Please answer A - F. Take your time. Thank you

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 rm that produces goods using capital Musing a production technology given by Y = ZF[K'N] invest in capital, where the future capital stock is given by K = (1 _ dJK +1 there is a government that finances current expenditures through taxation. , and can , 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) (1) Equilibrium in the current goods market determines the output demand curve and equilibrium in the labour market determines the output supply curve. Graphically depict the labour market and goods market equilibrium using the labour supply and demand schedules and the output demand and output supply schedules. (2 marks) e) Consider a temporary decrease in current taxes while holding government spending in the present and future constant. Using diagrams show the equilibrium effects on consumption, investment, the real interest rate, aggregate output, employment and the real wage. (5 marks) t) Consider a temporary increase in future total factor productivity, what are the equilibrium effects for current macroeconomic (capital, employment, output, labour) variables? Answer using diagrams and in words. What if the increase was permanent how would this affect the economy (again same macroeconomic variables)