Module 16D-The Magic of the Multiplier J.A.Sacco

The Multiplier Multiplier The ratio of the change in the equilibrium level of real national income to the change in any autonomous expenditures. It is the number by which a permanent change in autonomous expenditures is multiplied to get the change in the equilibrium level of real national income. Think of the multiplier as an amplifier of autonomous expenditures leading to a change in real national income.

and Investment per Year Real National Income per Year The Multiplier 6.0 C + I 45o C + I = Y C 5.0 4.0 and Investment per Year Planned Consumption ($ trillions) 3.0 -Without I -- equilibrium = $1.5 -With I -- equilibrium = $5 -The change in Y (3.5) was 5 times the change in I (.7) 2.0 1.0 0.3 WHY? 1.0 1.5 2.0 3.0 4.0 5.0 6.0 Real National Income per Year ($ trillions)

The Multiplier Question Answer How can $.7 trillion of I generate $3.5 trillion of Y Answer The autonomous spending multiplier Note- Any permanent decrease in autonomous spending will cause a larger decrease in the equilibrium level of real national income. Here the multiplier works in reverse.

The Multiplier Process Assumption: MPC = .8 or 4/5 Annual Increase Annual Increase Annual Increase in Real in Planned in Planned National Income Consumption Saving Round ($ billions per year) ($ billions per year) ($ billions per year) 1 ($100 billion per year increase in I 100.00 80.000 20.000 2 80.00 64.00 16.000 3 64.00 51.200 12.800 4 51.20 40.960 10.240 5 40.96 32.768 8.192 . . . . . . . . . . . . All later rounds 163.84 131.072 32.768 Totals 500.00 400.00 100.000 Multiplier is “5”

The Multiplier The Multiplier Formula Sacco Tip- The multiplier is the reciprocal of the MPS.

The Multiplier Example- If MPC is 4/5, then MPS is ___. What is the multiplier? Example- If the MPC is .50, then the MPS is___. What is the multiplier?

The Multiplier Examples

The Multiplier Question Answer How does the size of the MPC influence the value of the multiplier? Answer The smaller the MPS, the larger the multiplier. The larger the MPC, the larger the multiplier.

The Multiplier Question- What would happen to the multiplier if people saved more of their additional income? Less of their income? Answer- Multiplier smaller/larger.

The Multiplier Measuring the Change in Equilibrium Income from a Change in Autonomous Spending Multiplier x Change in autonomous spending = Change in Equilibrium Income (Output)

The Multiplier Q1- MPC=0.8. Change in autonomous spending is $100B. What is the change in real national income? Q2- If the multiplier is 4, how much additional gov’t spending would be necessary to increase the economy by $1B? Q3- If the multiplier is 4, how much would the gov’t have to cut spending to lower demand by $4B?

The Multiplier Answer 1- $500B Answer 2- $250M Answer 3- $1B

The Multiplier Question What does the multiplier tell us about the potential impact on the economy from a change in autonomous spending? When is the multiplier most important?

Changes in Investment and the Great Depression What does the Investment Schedule and Business Cycle suggest?

Tax Multiplier Up to this point have looked at the spending/expenditure multiplier on autonomous expenditures. What about a decrease or increase in taxes? It’s important to know that the typical household will treat a decrease in taxes as in increase in disposable income. Most will increase consumption by a factor of the MPC and save based on the MPS. It is important to know that less than 100% of this increase in disposable income will circulate throughout the economy because most households will save a portion of it

Tax Multiplier Example of the tax multiplier 1) MPC is .90, tax refund=$200. 2) Tax multiplier process begins but not on the entire $200, only on the consumed portion of $180 because $20 is saved 3) Therefore with an MPC of .90 the autonomous spending multiplier is 10, but the tax multiplier Tm, which is 9, is smaller. 4) Tax multiplier is always smaller by 1. The savings acts as a leakage.

Tax Multiplier So for our example: Tm=MPC x (Spending multiplier)=.90x(1/.10)= 9 *the tax multiplier is always smaller than the spending multiplier by 1. Always!!! Try This!- MPC is .80 and the government decides to impose a $50 decrease in taxes. How does this effect real national income? Explain your reasoning. Answer- Since the tax multiplier is 4, real national income would increase by $200 not by $250 as with the autonomous spending multiplier/ Note- Tax multiplier is negative with an increase in taxes!

Spending Multiplier vs.Tax Multiplier Scenario- The nation is in a recession. What would be more effective to help end the recession, a $500 B tax refund to the entire population or a $500B autonomous government expenditure? Explain your answer.

The Multiplier Effect When the Price Level Can Change The multiplier effect on equilibrium real national income will not be as great if part of the increase in nominal national income occurs because of increases in the price level.

Multiplier Effect on Equilibrium of Real National Income LRAS AD2 With $100 billion increase in autonomous spending SRAS AD1 Price Level 120 5.0 Real National Income per Year ($ trillions)

Multiplier Effect on Equilibrium of Real National Income LRAS AD2 SRAS AD1 125 5.3 With price adjustment, the multiplier effect is less. Price Level What is the point being made here? 120 SRAS 5.5 With constant prices, real national income increases to 5.5 trill. 5.0 Real National Income per Year ($ trillions)