the saving rate is 20%, what is the steady state capital-labor ratio?

Given Info:

Output per Worker (y) = 30,000;

depreciation rate (δ) = 13% = = 0.13;

population growth rate (n) = 2% = = 0.02;

savings rate (s) = 20% = = 0 .20

Calculation of Steady State Capital per Worker:

δk = sy

→ k = = = 45,153.84

Calculation of Steady State Capital-Labor Ratio:

k =[(s/(δ+n)]x

→ 45,153.84 = [(0.20/(0.13+.02)]x = (4/3)x

→ x = log(45,153.84)/log(4/3) = 37.25

x = 1/(1+a) →

x(1+a) = 1

x+xa = 1

a = (1/x)-1

a = (1/37.25)-1 = -145/149

since ratio can not be –ve

Thus, the steady state capital-labor ratio is 145:149