Consider a representative firm with the following real profit function over their two-period planning horizon:

Profit = (1-)(k^a₁n₁^1-a -w₁n₁) - inv₁^net +(1-)((k₂^an₂^1-a/1+r) - w₂n₂/1+r) - inv₂^net/1+r

where is a tax on the firm's revenues less wage expense, f(k_t, n_t) = k_t n_t¹ is the CobbDouglas production function, w_t is the real wage rate paid to labor input n_t , r is the real interest rate, and inv^net_t is the real flow of net investment defined as:

Inv_t^net = k_t+1 - (1- ?)k_t

where k_t is the current-period real stock of capital which depreciates at rate > 0. Assume that k₁ is predetermined.

Question:

a) Using the real profit function, derive the optimality conditions for n₁, n₂, and k₂