question is attatched:

1. (22 points) Consider a two-period economy where the representative rm uses a production technology given by Y; = ziF (Kt-,Ni) for i = 1,2, where K. is the capital input, that depreciates at the rate 6, and Ni is the labor input used by the rm in period 12 to produce Y}. Suppose that in period i, for i = 1, 2, the government levies a proportional tax, n, where 1'.- E (0, 1) on rms revenue Y}. So the taxes paid by the representative rm are Til/.5. The tax revenues are rebated lump-sum to households. Let TRi denote the lump sum transfer that the representative consumer receives. The representative rm owns capital, pays a wage rate 111 per unit of labor hired and can borrow or lend at the market real interest rate 7'. It decides on how much labor to hire in each period and how much capital to accmnulate for the following period in order to maximize the present discounted value of after-tax prots: 112(N23K2372122) V = H N K K Naijz 1( 1, 2, 1,T1,Z1)+ 1+2\" (a) 4 points) Write the equations describing the prot (pre-tax and after-tax) of the representative rm in both periods. (b) (4 points) Set-up the representative rm's problem, and derive the correspond- ing optimality conditions. (c) (2 points) Assume that the government balances its budget in every period. Write the government's budget constraints