Consider the data in the table below Investment TFP Per capi

Consider the data in the table below. Investment TFP Per capita GDP, 2010 Country U.S Mexico 21 22.1 0.289 0.437 (1) Assuming no differences in TFP or the rate of depreciatio n across countries, predict the ratio of per capita GDP of Mexico relative to that in the U.S. in steady state and explain. TEP is given by the level in the last column. Discuss the differences you find in these 12) Assuming two approaches

Solution

1. At the steady state of capital, the investment exactly offsets the depreciation. Investment equals the investment rate * total output. Investment is nothing but the change in capital. Change in output because of this change in capital will be guided by total factor productivity. Now, since total factot productivity and depreciation are same across the two countries in this case, the ratio of per capita GDP of Mexico relative to US at steady state equals the ratio of investment in the two countries which is (22.1*0.289)/(21*1) = 0.304

2. Now, if we do away with the assumption of constant TFP, the ratio of per capita GDP will change as now the total investment will be multiplied by TFP as well. Investment which is a change in capital when multiplied with TFP will give the total change in output as TFP gives the change in output for each unit change in capital. Hence, the ratio will be ( 22.1*0.289*0.437)/(21*1*1) = 0.132