# Compute the equilibrium interest rate

Assume the commodity market and the money market for an economy are described by the following IS and LM curve.

IS: Y = 11,000 - 250r; LM: Y = 8,000 + 250r.

a. Compute the equilibrium interest rate (r) and equilibrium real output (Y).

b. Suppose that fiscal policymakers raise taxes and cut government spending. As a result, the IS curve shifts left to Y = 10,000 - 250r. Compute the new equilibrium interest rate (r) and new equilibrium real output (Y).

c. Suppose that there is no change in fiscal policy, so that ther IS curve is Y = 11,000 - 250r. Instead monetary policymakers take action to reduce the money supply so that the LM curve shifts to Y = 7,000 + 250r. Compute equilibrium interest rate (r) and new equilibrium real output (Y).

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#### Solution Preview

a. Compute the equilibrium interest rate (r) and equilibrium real output (Y).

For equilibrium, 11,000 - 250r = 8,000 + 250r

Or 500r = 3000, which gives r = 3000/500 = 6.

At r = 6, Y = 11,000 - 250*6 = 9,500.

b. Suppose that fiscal ...

#### Solution Summary

Compute the equilibrium interest rate (r) and equilibrium real output (Y).

You are given the following information for the equations for investment demand, private saving, the government's budget deficit, and natural real GDP: Id=2400-125r, S=1760+75r, T-G=-360, and Yn=12000. Suppose that this is a closed economy. the equilibrium interest rate is the one at which national saving and investment demand are equal. (a) Derive the equation for national saving. Compute the government's budget deficit as a percent of natural real GDP. (b) compute the equilibrium interest rate. compute the amounts of investment demand, private saving, and national saving at the equilibrium interest rate. (c) Suppose that fiscal policymakers cut the government's budget deficit to 1 percent of natural Real GDP. calculate the new amound of the government's budget deficit. derive the new equation for national saving. Compute the new equilibrium interest rate. Compute the amounts of investment demand, private saving, and national saving as the new equilibrium interest rate.

Given the information from the problem above, assume a small open economy and that the foreign interest rate is 4.6 percent. (a) compute the amounts of investment demand, private saving, national saving, net exports, and net foreign borrowing at the foreign interest rate. Suppose that fiscal policy makers cut the government's budget deficit. Compute the new amounts of investment demand, private saving, national saving, and net exports. Is the economy now borrowing from the rest of the world or lending to the rest of the world? Suppose that instead of a small open economy, we have a large open economy, and that initially the domestic and foreign interest rate is 4.6 percent. Again, fiscal policy makers cut the government's budget deficit to 1 percent of natural real GDP. As a result, the domestic and foreign interest rates decline to 4.2 percent. Compute the new amounts of investment demand, private saving, the government's budget deficit, national saving, net exports, and either foreign borrowing or foreign lending at the new domestic and foreign interest rates.

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