# ECON 110 Multiplier Problem Commentary

St. Charles Community College
ECON 110 Principles of Macroeconomics
Answers and Commentary on Class Discussion Problem

(This problem is taken from an Application Question which is published in the Study Guide on Pages 256 and 257)

Background:

The Arbezani Finance Minister, Count Yamunni, gives you the following national income information for the closed economy of Arbez.  At the equilibrium output (income) level, the following values occur:

C = 13,000
I = 1,200
T = 2,500
MPC = .75
G = 3,000

Questions:

1.    Calculate the equilibrium output (income) level.

Answer:  The easiest way to handle this question is through the national expenditure equation:     Y = C + I + G. Note here that we are not including the international sector (Net Exports) because the problem stated that the economy of Arbez is a closed economy.  Substituting:  Y = 13,000  + 1,200 + 3,000 = 17,200.

2.    Calculate the equilibrium value of saving.

Answer:  The only equilibrium equation that we have that includes a saving term is the general equilibrium equation:  C + I + G = C + S + T.  Subtracting the consumption term from each side of the equation, we have: I + G = S + T.  Substituting: 1,200 + 3,000 = S + 2,500.  Solving: S = 1,200 + 3,000 – 2,500 = 1,700.

3.    Calculate the marginal propensity to save.

Answer:  We are given the marginal propensity to consume as .75, and we know that MPC + MPS=1.  Substituting: .75 + MPS = 1.  Solving: MPS = 1 - .75 = .25.

4.    Calculate the value of the expenditure multiplier.

Answer:  Thanks to question number 3, we now have enough information to calculate
the expenditure multiplier which is 1/MPS.  Substituting:  1/MPS = 1/.25 = 4.

5.    Does the government have a surplus or a deficit?  How much is it?

Answer:  Remember that if tax collections exceed government spending we have a fiscal surplus, and if government spending exceeds the tax collections we have a deficit.  Looking at the numbers that we are given at the start of this problem, we see that government spending exceeds the taxes received, so we have a fiscal deficit.  Numerically, the deficit = G – T.  Substituting: Deficit = 3,000 – 2,500 = 500.

6.    Count Yamunni believes that “In equilibrium, investment must equal personal savings.”  Is this true?  Explain.

Answer:  This is a trick question, and the statement has two errors.  First, the Count’s statement is true for an economy with no government activity. However, in this problem we have a governmental sector of the economy with both government spending and government taxation.   Therefore, the Count’s statement is incorrect.  He should have said, “in equilibrium, investment plus government spending must equal saving plus taxes received.”

His second error is in the use of the term ”savings”.  He should have said “saving”.  When we talk about government expenditures and equilibrium we are talking about measurements of flow.  Saving is a “flow” term. Savings is a “stock” term.

Consumer confidence declines dramatically.  Consumption spending falls by 60.

Note:  The authors of this problem have now changed the problem, and many
students are confused by this tactic.  It will happen many more times before we
finish.  It may be helpful for students to draw a line after question 6 to note the
change.

7.    How much of an effect does this have on equilibrium GDP?

Answer:  Now we get to use the multipliers we have and will calculate. The question here is how much will this change in consumption affect national income (output).  The appropriate equation to be used here is: ?Y = ?C · (the expenditure multiplier). Since we have already calculated the expenditure multiplier as 1/MPS or 4, we can substitute as follows:  ?Y = (60)(4) = 240.

8.    At the original GDP level, is there unplanned inventories accumulation or decumulation?

Answer:  Remember our class discussion on the role of inventories.  We have had a reduction in consumer spending.  Suppliers have been producing on the basis of planned inventories.  With this decrease in consumer spending, and with this drop in national income, we can now assume that inventories will be increasing or accumulating.

The administration wishes to restore the original production level by changing the tax level.

Note:  Again, the authors have changed the problem.  Again, you may wish to draw
a line under question number 8 to denote that the problem has changed

9.    What is the value of the tax multiplier?

Answer:  Again, thanks to problem number 4, we have enough information to calculate the tax multiplier.  The formula for the tax multiplier is –MPC/MPS.  Substituting, -MPC/ MPS = -.75/.25 = -3.

10.    By how much should taxes change? Is this a tax increase or tax decrease?

Answer:  The amount that national income will be changed by a change of taxes is expressed by the formula:  ?Y = ?T· (the tax multiplier).  Thanks to the previous question, we know the tax multiplier.  Also, we know from question number 7 that the economy has decreased by 240.  We can now solve for the unknown, the amount that taxes should change.  Substituting:  240 = ?T·(-3).  ?T = 240/-3 = -80.  The negative sign in the answer tells us that this will be a tax decrease.

11.    After the economy has reached its final equilibrium, what is the size of the deficit?

Answer:  The economy has now risen to a new equilibrium, thanks to the tax cut.  But now the difference between government spending and government tax receipts is even greater.  In problem number 5 we calculated that the deficit was 500.  With the new tax cut of 80 the fiscal deficit has now increased to 580.  Another way of saying this is:  Deficit = G – T =  3,000 –  (2,500 – 80) =  3,000 – 2,500 + 80) = 580.

12.    After the economy has reached its final equilibrium, what is the final value for consumption?

Answer:  This is another tricky question, but it is at the heart of macroeconomics.  The administration wanted to spur the economy, so they cut taxes.  The tax cut brought the economy back to its original level, but the spur of the economy was done at a price.  That price was the increase in the fiscal deficit.  The country has gone further into public debt to pay for an improved national income (output) level.

To answer the question precisely we must say that the consumption level is now back to its original level or 17,200 as a result of the tax cut.  If this is still confusing, go back to the national expenditure equation and substitute.  Y = C + I + G.  Substituting:  17,200 = C + 1,200 + 3,000.  C = 13,000.

Go back to the original values you were given for the economy.  Forget all about the change in consumption spending and the change in taxes.

The newly-elected President has pledged to eliminate the deficit.  She begins by cutting government spending by 200.  Assume no other changes have occurred.

Note:  Again the authors changed the problem.  Now we’re going to decrease G
by 200 to a new level of 2,800.

13.    Calculate the increase or decrease in the equilibrium income level.

Answer:  Again were going to utilize the expenditure multiplier to see how uch this decrease in government spending affects the economy.  The appropriate equation is:  ?Y = ?G·(expenditure multiplier).  Substituting:  ?Y = (-200)(4) = -800.

14.    Calculate the new equilibrium income level.

Answer:  The economy has decreased by 800.  Therefore the new national income (output) level is 17,200 – 800 = 16,400. What has happened is that the new President has decided to move toward balancing the budget by decreasing government spending.  This move also decreased the nations GDP.

Now the President responds to the recession by also cutting income taxes by 100. Assume no other new changes.

Note:  The authors have changed the problem again.  Now we get to worry about
the cut in government spending as well as a new tax cut of 100.

15.    Calculate the increase or decrease in the equilibrium income level caused only by the tax cut.

Answer:  As the problem states, we will worry only about the new tax cut for this problem.  The equation is:  ?Y = ?T·(tax multiplier).  Substituting:  ?Y = (-100)(-3) = 300.  The economy has grown by 300 as a result of this particular tax cut.

16.    Calculate the new equilibrium income level after the spending cut and the tax cut.

Answer:  In order to answer this question we must sum up the changes.  In question 14 we found that the change in government spending decreased the economy to the level of 16,400.  This new tax cut will spur or increase the economy by 300 giving us an new level of national income (output) of 16,700.

Now forget all about the fiscal policy information.  Assume that the change in government spending and taxes did not occur.  All values are as they were in the beginning.

A wave of pessimism sweeps the business community.  Planned investment falls by 150.

Note:  The authors have changed the problem again.  Now we’re going to worry about
investment, the only national expenditure variable that we haven’t played with yet.

17.     Calculate the change in the equilibrium value of income.

Answer:  The appropriate equation here is:  ?Y  = ?I·(the expenditure multiplier).  Substituting:  ?Y = (-150)(4) = -600.  Notice that we use a negative investment since the problem says that the investment level fell.

18.    Calculate the increase or decrease in consumption after the economy has reached its new equilibrium.

Answer:  There are two ways we could approach this question.  We could go back to the original national income equation of Y = C + I + G and calculate the answer.  If we did this, we would see that (17,200 - 600) = (13,000 - ?C) + (1,200 – 150) + 3,000 would mean that consumption would decrease by 450.

The other way to calculate this value, and the trickier method, is to go back to the equation for the marginal propensity to consume:  MPC = ?C/?Y.  Substituting:
.75 = ?C/ -600.  ?c = .75(-600) = -450.

19.    Calculate the increase or decrease in saving after the economy has reached its new equilibrium.

Answer:  There are three methods to arrive at the answer for this problem.    There is the method of going back to the equilibrium equation with these new values.  We can say that I + G = S + T and ?I + ?G = ?S + ?T.  But since there was no change in G or T, we have ?I = ?S and, therefore, ?S = -150.

The second method is to go back to the national output equation of Y = C + S + T and modifying it to read:  ?Y = ?C + ?S + ?T.  Substituting:  -600 = -450  +?S + 0  (since there was no change in taxes).  ?S = -150.

The third method is to use the same method as used in question 18 except that we will use the marginal propensity to save:   MPS = ?S/ ?Y.  Substituting:  .25 = ?S/-600.
?S = .25(-600) = -150.

This prolem is used with permission of the text publisher, Prentice Hall