Final answer:
To find the steady state value of capital per worker (k) in the Solow model with production function f(k) = 6k^0.5, savings rate s = 0.20, population growth n = 0.10, and depreciation d = 0.3, we solve the equation s · f(k) = (n + d) · k, leading to the steady state equilibrium value of k being 9.
Step-by-step explanation:
The student is asking about the steady state equilibrium value of capital per worker (k) in the Solow growth model—an economic model used to analyze long-term economic growth, which falls within the field of Economics. In the model, production is represented as a function of capital per worker, denoted as f(k). The steady state is reached when the accumulation of capital per worker is equal to the depreciation and dilution of capital due to population growth and physical depreciation. Here the production function is f(k) = 6k0.5, the savings rate (s) is 0.20, the population growth rate (n) is 0.10, and the depreciation rate (d) is 0.3.
To find the steady state value of k, we use the equation s · f(k) = (n + d) · k. By inserting the given values and solving for k, we find:
- 0.20 · 6k0.5 = (0.10 + 0.3) · k
- 1.2k0.5 = 0.4k
- k0.5 = k / 3
- k0.5 = k / 3
- k = (k / 3)2
- k = k2 / 9
- 9k = k2
- 0 = k2 - 9k
- 0 = k(k - 9)
This quadratic equation has two solutions, k = 0 and k = 9, but since we are looking for a positive value for capital per worker in a growing economy, the steady state equilibrium value of k is 9.