solve the following question in details

Question 7 An economy is populated by identical agents with expected lifetime utility given by: Eo EB' Inc Each period, agents rent their beginning-of-period capital stock (k,) to (identical) firms (the rental rate of capital is denoted r,) and also supply inelastically one unit of labor to firms (the wage rate is denoted w,). The income generated by these factor supplies are used to acquire consumption (c) and new capital. The depreciation rate of capital is assumed to be 100%. Firms choose labor and capital every period in order to maximize profits where output is given by the technology: where the law of motion for =, is = = =_18, where 0