Suppose Richland has the production function YR=ARLR1/2KR1/2, while Poorland has the production function YP=APLP1/2KP1/2. Assume that total factor productivity (A) is fixed – i.e. not growing -- in each country, but that L and K are evolving as described in the standard Solow model with population growth (i.e. their saving rates are given by sR and sP, their depreciation rates are given by dR and dP, and their population growth rates are given by nR and nP.)
a) Write down an expression for output per capita, Y/L, in each country.
b) Derive expressions for each country’s steady-state capital-labor ratio, in terms of its saving
rate, depreciation rate, and population growth rate.
c) Suppose dR = dP = 0.05, the saving rate in Richland is twice as large as that in Poorland, and
the population growth rate is 1% in Richland and 3% in Poorland. If steady-state output per capita is 28 times larger in Richland than in Poorland, then what must be true about the relative sizes of AR and AP? Briefly describe a few possible reasons Analyze the productivity differences.
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