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Outline: •Summing up aggregate expenditure (AE) •Income and aggregate expenditure •Inventories and equilibrium GDP •The 45 degree line •Determining equilibrium real GDP •Equilibrium real GDP and employment •Effect of a change in planned investment (IP) •The expenditure multiplier We we say that a particular component of spending is autonomous, we mean it is determined “outside” our model and is independent of current GDP or real income We assume that planned investment (IP), government expenditures (G), net taxes (T), and net exports (NX) are autonomous variables. 700 IP 500 400 G NX 0 Real GDP (1) Income or GDP (2) (3) (4) (5) NX (6)= (2)+(3) +(4)+(5) AE C IP G 2,000 2,000 700 3,000 2,600 4,000 Inv. I 500 400 3,600 -1,600 700 500 400 4,200 -1,200 3,200 700 500 400 4,800 -800 5,000 3,800 700 500 400 5,400 -400 6,000 4,400 700 500 400 6,000 0 7,000 5,000 700 500 400 6,600 400 8,000 5,600 700 500 400 7,200 800 9,000 6,200 700 500 400 7,800 1,200 10,000 6,800 700 500 400 8,400 1,600 All figures in billions per year (7) C + IP + G + NX C + IP + G AE (billions) C + IP C 2400 2000 1500 800 0 GDP (billions) AE (Billions) At every point on the line, AE = GDP 7,000 5,000 450 0 5,000 7,000 Real GDP (Billions) A AE 7,800 H 6,000 E K 4,200 C + IP + G + NX J 450 0 3,000 6,000 9,000 GDP •AE > GDP by vertical distance K-J •Plans of producing and spending units do not coincide •Unplanned inventory investment = - $1,200 •Tendency for firms (on average) to step up the pace of production and offer more employment • GDP > AE by vertical distance A-H •Plans of producing and spending units do not coincide •Unplanned inventory investment = $1,200 •Tendency for firms (on average) to scale back the on production and offer less employment •AE = GDP •Plans of producing and spending units coincide. •Unplanned inventory investment = 0 • No tendency for firms (on average) to step up the pace of production and offer more employment. Nor is there a tendency for firms to scale back on production and offer less employment. Classical (Special) Case: Full Employment Equilibrium AE C + IP + G + NX AE touches the 450 line at potential GDP Full employment GDP GDP General (Keynesian) Case: Underemployment Equilibrium AE A C + IP + G + NX H Y* Full employment GDP GDP Equilibrium GDP and employment AE AE2 AE1 0 Employment FE subscript means “full employment” 450 Y1 YFE Real GDP Production function LFE L1 0 Y1 YFE Real GDP •Assume the economy is in equilibrium when real GDP = $6,000. •What would happen if, other things being equal, planned investment (IP) increased by $1,000? How did a $1,000 change in IP bring about a $2,500 change in GDP? AE AE2 2 AE1 1 3,400 H IP 2,400 GDP 450 0 6,000 8,500 GDP It’s a bird It’s a plane No, it’s the multiplier effect! The Effect of a $1,000 Change in Investment MPC = .6 3000 2750 2500 2250 2176 2000 2306 2500 2384 1960 1750 1500 1600 1250 1000 750 1000 500 250 0 1 2 3 4 5 6 Time Perio d . . . . Chain of causation When firms increase investment by $1,000 billion, sales revenues at investment goods manufacturers (Boeing, Westinghouse, Cincinnati Milacron) will increase by $1,000 billion The $1,000 billion in revenue will be distributed as factor payments to those supplying resources necessary to produce capital goods—hence the change in spending generates $1,000 in income in the first round. Now households have $1,00 in additional income. What do they do with it? Their spending will increase by the MPC times the change in income—that is: C = .6 $1,000 = $600. Hence, households spend $600 billion and save $400 billion But the story does not end here, since McDonalds’s, Disney, Kraft, American Airlines, and Amheiser Busch will see their sales increase by $600 billion, and will distribute $600 billion in wages, salaries, rental income, and profits to those who supplied resources necessary to produce the additional consumer goods. Those who earned additional income in consumer goods industries will now increase their spending. By how much? C = .6 $600 = $320. This will result in additional production and factor payments. Spending will then increase. And so on. And so on. Round Additional Spending in This Round (Billions) Additional Spending in All Rounds (Billions) Initial increase in IP 1,000 1,000 2 3 4 600 360 216 1,600 1,960 2,176 5 6 . 130 78 . 2,306 2,384 . . . . All other rounds Very close to 116 . . . Very close to 2,500 Algebraic derivation of the multiplier Based on what we have learned so far, we can say (all figures in billions): GDP = $1,000 + $6,000 + $360 + $216 + . . . Factoring out $1,000 in IP, this becomes: GDP = $1,000[1 + 0.6 + 0.36 + 0.216 + . . .] = $1,000[1 + 0.6 + 0.62 + 0.63 + . . . ] We know that the $1,000 is the change in IP and the MPC is 0.6. To find the change in GDP resulting from any change in IP and any MPC: GDP = IP [1 + (MPC) + (MPC)2 + (MPC)3 + . . .] Let H be any variable with a value between 0 and 1. We can show that the infinite sum: 1 + H2 + H3 + H4 + . . . Always has a value of 1/(1 – H). We can replace H with MPC or b, since 0 < b < 1. Thus the multiplier is given by 1/(1- MPC). Using the general formula, we can restate what happens when investment spending changes: 1 GDP I P (1 MPC )