Econ 1 - Problem Set 8 With Solutions

Problem Set 8 Hard copies of your answers are due at the beginning of your section, either on Thursday, November 17, or Friday, November 18. For example, if your section starts at 10:00am on Friday, you should submit your answers to your TA in your section classroom at 10:00am on Friday, November 18. Late problems earn zero points. Note: you can work on these problems or your own, or in a small group with other current Econ 1 students. If you choose to work in a group, each student needs to hand in a separate, individual copy to his/her TA. 1. Imagine an economy in which real GDP is always constant, and a government that keeps the money supply fixed. The population is concerned with the effect of a possible war on the value of the domestic currency. Could this expectation have an effect on prices? Why or why not? Make sure your explanation is based on one or more of the economic models we studied. 2. Sometimes at the beginning of an economic boom, total employment increases sharply but the unemployment rate does not fall. Why might this occur?1 3. Suppose the government decided that housewives and househusbands should be counted as employed because they perform important services. How do you think this change would affect our measure of the labor force, the participation rate, and the unemployment rate?2 4. Ellen is downloading labor market data for the most recent month, but her internet connection is interrupted and this is all she is able to get. Unemployment rate = 5.0% Participation rate = 62.% Not in the labor force = 60 million Find the labor force, the working-age population, the number of employed workers, and the number of unemployed workers.3 5. Explain why the money multiplier is generally greater than 1. In what special case would it equal 1?4 1 2 3 4

O’Sullivan and Sheffrin, third edition, page 450. O’Sullivan and Sheffrin, third edition, page 450. Frank and Bernanke, first edition, page 480. Frank and Bernanke, first edition, page 633.

6. The money supply is $1,000 and the velocity of money is five. What is nominal income? Real income? What happens to nominal income if the money supply is doubled? What happens to real income?5 Extra practice problems (completely optional; no points awarded) 1. If the European Union is not able to eradicate an outbreak of the foot-andmouth and mad cow diseases and all other countries block its meat exports, how would it affect the consumption and investment shares of GDP of the European Union in the long run? Analyze verbally and graphically. 2. (a) If the Federal Reserve increases the money supply in the U.S. by 10% in 2001, while real GDP increases by only 2%, what will be the long run effect on prices? Explain. (b) Would your answer change if the increase in the money supply was simultaneous with an increased consumer desire to hold cash? Why? 3. Given the economic definition of money, which of the following goods would qualify as money? Why or why not? Explain briefly. (a) Cigarettes in POW (prisoner of war) camps during the Second World War. (b) Argentine pesos during the hyperinflation of the late 1980’s. (c) Deutsche marks in the United States. (d) U.S. dollars in Argentina now. Note: if you do not know the historical details surrounding any of these scenarios, please write any reasonable assumptions that you need to make in order to answer this question. 4. In trying to rescue the economy from a possible recession, the Fed gradually decreased the interest rate this year from 6% in January to 4% at the end of May. Suppose the demand for money is as follows: Nominal Interest 2% Rate Quantity of Money 936 (Billions of Dollars)

4%

6%

8%

918

900

882

a) Draw to scale a graph of the money demand and money supply before and after the interest rate cut (you may interpolate between points).

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Case and Fair, seventh edition, page 663.

b) Suppose that in January the total amount of currency and reserves were $400 billion and $50 billion, respectively. Calculate the monetary base and the money multiplier. How much has the money supply changed from January to May of this year? c) Assume that the Fed made open market operations to achieve such interest rate reduction. Calculate the exact total amount of the transactions executed by the Fed, and explain how they were implemented. You may assume that the reserve ratio and currency to deposit ratio are constant. d) Suppose that real GDP grows only 1% this year, and that the money supply stays constant for the rest of the year. What would be the inflation rate for this year? e) Assume that the energy crisis forces banks to suspend ATM service several hours a day starting in June. Are there any changes to your answer to part (d)? Explain why. 5. Taylor, chapter 19, problem 9, page 499 6. Taylor, chapter 19, problem 10, page 499

ECONOMICS 1 – FALL 2005 PROBLEM SET 8 SOLUTIONS Question 1 The best way to approach this problem is by using the quantity equation of money: MV=PY

or

Money Growth + Velocity Growth = Inflation + Real GDP Growth

If people are concerned about a war changing the value of the domestic currency, they are concerned that their money will be worth less in the future (they are concerned that there will be inflation). If their dollars will be worth less in the future, then they will want to get rid of their cash and spend more now, to get more value out of their dollars. If everyone is spending more now, then there are more transactions now. This means that a dollar bill is changing hands more times which implies that V goes up. Since the money supply (M) and real GDP (Y) are constant in this problem, an increase in velocity (V) will be matched by an increase in the price level (or GDP deflator) (P). Question 2 The unemployment rate is defined as U/LF, where LF is the labor force and U is the number of unemployed workers. Note that LF=E+U where E is the number of employed workers. To be classified as an unemployed worker, however, a worker must be actively looking for a job. During economic downturns, many workers exit the labor force completely, meaning that they stop actively searching for work. These people are often referred to as “discouraged workers”. By not including these types of workers in our unemployment estimates, in some sense, unemployment rates are biased downwards during economic recessions. Once the economy improves these discouraged workers reenter the labor force and begin actively searching for work, thus being counted as unemployed. So even though E rises, U also rises, and thus the unemployment rate does not fall. Question 3 First note the following definitions: Labor Force = E+U Participation Rate = (E+U)/WAP Unemployment Rate = U/(E+U) where E is the number of persons employed, U is the number unemployed, and WAP is the working-age population (persons above 16 years of age). If housewives and househusbands are now classified as employed, E, the number of employed persons will rise. Using the above definitions we have that the labor force will rise, the participation rate will rise, and the unemployment rate will fall.

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Question 4 Using the definitions above, we have the following set of equations: U/(E+U) = 0.05 Æ 0.05E = 0.95U Æ E = 19U (E+U)/WAP = 0.62 Æ (E+U) = 0.62*WAP E + U + N = WAP and N = 60 million Æ 0.62*WAP + 60m = WAP Æ 60m=0.38WAPÆ WAP=157.9 million LF = E+U = 0.62*WAP = 97.9 million U = LF/20 = 4.9 million E =19U = 93.0 million Question 5 MM = Money Supply = C + D = k + 1 Monetary Base C+R k+r The money multiplier (MM) is generally greater than one in because deposits (D) are generally greater than reserves (R). This is equivalent to saying that the reserve ratio (r) is generally less than one. The money multiplier would equal one in the special case where reserves are exactly equal to deposits, that is, if banks were not permitted to lend out any portion of deposits placed under their control. Question 6 We know that MV=PY, so nominal income (PY) must equal $5,000. Real income (Y) is just nominal income divided by the GDP deflator (P). If the money supply is doubled and we assume that velocity is constant, nominal income should also double. The effects on real income will depend on what happens to the price level. The prediction of the quantity theory of money is that if: (a) the economy is on a long-run growth path where real GDP growth equals potential GDP growth, and (b) the growth rate of the velocity of money is constant then an increase in money growth will be matched by an increase in inflation. Consequently, if (a) and (b) apply and there is a sudden doubling of the money supply, then we would expect this to be matched by a doubling of the price level so that there are no effects on real income.

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EXTRA PRACTICE PROBLEMS Question 1 Since the question asks about shares of GDP, we should use the Spending Allocation Model. If the meat exports from the European Union are blocked by the rest of the world, then net exports = exports – imports will decrease, shifting the X/Y line downwards. This, in turn, shifts the NG/Y line downward as well, and the equilibrium interest rate will fall. Hence, we will observe a movement along the C/Y and I/Y curves, increasing their respective shares of European GDP.

R

R

R

R

NG/Y

R1 R2

C/Y1

C/Y2

C/Y

I/Y1 I/Y2

I/Y

X/Y2 X/Y1

X/Y

Question 2 a) According to the growth form of the quantity equation of money: Money Growth + Velocity Growth = Real GDP Growth + Inflation In this case, Money Growth = 10%, Real GDP Growth = 2%, and we can assume the Velocity Growth = 0 in the short-run. (Remember, velocity tends to change very little from year to year). Plugging these values into the equation yields: 10% + 0% = 2% + Inflation Hence, we may conclude that Inflation = 8%, e.g. in the long-run, there will be positive pressure on prices.

b) An increased consumer desire to hold cash will lead to lower inflation in the long run than we saw in part (a). Why? The change in behavior corresponds to a decrease in the velocity of money (say by v%). As a result, we have from the original equation: 10% - v% = 2% + Inflation

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NG/Y

Inflation = 8% - v%, e.g. it is lower than it was in part (a). Another possible answer is that the increased consumer desire to hold cash will decrease the money multiplier, so money supply will increase by less than 10%. The result is the same: lower inflation.

Question 3 First, remember that money serves three functions, acting as: a medium of exchange, a store of value, and a unit of account. In each of these situations, you need to either argue why all three functions hold (and hence the example fits the economic definition of money) or why at least one does not (hence the example does not fit the economic definition of money). a) Possibly. Certainly, cigarettes could be considered a medium of exchange and a unit of account. But since cigarettes have a limited shelf-life, you could argue that they are not a store of value (e.g. Would you value a yearold cigarette the same as a new one?). b) No. Because of the hyperinflation, the Argentine peso was not a store of value (e.g. a peso today would lose its purchasing power if held until tomorrow). c) No. A Deutsche mark in the US is not a unit of account (e.g. the prices of textbooks at the Stanford Bookstore are not quoted in marks), nor is it a medium of exchange (for the most part, people in the US are not willing to accept as payment Deutsche marks). d) At one point when Argentina pegged its currency one-for-one to the U.S. dollar by law, it could be argued that the US dollar did qualify as money since it was accepted as a medium of exchange, a store of value, and a unit of account. Now the system is more complex, so it depends on your assumptions about current conditions in Argentina.

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Question 4 a) Money Supply

i

8%

6%

4%

Money Demand

2%

882

900

918

936

Q Money

b) First, calculate the Monetary Base: MB = Currency + Bank Reserves = $400b + $50b = $450b Next, Find the Money Multiplier: Money Supply = MB * Multiplier $900 = $450 * Multiplier 2 = Multiplier Finally, to get the interest rate to move from 6% to 4%, we know that the Fed must have increased the money supply by $18 billion ($918b – $ 900b). c) In order to increase the money supply via open market operations, the Fed must buy treasury bonds and expand the monetary base. Since the currency to deposit ratio and the reserve ratio are constant, we know that the money multiplier is constant at 2, the same as we found in part (b). Recall that the Money Supply = MB * Multiplier. So,

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to increase the money supply by $18 billion, the Fed must increase the monetary base by $9 billion.

d) Money Growth + Velocity Growth (918-900)/900 + 0 .02 + 0 Inflation

= = = =

Inflation + Real GDP Growth Inflation + .01 Inflation + .01 .01 or 1%

Note that, barring a shock, velocity tends to change very little from year to year. Thus, velocity growth should be assumed to be zero unless you are given a reason to think otherwise. E) This will create negative velocity growth, and, thus, will lower the inflation rate. The reasoning is identical to Taylor’s ATM example on page 564.

Question 5 Taylor Chapter 19, Problem 9 on Page 499. A.

Using the equation 1 = C/Y + I/Y + X/Y + G/Y, we can solve for R, then use the R to solve for the spending shares.

R = 0.1013 or 10.13% C/Y = 0.6897 or 68.97%, I/Y = 0.1590 or 15.90%, X/Y = -0.0487 or -4.87%, G/Y = 0.20 or 20% B.

Repeat part A using G/Y = 0.17:

R = 0.0859 or 8.59% C/Y = 0.6928 or 69.28%, I/Y = 0.1713 or 17.13%, X/Y = -0.0341 or -3.41%, G/Y = 0.17 or 17% Note that from the SAM, it makes sense that with a lower government spending share, interest rate will be lower and other shares higher.

Question 6 Taylor Chapter 19, Problem 10 on Page 499. A.

An increase in foreign demand shifts the X/Y line right, X/Y = 0.05 – 0.95(R – 0.05). The new interest rate and shares are:

R = 0.1269 or 12.69% C/Y = 0.6846 or 68.46%, I/Y = 0.1385 or 13.85%, X/Y = -0.0231 or -2.31%, G/Y = 0.20 or 20% Thus, compared to the original situation in 9A, interest rate went up, consumption and investment shares went down, and net export share went up, while government share remained the same.

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B.

A decrease in C follows from an increase in taxes, and the C/Y line shifts down, C/Y = 0.68 – 0.2(R – 0.05). The new interest rate and shares are:

R = 0.0910 or 9.10% C/Y = 0.6718 or 67.18%, I/Y = 0.1672 or 16.72%, X/Y = -0.0390 or -3.90%, G/Y = 0.20 or 20% Thus, compared to the original situation in 9A, consumption share fell. But investment and net exports shares rose, while government share remained the same. C.

An autonomous increase in shifts the I/Y: I/Y = 0.3 – 0.8(R – 0.05). Then the new interest and shares are:

R = 0.1526 or 15.26% C/Y = 0.6795 or 67.95%, I/Y = 0.2179 or 21.79%, X/Y = -0.0974 or -9.74%, G/Y = 0.20 or 20% Thus, compared to the original situation in 9A, interest rate rose, consumption and net exports shares fell, and investment share rose, while government share remained the same.

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