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 45-degree line NewAE line OldAE line 45° INCOME OR REAL GDP SPENDING AE line shifts up by this amount ($100 billion). Income or real GDP increases by this amount ($250 billion); the multiplier is 2.5. Old spending balance New spending balance

26_01T Algebraic approach to the multiplier Y = C + I + G + X Consider changes  Y =  C +  I +  G +  X Substituting  I = 0 and  X = 0 and  C =.6  Y gives  Y =.6  Y +  G Solving for  Y and dividing by  G results in what?  Y  G =   = 2.5 = the multiplier

Gory numerical detail of the multiplier ($billions)

26_02 BILLIONS OF DOLLARS $250 billion ROUND BILLIONS OF DOLLARS $167 billion ROUND MPC =.6 MPC =.4

Use geometric series formula to sum up: Total impact is 100( …) = 100(1/( )) =  Multiplier = 2.5

A little algebra 26_02T GENERAL FORMULA FOR THE MULTIPIER, Y = C + I + G + X In change form  Y =  C +  I +  G +  X let  I = 0 and  X = 0 and  C = MPC x  Y Substitute to get  Y = MPC x  Y +  G Gather all terms in  Y to get (1- MPC) x  Y = G Divide through by  G and by 1 - MPC to get  Y  G = 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

26_07T Letting net exports depend on income (Y)  Y =  C +  I +  G +  X Continue to assume that  I = 0 and  C =.6  Y But now  X = -.2  Y Plug in  I,  C, and  X to get  Y =.6  Y +  G -.2  Y Gather together the terms involving  Y to get ( )  Y =  G Divide both sides by  G, to get  Y  G = = 1.7 (the multiplier when MPI =.2)

26_05 INCOME OR REAL GDP SPENDING AE line when net exports do not depend on income C + I + G + X C + I + G C + I C C + I + G + X C + I + G C + I C INCOME OR REAL GDP SPENDING AE line when net exports depend on income Flatter Aggregate Expenditure LineSteeper 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 Income YEAR OF LIFE DOLLARS Income Constant consumption Consumption with a constant MPC YEAR OF LIFE DOLLARS

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