Question

In the Solow model, if f(k)=6k⁰.⁵,s=0.20,n=0.10, and d=0.3, what is the value of k at the steady state equilibrium?

In the Solow model, if f(k)=6k⁰.⁵,s=0.20,n=0.10, and d=0.3, what are the values of y and c at the steady state equilibrium?

Answer 1

In the Solow model with the given parameters, the steady state value of capital per worker is k* = 1, yielding a steady state output per worker of y* = 6 and a consumption per worker of c* = 4.8.

Step-by-step explanation:

In the context of the Solow model, one important concept is finding the steady state equilibrium where the capital per worker does not change over time. Given the production function f(k) = 6k⁰.⁵, the saving rate s = 0.20, the population growth rate n = 0.10, and the depreciation rate d = 0.30, we can find the steady state level of capital per worker (k*) using the following equation:

s ⋅ f(k*) = (n + d) ⋅ k*

Substituting the given values, we get:

0.20 ⋅ 6 ⋅ k*⁰.⁵ = (0.10 + 0.30) ⋅ k*

Solving for k*, we find that k* = 1. Now, to find the steady state level of output per worker (y*) and consumption per worker (c*), we plug k* into the production function and the consumption function accordingly:

y* = f(k*) = 6 ⋅ 1⁰.⁵ = 6c* = (1 - s) ⋅ y* = 0.80 ⋅ 6 = 4.8

At steady state, the values are y = 6 and c = 4.8.