Could you please answer it by providing step by step solution and explanation? I would be very grateful! (Intermediate Macroeconomic)

4. Consider the real intertemporal model with investment. The economy consists of two periods (current and future), there is a representative consumer who makes work-leisure choices and a consumption-saving choices, there is a representative firm that produces goods using capital labour using a production technology given by Y = ZFUCN) , and can I invest in capital, where the future capital stock is given by K _ (1 _d)K + I there is a government that nances current expenditures through taxation. , and nally a) Write down an expression for the lifetime budget constraint of the representative consumer. (2 marks) b) The representative rm will maximize current and future prots. Write down an expression for the present value of prots for the rm. (2 marks) 0) Derive the optimal investment rule for the rm. Draw the optimal investment schedule. (4 marks)