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Today’s topics • • • • Back to Chapter 26 to fill in some holes Finding the multiplier. Letting net exports depend on income. Forward looking theory of consumption. Defining and finding the multiplier • The multiplier is the ratio of the change in real GDP to the initial shift in aggregate expenditure • Four approaches to finding the multiplier – – – – Graph Algebra Numerical example Words • The money multiplier is a different animal! Graphical approach to the multiplier 26_01 SPENDING 45-degree line New spending balance New AE line Old AE line Old spending balance AE line shifts up by this amount ($100 billion). 45° Income or real GDP increases by this amount ($250 billion); the multiplier is 2.5. INCOME OR REAL GDP 26_01T Algebraic approach to the multiplier Y=C+I +G+X Consider changes DY = DC + DI + DG + DX Substituting DI = 0 and DX = 0 and DC = .6 DY gives DY = .6 DY + DG Solving for DY and dividing by DG results in what? DY 1 DG = 1 - .6 = 2.5 = the multiplier Gory numerical detail of the multiplier ($billions) Round 1 Round 2 Round 3 Change in real GDP 100 60 36 Cumulative change 100 160 196 . . . . . . 0 250 Round 26_02 BILLIONS OF 300 DOLLARS 250 $250 billion 200 150 100 50 0 1 2 3 4 5 6 7 8 9 10 11 ROUND 8 9 10 11 ROUND MPC = .6 BILLIONS OF 300 DOLLARS 250 200 $167 billion 150 100 50 0 1 2 3 4 5 6 7 MPC = .4 Use geometric series formula to sum up: Total impact is 100(1 + .6 +.62 +.6 3+.6 4+ …) = 100(1/(1 - 0.6)) = 250 ------------- Multiplier = 2.5 26_02T A little algebra GENERAL FORMULA FOR THE MULTIPIER, Y= C +I +G +X In change form DY = DC + DI + DG + DX let DI = 0 and DX = 0 and DC = MPC x DY Substitute to get DY = MPC x DY +DG Gather all terms in DY to get (1- MPC) x DY = DG Divide through by DG and by 1 - MPC to get DY 1 = DG 1 - MPC = the multiplier When net exports depend on income • Net exports = exports - imports • Exports depend on income abroad, not Y • Imports depend positively on Y – when income rises, Americans buy more foreign produced goods as well as more domestically produced goods • Thus, net exports depend positively on Y An example of the effect of income on net exports Income Exports Imports Net Exports 6,000 2,100 1,200 900 7,000 2,100 1,400 700 8,000 9,000 2,100 2,100 1,600 1,800 500 300 10,000 2,100 2,000 100 11,000 12,000 2,100 2,100 2,200 2,400 -100 -300 13,000 2,100 2,600 -500 14,000 2,100 2,800 -700 26_07T Letting net exports depend on income (Y) DY = DC + DI + DG + DX Continue to assume that DI = 0 and DC = .6DY But now DX = - .2DY Plug in DI, DC, and DX to get DY = .6DY + DG - .2DY Gather together the terms involving DY to get ( 1 - .6 + .2) DY = DG Divide both sides by DG, to get DY 1 = = 1.7 (the multiplier when MPI = .2) DG 1 - .6 + .2 26_05 SPENDING SPENDING AE line when net exports do not depend on income C+I+G+X C+I+G AE line when net exports depend on income C+I+G C+I+G+X C+I C+I C C INCOME OR REAL GDP Steeper Aggregate Expenditure Line INCOME OR REAL GDP Flatter Aggregate Expenditure Line Why is the multiplier uncertain? • Multiplier = 1/(1 - MPC) – Hence, if MPC is uncertain, the multiplier is uncertain • The main reason that the MPC is uncertain is that consumers are forward looking – They tend to anticipate or at least plan for the future, rather than simply respond mechanically to current income The forward looking model of consumption • Two similar versions of the story – Permanent income version – Life cycle version • Both lead to the interesting idea of consumption smoothing – If you find $10,000 in the sidewalk, how much do you spend this year? Only about $500 26_07 DOLLARS DOLLARS Income Consumption with a constant MPC YEAR OF LIFE Income Constant consumption YEAR OF LIFE Policy implications of the forward-looking model • A permanent tax cut has a greater effect on spending than a temporary tax cut • Examples of temporary tax cuts – 1968 tax surcharge – 1992 reduction in withholding • People will shift income to avoid tax increase – 1992 anticipation of a tax increase END OF LECTURE and HAPPY THANKSGIVING