Consider the production function used in class, \[ y=A k^{\alpha} h^{1-\alpha} \] (i) (5 points) Write the expressions for the steady state values ofkandyas a functionA,s,n,δ, andα. (ii) (5 points) Assuming that two countries have the same values only forAandα=1/3derive expression for the predicted steady state values of output per worker relative to as a ratio (of country 1 to country 2 ).s,h,δandnare different for the two countries. (iii) (5 points) Consider the data below for Honduras and the US. Calculate steady stateyof Honduras relative to the US. Evaluate your answer.
Question
Consider the production function used in class, (i) (5 points) Write the expressions for the steady state values ofkandyas a functionA,s,n,δ, andα. (ii) (5 points) Assuming that two countries have the same values only forAandα=1/3derive expression for the predicted steady state values of output per worker relative to as a ratio (of country 1 to country 2 ).s,h,δandnare different for the two countries. (iii) (5 points) Consider the data below for Honduras and the US. Calculate steady stateyof Honduras relative to the US. Evaluate your answer.
Solution
(i) The steady state values of capital per worker (k) and output per worker (y) can be derived from the Solow-Swan model of economic growth.
The steady state level of capital per worker (k*) is given by:
k* = [sA/(δ+n)]^(1/(1-α))
where: s = savings rate A = total factor productivity δ = depreciation rate n = population growth rate α = capital share of income
The steady state level of output per worker (y*) is given by:
y* = Ak*^α
(ii) If two countries have the same values for A and α, but different values for s, h, δ, and n, the steady state output per worker of country 1 relative to country 2 is given by:
(y1/y2) = (s1/s2)^(α/(1-α)) * (h1/h2) * (δ2+n2)/(δ1+n1)
(iii) To calculate the steady state output of Honduras relative to the US, we would need the values for s, h, δ, and n for both countries. Once we have these values, we can substitute them into the equation derived in part (ii) to get the relative steady state output.
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