>	Econ 100b Created 4/30/1996 Go to Brad De Long's Home Page

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P-Set Four Answers

Aggregate Demand

Economics 100b; Spring 1996; Brad DeLong

• multiplier = 1/(1-.6) = 2.5; multiplier = 1/(1-.75) = 4

2. Will income and production in the IS-LM model rise or fall if (a) the Federal Reserve decreases the money supply, and (b) taxes rise

• (a) shifts the LM curve to the left; (b) shifts the IS curve to the left; real GDP--income and production--falls; interest rates can go up or down

3. Suppose that the consumption function (in billions of dollars) is:

C = 200 + 0.75(Y-T)

And suppose that taxes are cut by $60 billion. What will be the shift in the equilibrium level of income and production Y?

• For any given level of the real interest rate r, the equilibrium level of Y will be lower by 4*60 = 240 billion (4 because a marginal propensity to consume of .75 corresponds to a multiplier of 4). Whether output falls by more than 240 billion or less than 240 billion depends on whether r rises or falls as a result of this cut in taxes.

4. Banks today pay interest on checking account deposits. Does this tend to make the LM curve flatter or steeper when drawn with income Y on the horizontal and interest rates i on the vertical axis?

• Steeper. An LM curve is flat if a small change in interest rates has a big effect reducing money demand--hence an expansion of output that requires more money for transactions purposes can be accomodated by the existing money stock with only a small increase in the nominal interest rate i. Paying interest on checking accounts reduces the implicit penalty for holding wealth in readily spendable form, and is likely to reduce the effect of a change in interest rates on money demand--hence steepen the LM curve.

5. Suppose that the economy has (with all spending numbers in billions, and with interest rates in percentage points):

Net taxes T of $1,000 A government deficit D of zero.
An investment function I = $1,500 - $50(r) A consumption function C = $1,400 + 0.6(Y-T)

Derive the I-S curve: use the national income identity Y = C+I+G and the government-budget identity G-T = DEF to solve for output and income Y as a function of the interest rate r. Suppose the Federal Reserve raises r from 4% to 8%. What happens to Y?

• Derive the IS curve: Y = 1400 + .6(Y-1000) + 1500 - 50r + 1000
  Y = 3300 + .6Y - 50 r
  .4Y = 3300 - 50 r
  Y = 8250 - 125r
  with r=4%, Y = 7750
  with r=8%, Y = 7250 .... down by 500

6. Consider (with all spending numbers in billions, and with interest rates in percentage points) the IS curve Y = $7,400 - $100(r) and the LM curve Y = $6,800 + $20(i). Suppose that expected inflation is zero, and there are no anticipated shifts in future monetary policy, so that i = r. What is the equilibrium level of output and income Y? What is the equilibrium level of interest rates i = r?

• First require that the Y determined by the IS curve is the same as the Y determined by the LM curve, and substitute r in for i:
  7400 - 100r = 6800 + 20i = 6800 + 20r
  600 = 120r
  r = 5(%), and so Y = 6900

7. Now suppose the government cuts taxes by $100 billion, and that the multiplier is 2.4. What is the new IS curve? What are the new equilibrium levels of output and income Y, and of interest rates r? Has Y increased by more or by less than the magnitude of the shift in the LM curve.

• New IS curve: Y = 7640 - 100r; 840 = 120r, so r=7(%) and Y= 6940. Note an ambiguity in the definition of "multiplier": do I mean the tax multiplier is 2.4, or the government spending-investment multiplier is 2.4? They are different: one is c'/(1-c'); the other is 1/(1-c')

8. Now suppose that investors and bond traders suddenly change their expectations, and now expect a future tightening of monetary policy so that r = i + 3%. What is the new equilibrium level of output and income Y? What are the new equilibrium levels of interest rates?

• IS curve: Y = 7640 - 100 r; LM curve: Y = 6800 + 20i = 6800 + 20(r - 3) = 6740 + 20r
  Thus 7640 - 100r = 6740 + 20 r,
  So: 900 = 120 r, and r = 7.5%
  The answer is that Y = 6890. Anticipated future monetary tightening has reduced output and reased unemployment, even though the Federal Reserve has not lifted a finger...