14.02 Quiz 1 Solutions
Question 1: TRUE OR FALSE
Pt = Nominal GDPt / Real GDPt so P2000~=1.136 and inflation is (P2000-P1999)/P1999 ~=42%.
A common mistake was to divide real by nominal GDP to get the value of the deflator, and this gives the wrong answer that P2000=.88 which would lead to an inflation rate of 10%.
Value added is equal to the value of total sales minus the value of inputs, or, equivalently, to the sum of wages and profits: Value Added = 250 – 130 = 80 + 40 = 120
Note that the question asks about the private savings rate. This is the fraction of income that is saved. From the paradox of savings, we know that (if I is not a function of Y) total savings will remain unchanged in equilibrium. A rise in c1 will increase the multiplier and lead to a higher equilibrium level of income. Thus the savings rate decreases.
The IS-LM model is a good description of the war the economy works in the SHORT run.
The money multiplier is 1/[c+(1-c)theta] So in the first case, when c=1/2, the multiplier is 1/(1/2(1+theta)). Since theta is less than one, the denominator is less than one, so the multiplier is greater than one. In the second case, when consumers hold all their money as cash, c=1 and the multiplier is one. The multiplier is larger in the first case. (Note that this is a question about changes in money supply, not money demand.)
Question 2: THE GOODS MARKET
a. Z = C + I + G = 10 + .8(Y – 50) + 20 + 50 = .8Y + 40
The equilibrium condition is Z = Y so: Y = .8Y + 40, which implies Y*=200.
Autonomous spending is 40, and the muliplier is 1/(1-.8) = 5.
The multiplier reflects the feedback effects of increased demand in the economy: higher demand increases income and higher income increases demand. In particular, it gives the factor by which equilibrium output increases for an increase in autonomous spending.
c. The simple way to do this is to use the multiplier. Since I is not a function of Y, the multiplier has not changed, it is still 5. The new level of investment is I = 40 – 100(.1) = 30 so I has increased by 10. The total increase in equilibrium output will be 10*multiplier = 10*5 = 50. The new equilibrium output is 250. Or, you can work through it from the aggregate demand function. You’ll get the same answer.
Note that the new aggregate demand line is parallel to the old aggregate demand line.
There is a negative relationship between equilibrium output and interest rates: higher interest rates yield lower equilibrium output. If investment is more sensitive to the interest rate the IS curve will be flatter. Investment is more sensitive to the interest rate if the same change in interest rates produces a larger change in investment (e.g. if instead of I = 40 – 100i we had of I = 40 – 500i). If investment changes more for the same change in the interest rate, we’ll have a larger change in equilibrium output.
Question 3: FINANCIAL MARKETS
a. The equilibrium interest rate is found by setting money supply equal to money demand:
25 = PY/50i = 100/50i so i = 2/25 = 0.08.
c. Similar to part (a): 25 = PY/50i = 75/50i so i = 3/50 = 0.06.
There is a positive relationship between equilibrium output and interest rates: lower output yields a lower equilibrium interest rate. If money demand is more sensitive to the interest rate the LM curve will be flatter. Money demand is more sensitive to the interest rate if the same change in the interest rate produces a larger change in money demand (e.g. if instead of Md=PY/50i we had Md=PY/100i). If money demand is more sensitive to the interest rate, then when money demand changes due to a change in output, it’ll take a smaller change in i to restore equilibrium in the financial market.
Question 4: IS-LM MODEL
a. Z = 100 + .75(Y-40) +80 +.1Y –150i +60; Y=(20/3)(210-150i); Y= 1400-1000i;
b. 1000= Y-3000i; Y= 1000 + 3000i;
c. Y= 1000 + 3000i; Y= 1400 –1000i; Y*=1300; i*=10%
d. First, note that taxes must rise to eliminate the budget deficit. Since taxes are a parameter in the goods market equations, this is a shift of the IS curve in on graph. In particular, it is a fiscal contraction, so the IS curve shifts to the left. Hence Y* falls and i* also falls for the new equilibrium.
e. To offset the contractionary fiscal policy, the Central Bank must perform an expansionary monetary policy. Thus it should raise the money supply. To increase the money supply, the Central Bank will buy bonds in the bond market. This increases the price of bonds, and lowers the interest rate for any level of output. In turn, this increase in the money supply shifts the LM curve to the right. Hence Y* rises and i* falls relative to part (d).
f. You should have used the IS-LM model to answer this question. The fall in the MPC will shift the IS curve to the left (recall the paradox of savings), while the Fed will use an expansionary monetary policy to lower interest rates, shifting the LM to the right. We are told that equilibrium output does not change, so the new curves should meet at a point directly below the old equilibrium. Since we wrote the question we are not surprised by the outcome: the policies required to increase the level of investment had a contractionary effect via the goods market, but an expansionary effect via the financial market. (No points were awarded based on your level of surprise.) The government might want to increase investment to stimulate growth in the economy in the long-run.