Fletcher School, Tufts University Exercise 1 Output Determination, Aggregate Demand and Fiscal Policy Prof. George Alogoskoufis
The Basic Keynesian Model Consider the following short run keynesian model of a closed economy: D = C + I + G Y D = Y T C = C + cy D I = I G = G T = T (1) (2) (3) (4) (5) (6) D denotes real aggregate demand, Y denotes real aggregate output and income, Y D denotes real aggregate disposable income, C denotes real aggregate private consumption expenditure, I denotes real aggregate gross investment expenditure, G denotes real aggregate government purchases and T denotes real aggregate taxes, net of government transfers. A bar above a letter denotes the autonomous (exogenous) component of the corresponding variable, assumed positive and c denotes the marginal propensity to consume, assumed positive and less than unity. Assuming that prices are fixed in the short run, continuous equilibrium in the output market implies that output adjusts to ensure that Y=D. 2
Discuss the structure of the model distinguishing between endogenous and exogenous variables, identities, behavioral equations and equilibrium conditions. The model suggests that because prices are fixed, output Y is determined by aggregate demand, which consists of aggregate private consumption C, aggregate investment I and aggregate government purchases G. Hence, aggregate output (income) Y is an endogenous variable, determined by the model. Disposable income is determined by an identity, which is the difference between aggregate output and taxes (net of transfers). Since aggregate output is an endogenous variable, disposable income is also an endogenous variable. Aggregate consumption is a positive function of disposable income and is also an endogenous variable. Investment, government expenditure and taxes (net of transfers) are determined outside the model, and are hence exogenous variables. The definition of aggregate demand D and disposable income YD is through the first two equations which are identities. The third equation, the consumption function, is a behavioral equation, as it is meant to describe the behavior of consumers. It consists of an autonomous component, and a behavioral parameter, c, the marginal propensity to consume. The other three equations define the exogenous variables as autonomous constants. The equality between aggregate demand and aggregate output and income is an equilibrium condition. 3
B. Using simple algebra, derive equilibrium output as a function of the autonomous (exogenous) components of spending and the marginal propensity to consume. Explain your findings. Substituting equations (1) to (6) in the equilibrium condition Y=D, we get that, Y = D = C + I + G = C + I + G ct + cy or that Solving for output, we get that, Y = C + I + G ct + cy Y = 1 ( 1 c C + I + G ct ) Equilibrium output is a multiple 1/(1-c) of the autonomous components of aggregate demand. This multiple is the multiplier. The effect of every autonomous component of aggregate demand is multiplied through the increase in the disposable income of consumers, which causes a second round effect on output and income, which in turn causes a third round effect, and so on. Thus, equilibrium output in the short run depends positively on the components of autonomous spending and negatively on autonomous taxes net of transfers. 4
C. Derive equilibrium output using a simple diagram of the keynesian cross. Explain your findings. Aggregate Demand D D 0 is defined as C 0 +I 0 +G 0 -ct 0 Slope = 1 Y=D D=D 0 +cy E Slope = c < 1 D 0 45 o Y E Output Y 5
D. Describe the properties of short run macroeconomic equilibrium in words. Production in this model is always equal to aggregate demand. Any autonomous component of aggregate demand leads to a corresponding increase in output and income. The increase in income leads to an immediate increase in aggregate consumption, a further increase in income, a further increase in consumption, a further increase in income, and so on. The process only stops when aggregate output and income is such that it can satisfy both autonomous demand and consumption demand. 6
E. Assume that government purchases rise by $1bn. What will be the effects on equilibrium output? Assume that taxes net of transfers are reduced by $1bn. What will be the effects on equilibrium output? What will be the effects on equilibrium output of a simultaneous increase in government purchases and taxes (net of transfers) by $1bn. The effects will be determined by the relevant multiplier. For an increase in government purchases by $1bn, equilibrium output will increase by 1/(1-c) $ billions. For a reduction in taxes net of transfers by $1bn, equilibrium output will increase by c/(1-c) $ billions. For a simultaneous increase in government purchases and taxes (net of transfers) by $1bn equilibrium output will increase by (1-c)/(1-c)=1$ billion. 7
F. The Effects of an Increase in Government Purchases and the Method of Financing Aggregate Demand D Balanced Budget Fiscal Expansion Fiscal Expansion through Borrowing E' Y=D D=C 0 +I 0 +G 1 -ct 0 +cy D=C 0 +I 0 +G 1 -ct 1 +cy D=C 0 +I 0 +G 0 -ct 0 +cy E'' D 1 E D 0 45 o Y E Y E'' Y E' Output Y, 2017-18 8
G. Assume that autonomous private consumption is equal to $17bn, autonomous investment is equal to $15bn, autonomous government purchases are equal to $20bn, and that there is a balanced government budget. What is the value of equilibrium output if the marginal propensity to consume is equal to 0.6; What is the value of equilibrium consumption? What will be the effects on equilibrium output and consumption of a drop in autonomous investment by 20%. How can the government react to this drop in autonomous investment in order to avoid a recession? Substituting the values given, equilibrium output is given by, Equilibrium consumption is given by, Y = 1 ( 1 c C + I + G ct ) Y= 2.5 x (17 + 15 + 20-0.6x20) = 2.5 x 40 = 100 C = 17 + 0.6x( 100-20) = 65 A drop in autonomous investment by 20% is equal to $3bn. Output will drop by 2.5x3bn or by 7.5bn or by 7.5%. The government can increase government purchases by 3bn or cut taxes by 5 bn., 2017-18 9