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GDP Multiplier

macroeconimics

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GDP Multiplier

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  1. ECON 110:Principles of Macroeconomics Gdp calculation & the multiplier Kevin Neuman Associate Prof. of Economics School of Business & Economics 436 College of Professional Studies kneuman@uwsp.edu (715) 346-3875

  2. Algebraic Determination of GDP GDP = Expenditures Y = C + I + G + (X-IM) Y = a + MPC*(Y-T) + I + G + (X-IM) Y = a + MPC*Y – MPC*T + I + G + (X-IM) Y – MPC*Y = a– MPC*T + I + G + (X-IM) Y*(1 – MPC) = a– MPC*T + I + G + (X-IM) a– MPC*T + I + G + (X-IM) (1-MPC) Y=

  3. Algebraic Determination of GDP (cont.) • If you have all the values you can calculate GDP • I=$900 G=$1,300 (X-IM)=-$100 T=$1,200 C=$300+0.75*(Y-T) a– MPC*T + I + G + (X-IM) (1-MPC) Y= $300– 0.75*$1,200 + $900 + $1,300 + (-$100) (1-0.75) Y= $300– $900 + $900 + $1,300 -$100 (0.25) $1,500 0.25 Y= = = $6,000

  4. Algebraic Determination of GDP (cont.) • What happens if you increase I by $300? • I=$1,200 G=$1,300 (X-IM)=-$100 T=$1,200 C=$300+0.75*(Y-T) • Increase spending by $300 and increase GDP by $1,200? • Real effect called the Multiplier Effect $300– 0.75*$1,200 + $1,200 + $1,300 + (-$100) (1-0.75) Y= $300– $900 + $1,200 + $1,300 -$100 (0.25) $1,800 0.25 Y= = = $7,200

  5. Multiplier Effect Intuition • Why does multiplier effect exist in the economy? • A dollar spent becomes a dollar of income for someone else • Original spending creates income and kicks off additional rounds of spending • Cumulative spending greater than initial amount which creates a larger increase in equilibrium GDP • Also creates a larger decrease in GDP with a decrease in spending

  6. Multiplier Effect Intuition (cont.)

  7. Multiplier Derivation • How big is the multiplier effect? • In our example the GDP effect was four times the spending, but a more general equation would be more informative • Intuitively the multiplier effect would be the change in GDP from a $1 increase in spending • Can derive a general multiplier formula using the GDP formula we already have • Change an expenditure in the formula by $1 and see how GDP changes

  8. Multiplier Derivation (cont.) a–MPC*T+I+G0+(X-IM) (1-MPC) Y0= a–MPC*T+I+(G0+1)+(X-IM) (1-MPC) Y1= a–MPC*T+I+(G0+1)+(X-IM) (1-MPC) a–MPC*T+I+G0+(X-IM) (1-MPC) Y1-Y0= - [a–MPC*T+I+(G0+1)+(X-IM)] – [a–MPC*T+I+G0+(X-IM)] (1-MPC) Y1-Y0= 1 (1-MPC) Y1-Y0= = Multiplier

  9. Multiplier Application • Effect on GDP of a $1 change in expenditures • If MPC =0.75 then Multiplier= 1/(1-0.75)=1/0.25= 4 • Increasing spending by $1 increases GDP by $4 • If MPC increases to 0.9 what happens to multiplier? • Multiplier=1/(1-0.9)=1/0.1 = 10 • The greater the MPC the greater the multiplier and vice versa 1 (1-MPC) Multiplier=

  10. Multiplier Application (cont.) • In our example spending increased by $300 so GDP should increase by $300*4=$1,200 • In general: GDP change= Multiplier * Expend. Change • Example: MPC = 0.8, G increase by $200, GDP ? • Multiplier = 1/(1-0.8) = 5 • GDP change = 5 * $200 = $1,000

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