Using Okun’s law, fill in the four pieces of missing data in the table below. The data are hypothetical. Year Real GDP Potential GDP Natural unemployment rate (%) Actual unemployment rate...

Using Okun’s law, fill in the four pieces of missing data in the table below. The data are hypothetical.

Year

Real GDP

Potential GDP

Natural unemployment rate (%)

Actual unemployment rate (%)

2012

7,840

8,000

(a)

6

2013

8,100

(b)

5

5

2014

(c)

8,200

4.5

4

2015

8,415

8,250

5

(d)

  1. The information below describes the current state of the economy of a country called “Macroland.”  Assume that in the short run, prices are fixed, so that the Keynesian model of the economy applies.
  • C =  800 + mpc(Y – T)“C” is consumption, and “Y” is real GDP
  • T = 1000                   “T” is taxes minus transfers
  • G = 900                    “G” is government purchases
  • IP = 600                     “IP” is planned investment
  • NX = 0                      “NX” is net exports
  • mpc = 0.8                           “mpc” = the marginal propensity to consume
  1. Calculate the short-run equilibrium level of real GDP.
  2. Calculate the income-expenditure multiplier.

Suppose that the economy started out at its potential, so that the short-run equilibrium level of GDP that you found above is equal to potential GDP. Now suppose that businesses suddenly become pessimistic about future consumer demand, and planned investment (IP) falls from 600 to 500. Prices, wages, and interest rates are stuck at their old levels, and the marginal propensity to consume does not change.  (Assume that all of these things are true for the rest of the question).

  1. Calculate the short-run equilibrium level of GDP now.
  2. Calculate the output gap.
  3. The government decides to return the economy to potential GDP (Y*) by changing taxes.  In what direction should taxes change (up or down), and by how much should they change, to return the economy exactly to Y*?
  4. Illustrate what happened in part (e) on a carefully labeled “Keynesian cross” diagram. Label (with numbers) the intercepts, the equations of the PAE lines, the short-run equilibrium levels of output before and after the policy change, and the potential output.
  1. Suppose the required reserve-deposit ratio is 20%.  Assume that banks always loan out as much as they are allowed. The money supply starts at $800 billion.

a)     Suppose the Fed conducts an open market operation which sells $15 billion in bonds that banks buy with their reserves. Assume that people do not hold onto any currency outside of banks -- they re-deposit it as soon as they get it. Will the Fed’s action cause the money supply to increase or decrease?  By how much? What will the total money supply be after this occurs?

b)     Suppose that after what happens in (a), the Fed decides to reduce the required reserve-deposit ratio to 10%.  Will this increase or decrease the money supply?  By how much?  What is the total money supply now? 

  1. Explain how each of the following developments might affect the supply of money, the demand for money, and the nominal interest rate, if at all. Illustrate each answer with a diagram of the supply and demand for money.

a)     The Fed’s bond traders buy bonds in an open market operation.

b)     A bank panic hits the nation.  People try to take all the money out of their checking accounts so they can hold it as cash.

c)     Rising oil prices cause an increase in inflation.

 

Principles of Macroeconomics by Robert H. Frank and Ben S. Bernanke 5th edition

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pohnpei397's profile pic

pohnpei397 | College Teacher | (Level 3) Distinguished Educator

Posted on

As you have so many questions, I will answer as many as I can in the space provided.

Okun’s law is a rule of thumb that is meant to show the impact of changes in the unemployment rate on aggregate output.  It states that the gap between full employment output and real output in an economy increases by 2% for every percentage point that the unemployment rate rises.  In the table you have given us, the real output in 2012 is 2% lower than the potential output.  This means that there must be 1% of excess unemployment.  Since the actual rate of unemployment is 6% and there is 1% of excess unemployment, the natural rate must be 5%.  In 2013, there is no difference between the natural and actual levels of unemployment.  Therefore, there will be no difference between potential and real output.  This means that the potential output is $8100.  In 2014, the actual rate of unemployment is .5% higher than the actual.  This means that the economy is beyond full employment.  Therefore, the real output will have to be 1% (twice the difference in the unemployment) higher than the potential.  Since the potential is $8200, the real output will be $9020.  In 2015, real output is 2% higher than the potential output.  This means that actual unemployment must be 1% lower than full employment levels.  Therefore, the actual rate of unemployment in 2015 is 4%.

Now, turning to your question about bank reserves and the money supply, we can see that the money supply will decrease if the Fed sells bonds to the banks,.  This is because the banks are taking money from their reserves (but not from their required reserves) and are giving it to the Fed in return for bonds.  This reduces the amount of money that can be loaned out.  In order to determine how much the money supply has been reduced, we need to use the money multiplier.  We generally find the money multiplier by using the equation

Money multiplier = 1/reserve requirement.

In this case, the money multiplier is 1/.2.  That means the money multiplier is 5.  When the Fed sells $15 billion worth of bonds, the effect on the overall money supply is found by multiplying the value of the bonds by 5.  In other words, the Fed’s action has reduced the money supply by $75 billion.  If the money supply had been $800 billion, it is now $725 billion.  If the Fed then decreases the reserve requirement to 10%, the money supply will be increased.  First, we must realize that an additional $72.5 billion can be loaned out because 10% of the money supply is being released from required reserves (since the reserve requirement is dropping from 20% to 10%).  But then, we will have to use the multiplier to determine the effect of this increase.  The multiplier in this case will be 10 because 1/.1 (the reserve requirement) is 10.  That means that the money supply will actually increase by $725 billion simply because the reserve requirement has been dramatically reduced.

Sources:

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