(10 points) Consider the following modification of a Solow model.The economy's production function is Cobb-Douglas Y= K(EL)l-a.The government taxes incomes proportionally at a rate r and invests fraction S of the tax proceedings into capital (while putting the rest offshore).Households save fraction s out of .their disposable income.Write down an equation for aggregate investment in the economy.Assuming that economy's efficiency of labor grows exponentially at g percent a year, population grows at n percent a year, and the depreciation rate equals , fnd the steady state value of capital per effective worker as a function of s, Sg, T, n, 5, g, and a.

(a) (llll| points) Which of the three hypothesesculture, geography, or institutions would be most liker to View foreign aid as essential for economic development? Briey explain. (b) (5 points) Suppose we observe the following growth rates in various economies. A European economy: g(Y/L) = 0.03, 9(K/L) = 0.03. A Latin American economy: g(Y/L) = 0.02, g(K/L) = 0.01. An Asian economy: 9(Y/L) = 0.06, 9(K/L) = 0.15. Using the data above, discuss whether or not each economy is on its balanced growth path. (c) (5 points) For each economy above compute the growth rate of TFP, assuming that the share of capital in total income equals 1/3. (d) (10 points) Consider the following data for real GDP per capita (in PPPadjusted 2011 constant dollars) for selected countries, and the implied average annual growth from 1960 to 2014. Real GDP per capita Implied average Country 1960 2014 annual growth United States $17,600,11 $52,292.28 2.04% Mexico $5,741.?5 $15,852.57 1.90% China $1,154.19 $12,472.51 4.51% Rwanda $962.58 $1,565.14 0.90% If Mexico, China, and Rwanda continue to grow at the rates in the table, how many years, starting from 2014, will it take each to catch up to the Unites Status in terms of PPPadjusted per capita GDP as of 2014? (e) (10 points) Let us make a conjecture that technology leveb are the same across countries so that the differences in GDP per capita are the result of dierences in capital per capita. Let the ratio of capital per worker in Portugal relative to' the U.S. value equals 0.12. Assume that production function for the US. and Portugal is Cobb-Douglas, oonstantreturnstoscale in capital and labor, with the share of capital costs in total income being equal to 35%. What would be the ratio of real wages in Portugal relative to the U.S. value? (1') (10 points) Consider the following modication of a Solow model. The economy's production function is Cobb-Douglas Y = K\"(EL)1'\". The government taxes incomes proportionally at a rate 'r and invests fraction 3,, of the tax proceedings into capital (while putting the rest offshore). Households save fraction s out of their disposable income. Write down an equation for aggregate investment in the economy. Assuming that economy's efciency of labor grows exponentially at 9 percent a year, population grows at 11 percent a year, and the depreciation rate equals 6, nd the steady state value of capital per effective worker as a function of s, 39, T, n, 6, g, and a