Consider the neoclassical growth model developed in class. The economy with constant population is composed of a very large number of infinitely-lived homo- geneous households with preferences described by:

1. (50 points) Consider the neoclassical growth model developed in class. The economy with constant population is composed of a very large number of innitely-lived homo- geneous households with preferences described by image). t=0 where at is consumption at date It. Households are endowed with one unit of productive time each period, 160 units of capital stock at date 0, and equal ownership shares of rms' prots. Households rent capital and labor services to competitive rms. Households can allocate their income to consumption or investment. There is a government that imposes a. tax 1' on capital income of households. Tax revenues are rebated back to households as a lump sum transfer T. Capital accumulation follows: Firms produce output according to the following production function Y; = AKng-a. a. (10) Dene a competitive equilibrium for this economy and a steadystate com petitive equilibrium. b. (15) Solve for the steadystate competitive equilibrium. 0. (10) Show how the capital income tax affects the real investment to output ratio and output per capita. in steady state. (1. (15) Suppose the economy is in steady state but subject to a onetime permanent increase in 1' and a decrease in A. Decompose the effects on the steadystate output per capita of these two changes