1. [30pts] Consider the following economy: Autonomous Consumption = $3 trillion Autonomous Investment = $1.5 trillion Autonomous Government Expenditure = $3.5 trillion Autonomous Taxes = $2.9 trillion Autonomous Net Exports = $ -1.2 trillion Autonomous Financial Frictions = 1 Marginal Propensity to Consume = 0.90 d = 0.3 X = 0.2 a. Derive the consumption function, the investment function, and the net export function. (10pts) b. Derive the simplified expression for the IS curve. (5pts) C. If the real interest rate is r= 3, what is the equilibrium output? If r = 6, what is equilibrium output? (5pts) d. Use your answers from part c to graph the IS curve. (4pts) e. If government purchases increase to $4.5 trillion, what will happen to equilibrium output at r = 3? What will happen to output at r = 6? illustrate the effect of the increased government purchases in your graph to part d. (6pts) 1. [30pts] Consider the following economy: Autonomous Consumption = $3 trillion Autonomous Investment = $1.5 trillion Autonomous Government Expenditure = $3.5 trillion Autonomous Taxes = $2.9 trillion Autonomous Net Exports = $ -1.2 trillion Autonomous Financial Frictions = 1 Marginal Propensity to Consume = 0.90 d = 0.3 X = 0.2 a. Derive the consumption function, the investment function, and the net export function. (10pts) b. Derive the simplified expression for the IS curve. (5pts) C. If the real interest rate is r= 3, what is the equilibrium output? If r = 6, what is equilibrium output? (5pts) d. Use your answers from part c to graph the IS curve. (4pts) e. If government purchases increase to $4.5 trillion, what will happen to equilibrium output at r = 3? What will happen to output at r = 6? illustrate the effect of the increased government purchases in your graph to part d. (6pts)