Question

An economy is characterized by the Solow model, with the production function y = √k, where y is output per worker and k is capital per worker. The steady-state level of output per worker is \(y^{ss}=A^{1/(1-\alpha)}(\frac{\gamma}{\delta})^{\alpha/(1-\alpha)}\) where Α, γ, δ and a denote productivity, share of output invested (in %), depreciation rate (in %) and capital's share in income (in fraction), respectively. Suppose that A = 1, k = 400, \(\gamma\) = 50%, δ = 5% and \(\alpha\)= 1/2. Then the current output, using the above information, is

• A. above the steady-state level of output per worker.
• B. at the steady-state level of output per worker.
• C. below the steady-state level of output per worker.
• D. at the Golden Rule level.

Answer 1

The Correct Option is A

To determine whether the current output is above, below, or at the steady-state level, we follow these steps:

1. Understand the given parameters and their values:
   • The production function is \(y = \sqrt{k}\), where \(y\) is output per worker and \(k\) is capital per worker.
   • The steady-state level of output per worker is given by \(y^{ss}=A^{1/(1-\alpha)}(\frac{\gamma}{\delta})^{\alpha/(1-\alpha)}\).
   • From the question, we have: \(A = 1\), \(k = 400\), \(\gamma = 0.5\), \(\delta = 0.05\), and \(\alpha = 0.5\).
2. Calculate current output per worker:
   • Since \(y = \sqrt{k}\), substituting \(y = \sqrt{400} = 20\)
3. Calculate the steady-state output per worker using the given expression:
   • Substitute the given values into the steady-state formula: 
     \(y^{ss} = 1^{1/(1-0.5)}\left(\frac{0.5}{0.05}\right)^{0.5/(1-0.5)}\)
   • Simplify the calculations:
     • \(y^{ss} = 1^2 \times 10^1 = 10\)
4. Compare the current output and the steady-state output:
   • Current output per worker \((y = 20)\) is greater than steady-state output \((y^{ss} = 10)\).
5. Conclude that the current output is above the steady-state level of output per worker.