4 Solving ISLM mathematically 1. Suppose C = 0.5(Y ~ T), f = 100 10007", 'f' = 100, and C\" = 200. Derive the IS curve using the Keynesian cross model. 2. Suppose P = 1, M3 = 200, (M/P)\"! = Y - 10001'. Derive the LM curve from the money market equilibrium. 3. Draw the IS and LM curves in the same gure. Solve for the equilibrium income (Y) and the interest rate (r). 4. Suppose the government expenditure (0) librium income (Y) and the interest rate ( In which direction? increased to 350. How does this change the equi r)? Does this shift the IS curve or the LM curve? 5. Now suppose that the government expenditure 6' remains at the original level (200) but the money supply (M 8) increases to 350 from 2 00. How does this change the equilibrium income (Y) and the interest rate (1')? Does this shift the IS curve or the LM curve? In which direction