Consider an economy in which taxes, planned investment, government spending on goods and services, and net exports are autonomous. However, autonomous consumption changes as the interest rate changes. You are given the following information:

Ca = 1,550 12r; c = 0.75; G = 1,880; NX = 150; Ta = 1,500; Ip = 1,800

Where Ca is autonomous consumption, r is interest rate, c is the proportion of disposable income spent on consumption, G is government spending on goods and services, NX is the net export, Ta is autonomous taxes, and Ip is planned investment.

a. Compute expenditure multiplier

b. Derive the equation for the autonomous planned spending

c. Derive the equation for the IS curve

d. Find the equilibrium level of income at an interest rate of 3%

e. If government spending increases by $200 billion, what would be the new equilibrium income? (Assume interest rate remains same at 3%).