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The Multiplier Model

The Multiplier Model. Aggregate Expenditures and Aggregate Supply: The Short Run. Learning Objectives. Understand how GDP is determined according to the logic of the multiplier model. Learn how to construct a graphical model.

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The Multiplier Model

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  1. The Multiplier Model Aggregate Expenditures and Aggregate Supply: The Short Run

  2. Learning Objectives • Understand how GDP is determined according to the logic of the multiplier model. • Learn how to construct a graphical model. • Know how to manipulate the components of the model to tell an economic story. • Understand the multiplier process.

  3. Income Determination • The aggregate expenditure/aggregate supply model is designed to explain how the different sectors of the economy interact to determine the size and composition of GDP (Y) in the short run. • The model is an equilibrium model. • Equilibrium is a state of rest where there are either no forces causing change or equal opposing forces.

  4. Equilibrium • Equilibrium is achieved in the model when aggregate spending or expenditures just equal aggregate supply or output. • Aggregate expenditures = Aggregate Supply AE AS

  5. Aggregate Expenditures • Aggregate expenditures are comprised of all spending done in the economy during a given period of time. • Aggregate expenditures are the sum of consumption spending by the household sector, investment spending by businesses, government spending by all levels of government, and net exports. • AE = C + I + G + (X-M)

  6. Aggregate Supply • Aggregate supply is GDP. It is all final goods and services produced during a given period of time. AS = GDP or Y • Aggregate supply is assumed to be perfectly responsive to spending. • Whenever expenditures change, aggregate supply changes by an equal amount.

  7. Aggregate Supply AE AS According to the circular flow diagram and the NIPA, GDP measured from the spending side equals GDP measured from the income side. We use this relationship to draw the AS line. Note that at point E, the distance 0B=0D=ED. Every point on the AS line represents some amount of GDP. B E 0 D Y

  8. Aggregate Supply • We depict aggregate supply graphically with a ray from the origin. • Every point on the ray represents GDP measured either from the expenditure side or from the income side. • GDP measured from the expenditure side is on the vertical axis. • GDP measured from the income side is on the horizontal axis. • The AS line in this model NEVER moves.

  9. Consumption Spending • Consumption is defined as all spending done by the household sector on durables, non-durables, and services. • Consumption is assumed to be determined primarily by disposable income (Yd), but it also may be affected by taxes, changes in the price level, and real wealth. • C = a0 + bYd is the consumption function.

  10. Consumption Function C AS C = a0 + bYd The intercept of the consumption function, a0, represents subsistence consumption. The slope of the consumption function, /\C//\Y, is called the marginal propensity to consume, MPC. The MPC shows by how much consumption changes as income changes. /\C /\Y a0 0 Y

  11. Consumption and Saving C AS The savings function can be derived from the consumption function. At point E, C = Yd, so S = 0. At point A, C>Yd by the amount AB, so S <0 by the amount A’B’. At point C, C<Yd by the amount CD, so S >0 by the amount C’D’. Note that the intercept of the savings function is –a, reflecting the fact that when Yd is 0, savings are drawn down. C C=a + bYd D E A B a 0 Y1 Y2 Y3 Y S S=-a + (1-b)Yd C’ B’ D’ 0 E Y A’ -a

  12. Investment • Investment is defined as all spending done by the business sector on plant, equipment, and inventories. • An important determinant of investment spending is the rate of interest. • There is a negative relationship between investment and the rate of interest. • As interest rates rise, investment falls. • As interest rates fall, investment rises.

  13. Interest Rates and Investment • The negative relationship between interest rates and investment exists because firms must either borrow or generate their own funds to invest. • As a result, firms are willing to invest in only those projects that pay a return in excess of the borrowing cost or rate of interest paid. • When rates are high, few projects are sufficiently profitable, but as rates fall, more and more projects become profitable.

  14. Investment and the Rate of Interest r At i2, the higher rate of interest, investment equals I1. Only a few projects are profitable at this high level. At i1, the lower rate of interest, investment equals I2. As the rate of interest falls, more projects become profitable. i2 i1 I 0 I1 I2 Investment

  15. Investment in the AE/AS Model AS C + I C + I2 = AE2 Investment enters the model as a lump sum. An increase in investment spending from I1 to I2 shifts aggregate expenditures from AE1 to AE2. A decrease in investment spending from I2 to I1 shifts aggregate expenditures from AE2 to AE1. Note that as investment changes so does equilibrium income, Y. B C + I1 = AE1 A 0 Y1 Y2 Y

  16. Saving and Investment AS C,I C+I Investment enters the AE/AS model as a lump-sum equal to the amount CD, and is shown by a parallel line drawn above C by the amount CD. Equilibrium occurs at point C. Investment enters the S/I model as a horizontal line that intercepts the vertical axis at the amount CD. Equilibrium occurs at the point C’. C C D E a 0 Y1 Y2 Y3 Y S,I S C’ I 0 E Y -a

  17. Government Spending • Government spending is defined as all spending done by all levels of government on goods and services. • Government spending enters the model as a lump-sum. • We invoke this simplifying assumption because there is no consistent relationship between government spending and the level of national income.

  18. Government in the AE/AS Model Government spending is drawn as a parallel line above C+I, reflecting the assumption that government spending enters the model as a lump-sum. The distance between C+I and C+I+G represents lump-sum government expenditures. At Y1, consumption equals the line segments Y1B, consumption plus investment is Y1A, consumption plus investment plus government spending is Y1E, investment is AB, and government spending is AE. C + I + G AS C+I+G C+I E C A B 0 Y1 Y

  19. Government in the AE/AS Model • Changes in government spending cause the government line and, therefore, the aggregate expenditure line to shift. • Increases in government spending shift G and therefore AE up. • Decreases in government spending shift G and therefore AE down.

  20. Government in the AE/AS Model C + I + G AS C+I+G3 = AE3 An increase in government spending from G2 to G3 shifts aggregate expenditures from AE2 to AE3. A decrease in government spending from G2 to G1 shifts aggregate expenditures from AE2 to AE1. Note that as government spending changes so does equilibrium income, Y. C+I+G2 = AE2 C C+I+G1 = AE1 B A 0 Y1 Y2 Y3 Y

  21. Saving, Investment and Government AS AE C+I+G F C+I Government enters the AE/AS model as a lump-sum equal to the amount FG, and is shown by a parallel line drawn above C+I by the amount FG. Equilibrium occurs at point F. Government enters the S/I model as a horizontal line that intercepts the vertical axis at the amount 0F. Equilibrium occurs at the point F’. G E a+I0 0 Y2 Y3 Y S,I G S F’ F G E G I 0 Y -a

  22. Practice AE AS C + I + G j C + I h C f g c e p b d n a m Y 0 Y1 Y2 Y3

  23. Practice • Assume Y = Y1 and using vertical line segments determine the following: • Consumption at Y1 • Investment at Y1 • Government spending at Y1 • Aggregate expenditures at Y1 • Consumption plus investment at Y1 • Investment plus government spending at Y1 • Repeat, assuming first that Y=Y2 and then Y=Y3

  24. Net Exports • Net exports are the difference between the goods and we produce for the rest of the world and the goods and services they produce for us. • Net exports equal exports minus imports • NX = (X- M) • Net exports enter the model as a lump sum.

  25. Determinants of Net Exports • Exports • Income in the rest of the world • As income in the rest of the world increases (decreases), they buy more (less) from us. • Relative prices • As our prices fall (rise) relative to prices in the rest of the world, they buy more (less) from us. • Exchange rate • As our currency appreciates (depreciates) relative to other currencies, they buy less (more) from us.

  26. Determinants of Net Exports • Imports • Income at home in the domestic economy • As domestic income increases (decreases), we buy more (less) from abroad. • Relative prices • As our prices fall (rise) relative to prices in the rest of the world, we buy less (more) from abroad. • Exchange rate • As our currency appreciates (depreciates) relative to other currencies, we buy more (less) from abroad.

  27. Net Exports in the AE/AS Model AS Net exports (NX) is drawn as a parallel line above C+I+G, reflecting the assumption that net exports enter the model as a lump-sum and that exports exceed imports. If imports exceed exports, net exports is drawn as a parallel line below C+I+G. The distance between C+I+G and C+I+G+NX represents lump-sum net export expenditures. At Y1, consumption equals the line segment Y1A, consumption plus investment is Y1B, consumption plus investment plus government spending is Y1C, and consumption plus investment plus government plus net exports is Y1E. C + I + G + NX C+I+G+NX E C+I+G C C+I B C A 0 Y1 Y

  28. Net Exports in the AE/AS Model • Changes in net exports cause the net exports line and, therefore, the aggregate expenditure line to shift. • Increases in net exports shift NX and AE up. • Decreases in net exports shift NX and AE down.

  29. Net Exports in the AE/AS Model C + I + G + NX AS An increase in net exports NX2 to NX3 shifts aggregate expenditures from AE2 to AE3. A decrease in net exports from NX2 to NX1 shifts aggregate expenditures from AE2 to AE1. Note that as net exports change so does equilibrium income, Y. C+I+G+NX3 = AE3 C+I+G+NX2 = AE2 C C+I+G+NX1 = AE1 B A 0 Y1 Y2 Y3 Y

  30. Practice • How will the following events affect the aggregate expenditure line and national income? Why? • An increase in consumer optimism • A decrease in taxes paid by consumers • A rise in the general price level • A rising preference for BMWs • A rise in the stock market • An increase in government spending • Real wealth increases • Interest rates decline • A fall in the value of the dollar

  31. Equilibrium in the Model • When the model is in equilibrium, all goods and services produced are demanded by the members of the various sectors of the economy. • Aggregate expenditures = Aggregate supply • The equilibrium in this model is stable. • There are forces built into the model that push it towards equilibrium.

  32. Stability of Equilibrium At Y equal to Y1 , AE > AS by the amount AB. The excess demand is met by an unexpected decrease in inventories. The sudden decrease signals producers to increase production. As production rises, employment and national income rise. AS AE= C + I + G + NX C AE D E At Y equal to Y3 , AE < AS by the amount CD. Insufficient demand leads to an unexpected increase in inventories. The sudden increase signals producers to decrease production. As production falls, employment and national income fall. A B 0 Y1 Y2 Y3 Y At Y2 , AE = AS.

  33. Equilibrium with Algebra Y = C + I + G C = a + bYd Yd = Y - T I = I G = G Y = a + b(Y-T) + I + G Y = a + bY - bT + I + G Y - bY = a - bT + I + G Y(1 - b) = a - bT + I + G Y = a - bT + I + G/(1-b) Y = C + I + G C = 300 + 0.8Yd Yd = Y - 1200 I = 900 G = 1300 Y = 300 + 0.8(Y-1200) + 900 + 1300 Y = 300 + 0.8Y - 960 + 900 + 1300 Y = 1540 + 0.8Y Y - 0.8Y = 1540 Y(1-0.8) = 1540 Y = 1540/0.2 = 7700

  34. Practice Y = C + I + G C = 100 + 0.9 Yd Yd = Y - T T = 30, I = 250, G = 300 • Find equilibrium Y. • Let the MPC = 0.8 and all other variables remain the same and find equilibrium Y. • Let the MPC = 0.9 and taxes increase to 40 and find equilibrium Y. • Is the equilibrium stable? Why?

  35. The Multiplier • The multiplieris the ratio of the change in equilibrium GDP (Y) divided by the original change in spending that causes the change in GDP. • Investment multiplier = /\Y//\I • Government spending multiplier = /\Y//\G • GDP changes by a greater amount because a single change in spending ripples through the economy changing production, employment, and consumption again and again.

  36. Multiplier Process The multiplier process begins at an initial equilibrium level of Y such as Y1, where AE=AS. It is initiated by an autonomous change in spending that causes AE to exceed AS. We show that change as a shift in AE from AE1 to AE2. Now at Y1, AE is greater than AS by the amount BE1. At this point, inventories fall and are replaced with new production that causes an increase in employment. As employment increases, income increases, and as income increases, consumption rises. We are now at D. We repeat the process until we reach E2. AS AE AE2 E2 G AE1 D F B C E1 0 Y1 Y2 Y

  37. Multiplier: Example • Let /\I = 100 and the MPC = 0.8 • /\I /\Yd/\C /\S • 100 100 80 20 • 80 64 16 • 64 51.2 12.8 • 51.2 40.96 10.2 • 40.96 32.76 8.2 • 500 400 100

  38. Multiplier Formulas • The numerical value of the multiplier can be found with the following formulas: • The formula for the investment and government spending multiplier is: • m = 1/(1-b) or equivalently m = 1/MPS • The formula for the lump-sum tax multiplier is: • m = -b/(1-b) or equivalently m = -b/MPS • Note that (1-b), the MPS, represents spending that is not occurring. • It is a leakage out of the spending stream, and as it becomes larger, the multiplier becomes smaller.

  39. Practice • Given the following, fill in the blanks • Yd Consumption MPC MPS Spending Multiplier • 5000 4000 • 4000 3200 • 3000 2400 • 2000 1600 • Yd = Disposable income

  40. Practice • Given the following, fill in the blanks • Yd Consumption MPC MPS Tax Multiplier • 5000 4000 • 4000 3200 • 3000 2400 • 2000 1600 • Yd = Disposable income

  41. Practice • Fill in theblanks in the table below: • MPC Multiplier Change in Y if /\I = $1000 • 0.9 • 0.8 • 0.75 • 0.6 • 0.5

  42. Practice • If the MPC is 0.9, and the government increases spending by 1.7 billion, by how much will Y change? • If the MPC is 0.9, and the government increases taxes by 1.7 billion, by how much will Y change? • If the MPC is 0.9, and the government simultaneously increases spending and increases taxes by 1.7 billion, by how much will Y change? • Any thoughts?

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