ECO 34730_Solutions to IS-LM Practice Problems

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Solutions to IS-LM Practice Problems

1)

Reproduce the following comparative static results:

Effect of an increase in

on

Y

r

C

I

G

+

+

?

-

CS

+

+

+

-

SP

+

+

?

+

T

-

-

-

+

M

+

-

+

+

P

-

+

-

-

MT

+

-

+

+

a) Increase in G: see IS-LM notes. b) Increase in CS: An increase in CS shifts the IS curve to the right. Thus, interest rates (r) and income (Y) must rise. For investment, since animal spirits are unchanged, only the interest rate matters. Thus, since r goes up, I must fall. For consumption, the effect looks ambiguous when using the consumption function (Y up means C up, r up means C down, CS up means C up), but in fact we can state that consumption must, in fact, go up. The key is to recall the National Income Accounting Identity ܻ =‫ܥ‬+‫ܫ‬+‫ܩ‬ Note that G is unchanged. We know Y must go up and I goes down. But if the Left-Hand Side of the equation goes up, the Right-Hand side must rise as well. Since I is falling and G is unchanged, the only way for C+I+G to go up is if C went up. c) Increase in SP: An increase in Animal Spirits shifts the IS curve right, so the interest rate and income must rise. The response of investment is tricky. It appears ambiguous, based on the investment function (SP up means I up, r up means I down), but in fact we can show that Investment had to go up. To see this consider the loanable funds diagram. The increase in SP means the investment demand curve shifts right. Then, the fact that Y goes up (from IS-LM outcome) means the savings curve must also shift right. However, the latter shift cannot be too big since we know that, in the end, the interest rate must end up higher than at the start. In any case, the rightward-shift in investment demand and the rightward-shift in the supply of savings function both increase investment. Thus, investment goes up even though the interest rate rises.

For consumption, the consumption function implies an ambiguous change in consumption since the income and interest rate effects are pushing consumption in opposite directions.

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d) Increase in T: An increase in taxes shifts the IS curve left, thereby lowering interest rates and output. The decrease in interest rates means investment must go up (since SP is unchanged).

Finally, since G is unchanged and I must rise, only a decrease in consumption can account for the decrease in GDP based on the national income accounting identity. e) Increase in M: An increase in the money supply shifts the LM curve right, lowering interest rates and raising GDP. Investment must rise since interest rates fell and SP is unchanged.

Consumption must rise since income went up, interest rates fell, and taxes and consumer sentiment are unchanged. f) Increase in P: An increase in prices is equivalent to a decrease in the real money supply, thus shifting the LM curve left. Answers are same as for increase in M but signs are reversed. g) Increase in MT: An increase in MT shifts the LM curve right, so the results are the same as for an increase in money supply.

2)

The Bush-Greenspan Policy Mix: In 2001, the Fed pursued a very expansionary monetary policy. At the same time, President George W. Bush pushed through legislation lowering income taxes. a) Illustrate the effects of such a policy mix on output. b) What happened to output in 2001? How do you reconcile the fact that both fiscal and monetary policy were expansionary with the fact that growth was so low in 2002? (Hint: what else happened?) a) Expansionary monetary policy means increases in the money supply, which leads to the LM curve shifting right. Lower income taxes is a form of expansionary fiscal policy and shifts the IS curve to the right. Thus, this policy mix should unambiguously raise GDP, but the net effect on interest rates should depend on which policy change was bigger and the slopes of the IS and LM curves. b) In 2001, the US economy was in a recession and output was shrinking, or close to it, as was also the case in 2002. This reflected the bursting of the Dotcom stock market bubble followed by the September 11th 2001 attacks. The expansionary monetary and fiscal policies were a response to the slow growth.

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3)

Policy Mixes: Suggest a policy mix (i.e. choose changes in M and G) to achieve the following objectives: a) Increase Y while keeping the interest rate constant b) Improve the budget balance (T-G) while keeping Y constant. What happens to the interest rate and investment? a) Expansionary monetary policy (raise M) and expansionary fiscal policy (raise G or lower T) will increase Y while keeping the interest rate approximately constant, since the former shifts the LM curve right and the latter shifts the IS curve right. b) Improving the trade balance typically entails higher taxes and/or lower government spending.

Both policies tend to shift the IS curve left, decreasing GDP, lowering interest rates, but raising investment.

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