chapt er monetary policy* - ap...

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14 MONETARY POLICY*

K e y C o n c e p t s

Monetary Policy Objectives and Framework

The goals of monetary policy are to achieve “max-imum employment, stable prices, and moderate long-term interest rates.” Price stability is the key for achieving these goals. Price stability creates low inflation, which leads to low nominal interest rates and keeps real GDP close to potential GDP.

Monetary policy can attain its goals by keeping the growth rate of the quantity of money in line with the growth rate of potential GDP.

To determine if the goal of stable prices is being achieved, the Fed uses the core inflation rate, the in-flation rate calculated using the core PCE (personal consumption expenditure) deflator, which removes food and fuel prices from the PCE deflator. The core inflation rate is more stable than the CPI inflation rate. A core inflation rate of between 1 and 2 percent a year is generally assumed to be equivalent to price stability. To determine if the goal of maximum employment is being achieved, the Fed looks at a large number of in-dicators but the key is the output gap, the percentage deviation of real GDP from potential GDP. The Fed tries to minimize the output gap.

The Federal Open Market Committee (FOMC) is the Fed’s main policy-making group. It meets 8 times a year and the Fed releases the minutes of each meeting 3 weeks after the meeting.

The Conduct of Monetary Policy

A monetary policy instrument is a variable the Fed can directly control or closely target. The Fed could target the quantity of money or the short-term interest rate. Only one of these variables can be targeted at a time. The Fed chooses to target a short-term interest

* This chapter is Chapter 31 in Economics.

rate, the federal funds rate which is the interest rate on overnight loans of reserves that banks make to each other. When the Fed changes the federal funds rate, it generally does so by a quarter of a percentage point. The federal fund rate is determined by the equilibrium in the reserves market. The Fed uses open market operations, the purchase or sale of government securities by the Fed, to achieve its target for the federal funds rate.

When the Fed buys government securities, banks’ reserves increase. When the Fed sells government securities, banks’ reserves decrease.

The Federal Reserve can hit its federal funds interest rate target by using its open market operations to change the quantity of reserves. If the Fed wants to lower the federal funds rate, it increases the quantity of reserves by buying government securities; if the Fed wants to raise the federal funds rate, it decreases the quantity of reserves by selling government securities. To make its decision on what will be its target federal funds rate the Fed forecasts the inflation rate, the unemployment rate, and the output gap.

If inflation is above or forecast to move above what the Fed wants, the Fed raises the federal funds rate; if inflation is lower than desired, the Fed lowers the federal funds rate.

If the unemployment rate is below the natural un-employment rate, the Fed raises the federal funds rate; if the unemployment rate is above the natural unemployment rate, the Fed lowers the federal funds rate.

If the output gap is positive, so there is an infla-tionary gap, the Fed raises the federal funds rate; if the output gap is negative so there is a recessionary gap, the Fed lowers the federal funds rate.

Monetary Policy Transmission

The Fed’s actions ripple through the economy. A lower federal funds rate:

Lowers other short-term interest rates.

C h a p t e r

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Decreases the U.S. interest rate differential (the U.S. interest rate minus the interest rate in another country), which lowers the exchange rate and then increases net exports and aggregate demand.

Increases the quantity of money and increases bank loans. The increase in bank loans increases the supply of loanable funds and (temporarily) lowers the long-term real interest rate.

Increases investment and consumption expendi-ture, which both increase aggregate demand.

Aggregate demand increases, creating a multiplier process, which further increases aggregate demand.

The increase in aggregate demand raises real GDP growth and the inflation rate. Figure 14.1 shows the increase in real GDP and the price level result-ing from the increase in aggregate demand.

Recession and the Fed If real GDP is less than potential GDP, a recessionary gap exists. With a recessionary gap the Fed lowers the federal funds rate in order to increase aggregate de-mand. Real GDP and employment increase, which offset the recession.

Inflation and the Fed If real GDP exceeds potential GDP, an inflationary gap exists. In this case the Fed raises the federal funds rate to decrease aggregate demand and thereby lower the price level and avoid inflation. The actual links between the Fed’s policy and changes

in real GDP are loose and have lags. The changes in the federal funds rate must work though many sectors to change the long-term real interest rate and the change in the real interest rate depends on how inflation expec-tations change. While these effects are working out, yet other factors might change, making monetary policy difficult.

Extraordinary Monetary Stimulus

In 2007 a financial crisis occurred that brought the recession of 2008-2009. The crisis was marked by three events:

Widespread fall in asset prices — Housing prices started to rapidly fall, which decreased the value of assets based on housing. Banks suffered capital losses and were threatened with insolvency.

Significant currency drain —People with money market fund deposits withdrew them because they feared the money market fund might become in-solvent. This action decreased liquidity.

Run on banks —People with bank deposits with-drew the deposits because they feared the bank would fail. If enough people withdraw deposits, the bank becomes illiquid and does, indeed, fail.

Banks reacted by calling in loans and the supply of loanable funds drastically decreased, which lead to a substantial decrease in investment. The Fed and other government agencies reacted: Open market operations — The Fed lowered the

federal funds rate to near zero to give banks re-serves and increase their liquidity.

Extension of deposit insurance — The amount of banks’ deposits that are insured by the government was increased to decrease people’s incentives to withdraw their funds from banks.

Term auction credit, primary dealer and other broker credit, and asset-backed commercial paper money market mutual fund liquidity — These three programs allowed financial institutions to swap troubled assets for reserves and thereby in-crease their liquidity.

TARP 1 and TARP 2 — The TARP (Troubled Asset Relief Program) 1 program was designed for the U.S. Treasury to buy troubled assets from fi-nancial firms. It was replaced by TARP 2, under which the U.S. Treasury made direct investments in financial firms by purchasing equity shares in the firms.

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Fair market value— This change allowed financial firms increase the accounting value of their assets, thereby decreasing the risk of insolvency.

The recovery from the recession has been slow, pri-marily due to slow growth in investment. Investment remains low because of uncertainty. A monetary policy that helps limit uncertainty is inflation rate targeting. Inflation rate targeting — The Fed could use in-

flation rate targeting, in which the Fed would make a public commitment to meet an explicit in-flation target and then explain how its policy ac-tions will achieve that target. Other central banks use inflation rate targeting. The advantage of this policy is that it makes the goals of monetary policy explicit and makes accountability easy.

H e l p f u l H i n t s

1. ROLE OF THE LOANABLE FUNDS MARKET : The loanable funds market plays a key role in transmit-ting monetary policy from the initial change in the federal funds rate to the ultimate change in real GDP and the price level. One point to keep in mind about this process and the loanable funds market is that banks’ loans are part of the supply of loanable funds. When the Fed changes the federal rate using an open market operation, the Fed changes banks’ reserves, which then changes the quantity of loans banks can make. So if the Fed buys government securities, it sells reserves to banks, which leads the banks to increase their loans. The increase in bank loans increases the sup-ply of loanable funds.

It also is important to keep in mind that the effect on the interest rate in the loanable funds market is a short-run effect. In the short run, the real interest rate adjusts so that the loanable funds market is in equilibrium. For instance, if the Fed lowers the federal funds rate, the supply of loanable funds in-creases and, in the short run, the real interest rate falls. However in the long run, the real interest re-turns to its initial value. The result that in the long run the real interest rate returns to its starting value is similar to the result that in the long run real GDP returns to potential GDP and employment returns to full employment.

Q u e s t i o n s

True/False and Explain


11. The Fed’s key goal is achieving price level stability.

12. The core inflation rate is the inflation rate of fuel and food prices.

3. The Federal Reserve never reveals its monetary policy.


14. The Fed has chosen to use the monetary base as its policy instrument.

15. When the Federal Reserve buys government securi-ties, banks’ reserves increase.

16. When the Federal Reserve sells government securities, it shifts the demand curve for reserves rightward.


17. Higher interest rates affect consumption expendi-ture, investment, and net exports.

18. By controlling the federal funds rate, the Fed has precise control over the long-term real interest rate.

19. A decrease in the federal funds rate increases aggre-gate demand.

10. To fight inflation, the Fed raises the federal funds rate.

11. If the Fed changes its monetary policy, the imme-diate effect is to change short-run aggregate supply and shift the SAS curve.

12. One factor that makes it difficult to conduct mone-tary policy is the time lags in the monetary policy transmission process.


13. One factor that influenced the financial crisis of 2007 was the rapid run-up in asset prices.

14. In response to the financial crisis of 2007, the Fed used open market operations to increase banks’ re-serves.

15. Monetary policy must focus on actual variables, such as inflation or unemployment, and cannot be concerned with people’s inflation expectations.

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Multiple Choice


11. Which of the following is NOT one of the Fed’s monetary policy goals? a. Conducting open market operations. b. Promoting maximum employment. c. Insuring price stability. d. Keeping long-term interest rates moderate.

12. The core inflation rate ____ the CPI inflation rate. a. is always lower than b. is always higher than c. fluctuates less than d. cannot be compared to


13. Which of the following is NOT one of the Fed’s potential policy instruments? a. The federal funds rate b. The quantity of the monetary base c. The exchange rate d. The inflation rate

14. For its policy instrument(s), the Fed chooses to use a. only the quantity of the monetary base. b. the quantity of the monetary base and the federal

funds rate. c. only the federal funds rate d. the federal funds rate and the exchange rate

15. In 2009 and 2010, the Fed has set the federal funds rate at a. near record highs. b. approximately 10 percent. c. rates that have fluctuated significantly more than

normal. d. virtually equal to 0 percent.

16. An open market sale of government securities by the Fed ____ banks reserves and ____ the federal funds rate. a. increases; raises b. increases; lowers c. decreases; raises d. decreases; lowers

17. When the federal funds interest rate is 6 percent, the quantity of reserves demanded is $100 billion. If the quantity of reserves is actually $110 billion, then thea. demand for reserves increases and the demand

for reserves curve shifts rightward. b. demand for reserves decreases and the demand

for reserves curve shifts leftward. c. federal funds rate rises. d. federal funds rate falls.


18. If the Fed raises the federal funds a. investment and consumption expenditure de-

crease. b. the price of the dollar rises on the foreign ex-

change market so net exports decrease. c. a multiplier process that affects aggregate de-

mand occurs. d. All of the above answers are correct.

19. If the Fed lowers the federal funds a. the long-term real interest rate rises. b. aggregate demand decreases. c. the exchange rate falls. d. the quantity of money decreases.

10. If the Fed raises the federal funds rate, the quantity of money ____ and the supply of loanable funds ____. a. increases; increases b. increases; decreases c. decreases; increases d. decreases; decreases

11. To combat inflation, the Fed ____ the federal funds rate and as a result, the quantity of loans ____. a. lowers; decreases b. lowers; increases c. raises; decreases d. raises; increases

12. To eliminate an inflationary gap, the Fed ____ the federal funds rate and, as a result, aggregate demand ____. a. raises; increases b. raises; decreases c. lowers; increases d. lowers; decreases



13. The Fed’s actions to fight a recession shift the a. aggregate demand curve rightward. b. aggregate demand curve leftward. c. long-run aggregate supply curve rightward. d. long-run aggregate supply curve leftward.

14. A fall in the federal funds rate shifts the a. AD curve rightward. b. SAS curve rightward. c. LAS curve rightward. d. AD curve leftward.

15. If the Fed lowers the federal funds rate, it ____ the price level and ____ real GDP. a. raises; increases b. raises; does not change c. raises; decreases d. does not change; increases


16. When asset prices fall so that banks suffer a capital loss, the face the potential problem of ___; when the currency drain rises significantly, banks face the po-tential problem of ____. a. illiquidity; illiquidity b. illiquidity; insolvency c. insolvency; illiquidity d. insolvency; insolvency

17. A major factor why the recovery following the reces-sion of 2008-2009 has been slow is a. the decrease in government expenditure. b. the Fed’s policy of quickly boosting the federal

funds rate. c. the failure of consumption expenditure to re-

spond to the Fed’s interest rate policy. d. the low level of investment that has kept aggre-

gate demand low.

18. If the Fed adopted inflation rate targeting, it would make an explicit commitment to achieving an infla-tion target. In addition, the Fed also would inter-vene in the foreign exchange market to determine the U.S. exchange rate. a. Both sentences are true. b. Only the first sentence is true. c. Only the second sentence is true. d. Both sentences are false.

Short Answer Problems

1. The quantity of reserves is $50 billion, the reserves

market is in equilibrium, and the demand curve for reserves is illustrated in Figure 14.2. a. What is the equilibrium federal funds rate? b. If the Fed wants to lower the federal funds rate

to 4 percent, what must it do? Draw this change in Figure 14.2.

2. In Figure 14.3, show the effect raising the federal

funds rate has in the loanable funds market. Why is there this effect?

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3. Explain how the Fed lowers the federal funds rate. Then explain how lowering the federal funds rate affects the quantity of money and the supply of loanable funds.

4. Explain how lowering the federal funds rate affects the U.S. exchange rate.

5. Explain how lowering the federal funds rate affects consumption and investment.

6. In Figure 14.4 show how a decrease in the federal

funds rate affects the price level and real GDP.

7. Igor has been put charge of the Fed. Igor likes this job because it involves using his brain rather than collecting them. Igor thinks that the inflation rate is too high. If Igor convinces the rest of the mem-bers of the FOMC that his concern is correct, what policy action the Fed will take and how does this action affect the economy?

8. Why can’t the Fed precisely guide the U.S. econo-my and avoid both recessions and inflations?

9. Explain the difference between a bank becoming insolvent and a bank becoming illiquid.

You’re the Teacher

1. Your friend is talking: “I know that the Fed tries to keep prices stable, long-term interest rates at a rea-sonable level, and employment close to full em-ployment. But the book says that all three of these goals can be achieved if the Fed concentrates on price stability. How in the world can this be?” This question is both interesting and important. Answer it for your friend so that your friend can see its im-portance.



A n s w e r s

True/False Answers


11. T If the Fed meets its goal of price stability, then its goals of maximum employment and moder-ate long-term interest rates are easier to achieve.

12. F The core inflation is calculated using the core PCE deflator which omits fuel and food prices.

13. F The minutes of each FOMC meeting are made public three weeks after the meeting.


14. F The Fed has chosen to use the federal funds rate as its policy instrument.

15. T When the Fed buys government securities, the Fed pays for these purchases by increasing banks’ reserves.

16. F The Fed’s sale of government securities decreases the quantity of reserves but does not shift the demand curve for reserves.


17. T Higher interest rates ripple through the econo-my, affecting many sectors.

18. F The Fed has no direct control over the crucial long-term real interest rate.

19. T Changing aggregate demand is part of the ripple effect of monetary policy.

10. T By raising the federal funds rate, aggregate de-mand decreases which lowers the price level.

11. F The short-run aggregate supply does not imme-diately change in response to monetary policy.

12. T The time lags mean that determining the proper policy is difficult because the policy must be what will be needed in the future rather than what is needed in the present.


13. F A major factor that led to the financial crisis was the rapid fall in asset prices.

14. T The Fed used massive open market operations to increase banks’ reserves and supply them with liquidity.

15. F People’s inflation expectations are a crucial component of monetary policy.

Multiple Choice Answers


11. a Conducting open market operations is typically how the Fed operates to meet its monetary poli-cy goals.

12. c The core inflation rate removes the influence of changes in the prices of food and fuels. Because these prices are quite variable, the core inflation rate fluctuates less than the actual CPI inflation rate.


13. d The inflation rate is one of the Fed’s goals, not one of its instruments.

14. c The Fed could use either the federal funds rate, the quantity of money, or the exchange rate as its policy instrument. The Fed chooses to use the federal funds rate.

15. d The Fed has set the federal funds rate at a record low to combat the financial crisis and the ensu-ing recession.

16. c The open market sale decreases banks’ reserves, which raises the federal funds rate.

17. d There is a surplus of reserves so the federal funds rate falls until it reaches its new equilibrium.


18. d Each of the answers describes one of the ripples from the Fed’s policy.

19. c By lowering the federal fund rate, in the foreign exchange market the demand for U.S. dollars decreases so the exchange rate falls.

10. d To raise the federal funds rate the Fed sells U.S. government securities, which decreases banks’ reserves, thereby decreasing their loans and the quantity of money.

11. c By raising the federal funds rate and decreasing the quantity of loans, the Fed decreases aggre-gate demand.

12. b An inflationary gap means that real GDP ex-ceeds potential GDP, so by raising the federal funds rate the Fed decreases aggregate demand and real GDP.

13. a By shifting the aggregate demand curve right-ward, the Fed increases real GDP, thereby off-setting the recession.

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14. a A fall in the federal funds rate increases aggregate demand, thereby shifting the AD curve rightward.

15. a The AD curve shifts rightward so in the econo-my moves along its upward sloping SAS curve to a higher price level and increased real GDP.


16. c Insolvency occurs when the bank’s assets are no longer sufficient to meet its liabilities; illiquidity occurs when the bank cannot meet its deposi-tors’ demands for return of their funds.

17. d The fact that investment has not significantly rebounded from its recession lows is the factor that is slowing the recovery from the 2008-2009 recession.

18. b The first sentence accurately describes part of an inflation rate targeting rule. The second sentence, however, is not part of inflation rate targeting.

Answers to Short Answer Problems

1. a. The equilibrium federal funds rate is 6 percent because that is the rate which sets the quantity of reserves demanded equal to the quantity sup-plied.

b. To change the federal funds rate to 4 percent, the Fed must increase the quantity of reserves to $60 billion, as illustrated in Figure 14.5.

2. To raise the federal funds rate, the Fed will sell gov-

ernment securities to banks, thereby decreasing banks’ reserves. When banks’ reserves decrease, banks cut back on their loans, which decreases the supply of loanable funds. Figure 14.6 shows the ef-fect in the loanable funds market. The supply curve

of loanable funds shifts leftward, from SLF0 to SLF1 and the real interest rate rises, in the figure from 5 percent per year to 6 percent per year.

3. In order to lower the federal funds rate, the Fed conducts open market operations in which it buys U.S. government securities. When the Fed buys government securities, it pays for these purchases by increasing banks’ reserves. Banks then have excess reserves, which they loan. As a result, the quantity of money increases and the supply of loanable funds also increases.

4. Lowering the federal funds rate lowers the U.S. ex-change rate. With the lower U.S. interest rates, the U.S. interest rate differential falls. As a result, for-eign savers demand fewer U.S. dollars because they will buy fewer U.S. assets. And U.S. savers supply more dollars in order to buy foreign exchange to use to purchase foreign assets. The decrease in demand for U.S. dollars coupled with the increase in the supply of U.S. dollars lowers the U.S. exchange rate.

5. Lowering the federal funds rate increases consump-tion expenditure and investment. To lower the fed-eral funds rate, the Fed conducts open market operations and buys U.S. government securities.



When the Fed buys government securities, it pays for these purchases by increasing banks’ reserves. Banks then have excess reserves, which they loan so the supply of loanable funds increases. The increase in the supply of loanable funds lowers the real inter-est rate. The fall in the real interest then increases consumption expenditure and investment.

6. If the Fed cuts the federal funds rate, the quantity of

reserves and the quantity of money increase. The supply of loanable funds increases so that the long-term real interest rate falls. As a result, consumption expenditure, investment, and net exports all in-crease, thereby increasing aggregate demand. The increase in aggregate demand means the aggregate

demand curve shifts rightward, from AD0 to AD1 in Figure 14.7. The price level rises, in the figure from 100 to 110, and real GDP increases, in the figure from $12 trillion to $13 trillion.

7. Because he thinks the inflation rate is too high, Igor wants to decrease aggregate demand in order to lower the price level and thereby slow the inflation rate. The proper policy for Igor to propose to the Fed is to raise the federal funds rate. To raise the federal funds rate the Fed sells government securi-ties to banks, thereby decreasing banks’ reserves. When banks’ reserves decrease, banks cut back on their loans, which decreases the supply of loanable funds and raises the long-term real interest rate. In turn, the higher real interest rate decreases con-sumption expenditure and investment. The U.S.

exchange rate rises, which decreases net exports. As a result of the decrease in consumption expenditure, investment, and net exports, aggregate demand de-creases, thereby lowering the price level and slowing the inflation rate. (The decrease in aggregate de-mand also decreases real GDP.)

8. The Fed faces two related issues that make it impos-sible for it to guide the economy and constantly avoid both recession and inflation. First, the links in the chain that connects monetary policy actions, that is, changes in the federal funds rate, with the ultimate change in real GDP and the price level are loose and indirect. In particular, the Fed’s change in the federal funds rate must first change banks’ loans, which then must impact the loanable funds market to change the real interest rate. Then the change in the real interest rate must change investment, con-sumption, and/or net exports in order to affect ag-gregate demand. Finally the change in aggregate demand changes the price level and real GDP. If any of these links breaks, the policy has no effect. The second issue the Fed faces is that the time it takes for all the adjustments to work out can be long and can be variable. As a result, when the im-pact is finally felt on real GDP and the price level, the economic environment might have changed. The change in the environment means that the pol-icy might be counterproductive, that is, the policy might reinforces recessionary or inflationary forces that have arisen since the policy was undertaken.

9. Insolvency and illiquidity, while potentially related, nonetheless refer to separate problems. Insolvency occurs when a bank’s assets become worth less than the bank’s liabilities. In this situation the bank is bankrupt. Illiquidity occurs when a bank cannot meet the demands of its depositors for their funds. A bank can be insolvent but liquid. Conversely a bank can be solvent but illiquid. However a bank faced with a run on by its depositors might try to acquire liquidity by selling its assets and receive such low prices that the bank becomes insolvent.

You’re the Teacher

1. “This is a great question. Here is a great answer! First off, in the short run these goals can conflict with each other and price stability is not the perfect answer. For instance, if the nation faces a recession-ary gap, we know that the Fed can lower the federal funds rate with the result that real GDP increases

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and the price level rises. In this case, the Fed has boosted employment but at the cost of raising the price level and so increasing the inflation rate.”

“What the book says, however, is that in the long run achieving price stability helps the Fed reach its other goals so that in the long run these goals do not conflict. I think seeing how price stability gives moderate long-term interest rates is pretty quick. After all, the nominal interest rate equals the real in-terest rate plus the expected inflation rate. In the long run, the Fed can’t affect the real interest rate. And if prices are stable, then the expected inflation rate will be low, maybe even zero. So the nominal interest rate will surely be as low or almost as low as

possible if the price level is stable. Now, what about achieving maximum employment? Well, the deal is that we get maximum employment when people make the best decisions about working and firms make the best decisions about hiring. These deci-sions are easier to make if prices are stable because then people and firms don’t have to try to figure out how inflation will affect them in the future. If prices are stable, we get maximum employment. So, at least in the long run, it all boils down to price sta-bility in order to keep inflation and inflation expec-tations as low as possible.”



C h a p t e r Q u i z

11. If the Fed is trying to fight a recession, it will a. lower the inflation rate. b. lower the federal funds rate. c. raise the U.S. exchange rate. d. decrease the quantity of money.

12. When the Fed raises the federal funds rate, a. aggregate demand decreases. b. the long-term real interest rate falls. c. the quantity of loans increases. d. net exports increase.

13. To help combat the recent recession, the Fed has a. kept the federal funds rate high so that banks’

profits can grow. b. switched to a policy of targeting the inflation rate

because that policy lessens the uncertainty that hampers investment.

c. moved very aggressively to increase banks’ re-serves, using both open market operations as well as directly swapping reserves for banks’ troubled assets.

d. opted to undertake policies designed to directly target aggregate supply rather than attempting to affect aggregate demand.

14. The Fed’s actions to fight a recessionary gap shift thea. aggregate demand curve rightward. b. aggregate demand curve leftward. c. long-run aggregate supply curve rightward. d. long-run aggregate supply curve leftward.

15. If banks’ reserves increase, the a. demand for loanable funds increases. b. demand for loanable funds decreases. c. supply of loanable funds increases. d. supply of loanable funds decreases.

16. If the Fed purchases U.S. government securities, the federal funds rate ____ and the quantity of banks’ loans ____. a. rises; increases b. rises; decreases c. falls; increases d. falls; decreases

17. Which of the following is an objective of monetary policy? a. to conduct open market operations b. to choose the proper policy instrument c. to promote stable prices d. to insure equilibrium in the market for reserves

18. The Fed’s ability to influence economic conditions is limited by the a. extreme sensitivity of investment to the real in-

terest rate. b. fact that changes in the federal funds rate are not

immediately transmitted to aggregate demand. c. multiplier effect between changes in investment

and changes in taxes. d. fact that the Fed must coordinate its monetary

policy with fiscal policy.

19. If the Fed hikes the federal funds rate, then the quantity of money ____. a. increases b. does not change c. decreases d. probably changes, but without more information

it is not possible to determine if it increases, de-creases, or does not change

10. If the Fed raises the federal funds rate, the supply of loanable funds ____ and real GDP ____. a. increases; increases b. decreases; increases c. increases; decreases d. decreases; decreases

The answers for this Chapter Quiz are on page 254

chapt er monetary policy* - ap...

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