Q. Assume that the production function for all countries is given by y = Ak1/3. Assume that the depreciation rate d and the population growth rate n are the same for all countries. Do not assign these parameters (d and n) numerical values.
In this problem you will not be concerned with either the value of k or the value of k relative to that of the U.S. for any of the countries. )
(a) Making use of our usual basic Solow model, derive a formula for steady-state output per worker y* as a function of A, s, d, and n.
(b) Making use of your result in part (a) derive a formula for the ratio of any country's steady-state output per worker to that for the U.S. For the remainder of this problem, re-interpret the steady-state variables y* as giving values for steady-state output per capita.
(c) Using the formula from part (b), and the saving rate and TFP numbers in the table, for each country calculate the ratio of that country's steady-state output per capita to the steady-state output per capita for the U.S. You might find at least one of the results you get striking.
(d) Now use the 2007 numbers in the first column to compute, for each of the four countries, the percentage gap between the steady-state ratio obtained in part (c) and the actual 2007 ratio in the table. We will briefly cover the fact that in the context of the Solow model, the further a country is from its steady state, the faster its economy grows. In light of this, comment on the results you have obtained.