Neoclassical growth model Consider a following economy. Time is discrete and has an innite horizon (t = 0,1,2, . . . ). There is one representative household and one representative rm. There are three markets. Goods, labor, and capital. Final output produced bv the rm can be either consumed or invested by the household. Household has a log utility over the lifetime consumption of nal goods, with discount factor g3 E (0,1): U[c) = Zfi'logbct). The household takes prices as given, and chooses how much to consume and invest under her lifetime budget constraint. She earns labor and capital income, by providing labor and capital rental services to the rm. She is endowed with initial level of capital ED and labor hours ever}r period I = 1. |Capital depreciates every period by rate :5, so the law of motion is: k,\" = [1 (3)36, + it, where it is an investment in period t. Firm maximizes its prot every period. Firm's production function is given as the following: u 1 p;1 _,;._ Piss) = was; + (1 mm.\" )9-1. a E (0.1) Firm takes output prioes (pt), capital rental rates (1",), and wages (wt) as given. [That is, things are the same as in the lecture note except for the production function.) ( ( b Set up the rm's problem a Set up the household's problem ) l (c) Write down the market clearing conditions. (d) Set up and characterize the social plannerls problem (e) Solve for the steady state. 31 [f Set up and characterise the competitive equilibrium