14.02 Quiz 1 Solutions

Part I: True or False (2 points each)

1.  False.  The Fed targets inflation/output.  An increase in government spending will increase equilibrium output.  Since this lowers unemployment it will tend to increase inflation.  The stricter the Fed's inflation target, the more it will reduce the money supply to increase interest rates, offsetting the expansionary pressure of the increase in spending.  (See slides 12 and 13 of Fiscal Policy.)

2.  False.  You should draw the IS-LM graph.  A cut in government spending shifts the IS curve to the left, hence it lowers both equilibrium interest rate and output.  A lower interest rate will indeed stimulate investment, but lower output reduces investment.  The total effect on investment is not clear.  (See slides 8-10 of IS-LM.)

3.  True.  This can be seen directly from the Phillips Curve: RP-RP\1=(A0-RA)-(A1+B1)(U-U@vol).  The NAIRU is U which solves RP-RP\1=0 (i.e., the rate of unemployment at which inflation does not change).  So the NAIRU is (A0-RA)/(A1+B1) + U@vol (note that we often consider the case where A0=RA, which is approximately true when the relationship is estimated).  The discussion of demographics in class provides an example of this point: the higher the youth share of unemployment, the higher the NAIRU.  This is due in part to youth being more likely to be voluntarily unemployed than older workers.  (See slides 8 and 17 of Unemployment vs. Changes in Inflation.)

4.  False.  The NAIRU is the non-accelerating inflation rate of unemployment.  If the constant in the Phillips curve is zero (see the solution to T-F #3), then it is equal to voluntary unemployment.  In this case it is the level of unemployment at which everyone who wants a job at the current market wage has one.

5.  True.  The greater the sensitivity of investment and consumer demand to the interest rate, the flatter the IS curve.  For a given shift in the LM curve, the flatter the IS curve the greater the increase in equilibrium income.  (If the IS curve were vertical, i.e. if output didn't depend on the interest rate, equilibrium output would not move at all.)

6.  False.  The LM curve slopes upward, not downward.

7.  True.  Output growth can increase from increased growth in productivity or labor inputs as well.

8.  False.  Today's capital stock also depends on depreciation: K=K\1+I-D.  (See slide 17 of Core Growth Theory.)

9.  False.  The average value of the estimated errors must equal zero, but the average value of the true errors in the sample may not be zero (think of drawing a sample of one observation, what is the likelihood of picking a point with zero true error?).  The average value of the true errors in the population is assumed to be zero.  (See True-False f on Problem Set 3.)

10.  False.  R-squared does not indicate causality in the data.

11.  False.  A correct answer should note that there are many transactions that do not add to GNP (or GDP): government transfers, re-sales of assets, and purchases of intermediate goods for example.

12.  False.  NNP=GDP-Depreciation (or CCA: capital consumption allowance).  (See Slide 4 of National Income Accounts.)

13.  False.  There are two mistakes in this statement: an increase in G shifts the IS curve to the right not the left, and the multiplier is the inverse of one minus the marginal propensity to spend on GDP on domestic output.  Either is acceptable to demonstrate the statement is false.

14.  False.  The demand for money is positively related to income, but negatively related to interest rates.  (See slide 12 of IS-LM.)

15.  False.  The tradeoff observed in the 1960s was a simple relationship between the level of inflation and the level of unemployment (see slide 11 of Lecture 2).  This relationship does not hold in general (see slide 13 of Lecture 2).  Rather the modern, 'modified', Phillips Curve tells us that the tradeoff is a relationship between the change of inflation and the level of unemployment.

Part II:  Multiple Choice (3 points each)

1.  D  Every term in C, I, G, and M that multiplies Y represents a feedback effect in the economy and hence should be included in the multiplier.  (See slides 2-5 and 8-10 of IS-LM.)

2.  B  Options C, D, and E will all decrease output.  Cutting taxes will increase output, but by less than increasing government spending by an equal amount.  This is because the MPC of government is one, while the MPC of consumers is less than one.  (See Part 3, Question 4 on Problem Set 1.)

3.  D  Increased levels of infrastructure (such as health resources or better highways)can directly increase the productivity of workers.  (See slide 10 from Core Growth Theory.)  Options A and C will increase equilibrium output, but not productivity (employment rises with increased output in the goods market model).  Since transfers from the government are not payment for labor, they should not directly change productivity, so B is incorrect.  E is a change in the quantity of labor (and may in fact lower the average productivity of the workforce since they are low-skilled).

4.  C  You should draw the IS-LM graph!!!  An increase in the money supply shifts the LM curve to the right/down; an increase in taxes shifts the IS curve to the left/down.  It is then clearly and easily seen that the interest rate must fall, while output may increase or decrease depending on the magnitude of the two changes.

5.  D  The Phillips Curve relation tells us directly that increases in involuntary unemployment lead to decreases in the rate of inflation.  A, B, and E are all directly inflationary, while C should have no direct effect on inflation.

6.  H  We know that in a regression of the form lnC=A+BlnY+E the coefficient B is the elasticity of consumption with respect to income: B=(dC/C)/(dY/Y) (see T-F c or question 4 of Problem Set 3).  We also know that the estimate of B is cov(lnC,lnY)/var(lnY) (see T-F a of Problem Set 3, or the OLS handout).

Part III

1. 7 points total

(a) I = 190 –10(r-5)

(b) C = 3/4(YD)= 3/4(Y-T+Tr)= 3/5(Y)

(c) T = 3/10(Y)

(d) Tr = 1/10(Y)

(e) YD = (Y-T+Tr) = (Y- 3/10Y+1/10Y) = 4/5(Y)

(f) M= 1/6(C) = 1/6( ¾(YD)) = 1/6(3/5(Y)) = 1/10(Y)

(g) GDP=Y=C +I +G+X –M

1. 5 points

GDP =Y = C + I + G + X – M >>

Y= 3/5(Y) + 190 –10(r-5) + 200 + 100 – 1/10(Y)

Y- 3/5(Y) + 1/10(Y) = 490 – 10r + 50

Y = 2(540 –10r)

1. 3 points total

(a)  Y = 2(540-10(4)) = 1000

(b)  C= 3/5(Y) = 600

(c)  I = 190 – 10(4-5) = 200

1. 2 points total

(a)  Taxes = 3/10(Y) = 300

(b)  Transfers = 1/10(Y) = 100

(c)      Government Purchases = 200

(d)      Total Outlays = G + Tr = 300

(e)   Surplus = Taxes – Total Outlays = 0

Part IV

1. (3 points)  The IS Curve created above describes equilibrium pairs of  OUTPUT and   INTEREST RATES   that correspond to balance in the  GOODS  market, given assumptions for FISCAL policy.
2. (3 points)  The LM Curve, in contrast, describes equilibrium pairs of the same variables with respect to the MONEY (or FINANCIAL)  market(s), given assumed values for the MONEY SUPPLY  and the PRICE LEVEL .
3. (9 points)  Money demand is inversely related to the interest rate – as interest rates rise, the cost of holding money rises.  As output (Y) increases, the money demand curve shifts up (people want to conduct more transactions); therefore, people want to hold more money at any level of the interest rate.  Since money supply is exogenously fixed, this leads to an increase in the interest rate such that the money market will be in equilibrium at the new level of money demand.  This gives us an upward sloping LM curve in i-Y space.

-- or, an alternative answer --

Increased output leads to an increased demand for money (people want to conduct more transactions).  As people move from bonds to money, they drive the price of bonds down, and thus push interest rates up.  Since money supply is fixed, the interest rate will rise enough to re-equilibrate the money market at the original level of money supply – rising interest rates lead to lower money demand.  Therefore a rise in Y leads to a rise in interest rates.  This gives us the upward sloping LM curve in i-Y space.