Consider the problem of a firm who produces output in the present and the future period. Thisfirm is endowed withKunits of capital in the current period which is exogenously given. Thefirm can, however, choose future capital stockKthrough investmentI. In particular, we have thefollowing capital accumulation equation:K=I.(1)Note that this capital accumulation equation implies that capital is fully depreciated in each period(d= 1).The firm's profit is=YwNIin the current period, whereY=zF(K,N) is output,wiswage, andNis employed labor. Similarly, the profit in the future period is given by=YwN,whereY=zF(K,N) is future output,wis future wage,Nis future labor demand. Note thatthere is no value of capital left over after production in the future period due to full depreciation(d= 1). The firm maximizes the present value of profits given byV=+1 +r.

Answer the following questions.1. Write down the firm's profit maximization problem.2.

Derive labor demands for both the current period and the future period as functionsofKandK.23.

Derive the optimal rule of investmen