Chapter 7 Notes

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ECS 1601
Oct 7, 2023
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Chapter 7: The Keynesian Model with a Government and a Foreign Sector 7.1 The Keynesian model with a government sector We see how the introduction of the government sector impacts the Keynesian model This means that we have to consider the impact of government spending G and taxes T on o the level of aggregate spending ( A ) o the multiplier ( ) o equilibrium income ( Y ) We start by explaining G and T ( we want to know whether there are any systematic links between G or T and the level of income Y) Government spending (G) What determines the size of government spending? o government spending is essentially a political issue o In other words, government spending is related to political objectives rather than to the level of income Y In fact, government spending G has often been increased after income Y has fallen o There is thus no systematic relationship between G and Y In symbols we express this as o G = Ḡ o where the bar above the G indicates that G is autonomous with respect to Y o This is represented in figure 7-1 (just a horizontal line) o In other words, the level of G is independent of the level of Y
Figure 7-1 Government spending How does the introduction of G affect the level of aggregate spending A? o Government spending on goods and services G has to be added to the other components of aggregate spending ( consumption spending C and investment spending I) o A = C + I + G Graphically we have to add G to C + I at each level of Y o This is illustrated by a parallel upward shif of the A curve as indicated in Figure 7-2 Since G is autonomous (i.e. G = Ḡ), it affects the position of the A curve, but the slope of the curve remains unchanged o the aggregate spending curve A is still parallel to the consumption function C Remember that the multiplier is related to the marginal propensity to consume c , that is, to the slope of the A curve o government spending therefore does not affect the size of the multiplier The 45-degree line is also shown in Figure 7-2 Note that the introduction of government spending moves the aggregate spending curve upwards to A' As autonomous expenditure has now increased by the amount of government spending, the new aggregate spending curve A', which includes government spending, cuts the vertical axis at a higher level of spending A' The new aggregate spending curve A' cuts the 45-degree line at higher income level Y2. o The equilibrium level of income will now be at Y2 Figure 7-2: Aggregate spending in the economy with a government sector
Algebraically, the model may be represented as follows: o Y = A (7-1) o Y = C+ Ī + Ḡ (7-2) o C = Ć + cY (7-3) Equation 7-1 represents the equilibrium condition o Total income Y is in equilibrium only when it is equal to aggregate spending A Equation 7-3 represents the consumption function To calculate the equilibrium level of income Y, we start with the equilibrium condition (Equation 7-1): Y = A The next step is to substitute A with the right-hand side of Equation 7-2: Y = C + Ī + Ḡ Then substitute C with the right-hand side of Equation 7-3: Y = (Ć + c Y ) + Ī + Ḡ All that remains is to simply the equation: Y = (Ć + c Y ) + Ī + Ḡ Y - c Y = Ć + Ī + Ḡ Y (1 - c) = Ć + Ī + Ḡ Y0 = 1 ( 1 c ) (Ć + Ī + Ḡ) The only difference between Equation 7-4 and Equation 6-7 is the addition of government spending to autonomous spending. As in Equation 6-8, the general formula is still o Y0 = ( Ā ) o where Y0 = equilibrium level of income
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