2. (30 points) Provide short answers to each question below.

(e)Consider the following modification of a Solow model. The econ- omy's production function is Cobb-Douglas Y = K(EL)1. The government taxes incomes proportionally at a rate and invests all of the tax proceedings into capital. Households save fraction s out of their disposable income, which is Y T = Y Y . Write down an equation for aggregate investment in the economy. Assuming that efficiency of labor grows exponentially at g percent a year, population grows at n percent a year, and the depreciation rate equals , find the steady state value of capital per effective worker as a function of s, , n, , g, and .

(e) (10 points) Consider the following modification of a Solow model. The econ- omy's production function is Cobb-Douglas Y = K(EL) 1-. The government taxes incomes proportionally at a rate 7 and invests all of the tax proceedings into capital. Households save fraction s out of their disposable income, which is Y - T = Y -TY. Write down an equation for aggregate investment in the economy. Assuming that efficiency of labor grows exponentially at g percent a year, population grows at n percent a year, and the depreciation rate equals d, find the steady state value of capital per effective worker as a function of s, T, n, 8, g, and a