2. Aggregate Demand and Output in the Short Run: The Model of the Keynesian Cross

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1 Fletcher School of Law and Diplomacy, Tufts University 2. Aggregate Demand and Output in the Short Run: The Model of the Keynesian Cross E212 Macroeconomics Prof. George Alogoskoufis

3 The Market for Goods and Services and Aggregate Demand in the Short Run When economists think about year-to-year movements in economic activity, they focus on the interactions among production, income, and demand: 1. Changes in the aggregate demand for goods and services lead to changes in production. 2. Changes in production lead to changes in income (and employment). 3. Changes in income (and employment) lead to changes in the demand for goods and services. This view of aggregate economic activity in the short run, which is the mainstream view among macroeconomists, is due to the General Theory of Keynes (1936), who developed it in response to the great depression and the inability of so called classical economics to account for it.!3

John Maynard Keynes (1883-1946) English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments.

4 John Maynard Keynes ( ) English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. In his pathbreaking book The General Theory of Employment, Interest and Money (1936) he built on and greatly refined earlier work on the causes of business cycles in order to explain the Great Depression of the 1930s. He is widely considered to be one of the most influential economists of the 20th century and the founder of modern macroeconomics.!4

5 The Composition of Aggregate Demand The composition of aggregate demand (D) in a closed economy includes three elements: consumption (denoted by C), investment (denoted by I) and government purchases (denoted by G). It can thus be written as, D=C+I+G First comes consumption. These are the goods and services purchased by consumers, ranging from food to airline tickets, to new cars, and so on. Consumption is by far the largest component of GDP. In 2014, it accounted for 68% of GDP. Second comes investment. Investment is the sum of nonresidential investment, the purchase by firms of new plants or new machines (from turbines to computers), and residential investment, the purchase by people of new houses or apartments. Nonresidential investment and residential investment, and the decisions behind them, have more in common than might appear at first. Firms buy machines or plants to produce output in the future. People buy houses or apartments to get housing services in the future. In both cases, the decision to buy depends on the services these goods will yield in the future, so it makes sense to treat them together. Together, non-residential and residential investment accounted for 16.0% of GDP in Another type of investment is inventory investment, the holding of stocks of produced goods to satisfy future demand. Third comes government purchases. This represents the purchases of goods and services by the federal, state, and local governments. The goods range from airplanes to office equipment. The services include services provided by government employees: In effect, the national income accounts treat the government as buying the services provided by government employees and then providing these services to the public, free of charge. In 2014 this amounted to 18.1% of GDP.!5

6 The Basic Keynesian Macroeconomic Model We now need to think about the determinants of output Y. To make the task easier we shall use a model, which depends on a number of simplifications [Note that a model nearly always starts with Assume (or Suppose ). This is an indication that reality is about to be simplified to focus on the issue at hand. On the role of models in economics see Rodrik D. (2016), Economics Rules, New York, Norton.] We first assume that all firms produce the same good, which can then be used by consumers for consumption, by firms for investment, or by the government. With this (big) simplification, we need to look at only one market the market for the good and think about what determines supply and demand in that market. We next assume that firms are willing to supply any amount of the good at a given price level P. This assumption allows us to focus on the role demand plays in the determination of output. As we shall see later in the course, this assumption is valid only in the short run. When we move to the study of the medium run, we shall abandon it. But for the moment, it will simplify our discussion of short run equilibrium. In addition, we shall assume that the economy is closed that it does not trade with the rest of the world: Both exports and imports are zero. This assumption clearly goes against the facts: Modern economies trade with the rest of the world. Later on we will abandon this assumption as well, and look at what happens when the economy is open. But, for the moment, this assumption will also simplify our discussion because we won t have to think about what determines exports and imports. These assumptions, plus an additional set of assumptions about the determinants of consumption, investment and government purchases will define the basic keynesian macroeconomic model, otherwise known as the keynesian cross.!6

7 The Keynesian Consumption Function Consumption decisions depend on many factors. But the main one is surely income, or, more precisely, disposable income, the income that remains once consumers have received transfers from the government and paid their taxes. When their disposable income goes up, people buy more goods; when it goes down, they buy fewer goods. Disposable income is defined by, Y D =Y-T where T denotes taxes minus transfers. Let C denote consumption. We can then assume that, C=C(Y D ) This is a formal way of stating that aggregate consumption C is a function of aggregate disposable income Y D. This function is called the consumption function. The assumption is that when disposable income increases, so does consumption. It will also be assumed that when disposable income increases, consumption increases by less than the increase in disposable income, as consumers tend to save part of their disposable income. These simple assumptions are the basis of the so called keynesian consumption function, a key ingredient of the basic keynesian model. [Economists call an equation such as the consumption function a behavioral equation, to indicate that the equation captures some aspect of behavior in this case, the behavior of consumers. A definition, such as the definition of disposable income, is an identity, to be distinguished from a behavioral equation.!7

8 A Simple Linear Consumption Function In order to simplify matters even further, we shall further assume that the relation between consumption and disposable income is given by the simple linear equation of the form, C=C 0 +cy D =C 0 +c(y-t) The relation between consumption and disposable income is then characterized by two parameters. C 0 is autonomous consumption, i.e what consumers consume independently of their level of income, or what consumers would consume even if their disposable income was equal to zero. c is a measure of the effect that an extra dollar of additional disposable income has on consumption. This parameter is called the marginal propensity to consume. With the assumptions that we made about the consumption function, i.e that as disposable income increases people consume more, but less than the increase in disposable income, it follows that c is positive and less than unity. Thus, the linear keynesian consumption function implies that, 0 < c < 1 It is useful to depict the relation between consumption and disposable income implied by this linear consumption function in the form of a simple diagram.!8

9 A Diagrammatic Exposition of the Linear Consumption Function Consumption C C 0 Slope = c Disposable Income Y D!9

10 Investment Models have two types of variables. Some variables depend on other variables in the model and are therefore explained within the model. Variables like these are called endogenous. This was the case for consumption which was assumed to depend on disposable income. Other variables are not explained within the model but are instead taken as given. Variables like these are called exogenous. This is how we shall treat investment here. We will take investment as being exogenous (or autonomous) and given by, I=I 0 where I 0 is an exogenous (autonomous) parameter. We take investment as given in order to keep our model as simple as possible. But the assumption is not innocuous. It implies that, when we later look at the effects of changes in output, we will assume that investment does not respond to changes in output. It is not hard to see that this implication may be a bad description of reality. Firms that experience an increase in production might well decide they need more machines and increase their investment as a result. For now, though, we will leave this mechanism out of the model in the interests of analytical simplicity.!10

11 Government Purchases and Taxes net of Transfers The third component of demand in our model is government purchases, G. Together with taxes net of transfers, denoted by T, G describes fiscal policy the choice of taxes and spending by the government. Just as we just did for investment, we will take G and T as exogenous. This is for two reasons. First, the decisions on how to spend and how to tax by the government are mainly driven by political and not necessarily economic considerations. Thus, they do not necessarily depend on other macroeconomic variables. Second, and more importantly, one of the tasks of macroeconomics is to think about the implications of alternative spending and tax decisions. We want to be able to say, If the government were to choose these values for G and T, this is what would happen. The approach in this course will thus typically treat G and T as variables chosen by the government and will not try to explain them within the model. We shall thus assume that, G=G 0 T=T 0 where G 0 and T 0 are exogenous parameters chosen by the government.!11

12 Goods Market Equilibrium in a Closed Economy There is one main point that needs to be clearly understood with regard to goods market equilibrium in a closed economy. The relationship between domestic output and income and domestic spending. In a closed economy these two must, in equilibrium, be equal. Thus, in a closed economy, we must necessarily have that, Y = D = C + I + G This the key condition that determines short run equilibrium in our model. If aggregate demand is higher than output, given our assumptions, firms will increase output to meet the excess demand. Hence output is not in equilibrium. If aggregate demand is lower than output, firms will decrease output to eliminate the excess supply. Hence output is not in equilibrium either. Only when output is equal to aggregate demand will there be no incentive for firms to either increase or decrease output and output will be in short run equilibrium.!12

13 Alternative Interpretations of Goods Market Equilibrium in a Closed Economy In a closed economy, we have shown that in equilibrium we must necessarily have that, Y = C + I + G This equilibrium condition can be rearranged to imply that, Y - C - G = I In this form, the equilibrium condition implies that the excess of income over current spending by consumers and the government (domestic savings) must, in equilibrium be equal to investment. If we add and subtract taxes net of government transfers T on the left hand side, we get, (Y-T-C) + (T-G) = I In this form the equilibrium condition implies that in a closed economy investment is equal to the sum of private savings and government savings. All three forms of the equilibrium condition are equivalent. In what follows we shall first concentrate on the first form.!13

14 The Basic Short Term Keynesian Model Identities Behavioral Equations Equilibrium Condition D=C+I+G Y D =Y-T C=C 0 +cy D =C 0 +c(y-t) I=I 0 G=G 0 T=T 0 Y=D=C+I+G Note that the exogenous parameters of the model are C 0, I 0, G 0, T 0, i.e autonomous consumption, investment, government purchases and taxes net of transfers, and the marginal propensity to consume c, which is positive and less than unity.!14

15 The Determination of Equilibrium Output We can now use the full model to determine equilibrium output. As we have noted, equilibrium is the case where output is equal to aggregate demand, as determined by the consumption function, and the assumptions that aggregate investment, government purchases and taxes net of transfers are exogenously given. Hence, given are assumptions about the determinants of consumption, investment, government purchases and taxes net of transfers, in equilibrium, we have that, in equilibrium, Y = D = C+I+G = C 0 + c(y-t 0 )+I 0 +G 0 In short run equilibrium, output has to be equal to aggregate demand. However, because of the assumed behavior of consumers, aggregate demand is a positive function of output. The equilibrium can be analyzed in either of three ways: 1. Using algebra 2. Using diagrams 3. Using verbal explanation!15

16 Algebraic Analysis of the Determination of Equilibrium Output From the behavioral equations and the equilibrium condition, Solving for the endogenous variable Y, Y = C 0 + c(y-t 0 )+I 0 +G 0 Y =(1/(1-c)) (C 0 + I 0 + G 0 - ct 0 ) Thus, equilibrium output in the short run depends positively on the components of autonomous spending and negatively on autonomous taxes net of transfers. We shall denote the autonomous components of spending as D 0, defined by, The effect of autonomous spending on output is given by, D 0 = C 0 + I 0 + G 0 - ct 0 1/(1-c)>0 This effect is called the multiplier. The multiplier measures the effect of a $1 change in autonomous spending on equilibrium output. As it is the inverse of one minus the marginal propensity to consume c, the multiplier is higher than unity. The multiplier depends positively on the marginal propensity to consume. Therefore, the higher the marginal propensity to consume out of disposable income, the higher the multiplier and the short run effects of autonomous spending on output. The reason is that for every unit of autonomous spending consumer increase consumption by c, which causes a further increase in income, a further increase in consumption by c 2, a further increase in output and income, a further increase in consumption by c 3 and so on. This process converges to 1/(1-c) once all the rounds of further increases in consumption have been concluded.!16

17 Diagrammatic Analysis of the Determination of Equilibrium Output: The Keynesian Cross 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!17

18 Diagrammatic Analysis of the Short Run Output Effects on an Increase in Autonomous Spending Aggregate Demand D E' Y=D D=D 1 +cy D=D 0 +cy E D 1 D 0 45 o Y E Y E' Output Y!18

19 Explaining the Diagrammatic Exposition Assume that autonomous spending increases from D 0 to D 1. The first round effect on aggregate demand is equal to, D 1 - D 0 As a result of the increase in aggregate demand, output and income in the first round also increases by D 1 - D 0. But this is not the end of the story. The increase in output and income by D 1 - D 0 causes a second round increase in consumption, and therefore aggregate demand, by, c(d 1 - D 0 ) As a result there is a further second round increase in output and income by c(d 1 - D 0 ). This is not the end of the story either. The increase in output and income by c(d 1 - D 0 ) causes a third round increase in consumption, and therefore aggregate demand, by, c[c(d 1 - D 0 )]=c 2 (D 1 - D 0 ) There will further rounds of increases. After n+1 rounds the further increase will be given by, c n (D 1 - D 0 ) Hence, the total increase in output after n+1 rounds of increases in aggregate demand will be given by, (1+c+c 2 + +c n )(D 1 - D 0 ) A sum such as the one in the first parenthesis is called a geometric series. Geometric series will frequently appear in this course. One property of geometric series is that, when c is less than one, as it is here, and as n gets larger and larger, the sum keeps increasing but approaches a limit. That limit is 1/(1-c), making the eventual increase in output 1/(1-c)(D 1 - D 0 ). Hence the multiplier.!19

20 How Long Does it Take for Output to Adjust An important question that is often relevant is the question of how long will it take for output to adjust from one short run equilibrium position to another. Under the assumptions we have made so far, the answer is: Right away! In writing the equilibrium condition, we have assumed that production is always equal to demand. In other words, we have assumed that production responds to demand instantaneously. In writing the consumption function we have assumed that consumption responds to changes in disposable income instantaneously. Under these two assumptions, the economy goes instantaneously from point E to point E in our last diagram. The increase in demand leads to an immediate increase in production, the increase in income associated with the increase in production leads to an immediate increase in demand, and so on. There is nothing wrong in thinking about the adjustment in terms of successive rounds as we did earlier, even though the equations indicate that all these rounds happen at once. This instantaneous adjustment is not really plausible: A firm that faces an increase in demand might well decide to wait before adjusting its production, meanwhile drawing down its inventories to satisfy demand. A worker who gets extra income might not adjust her consumption right away. These delays imply that the adjustment of output will take time. Formally describing this adjustment of output over time that is, writing the equations for what economists call the dynamics of adjustment, and solving this more complicated model would be too hard to do here, but it can be done if we are prepared to be specific about the speed of adjustment.!20

21 Aggregate Demand and the Great Recession in the USA Recession Real GDP Real Private Consumption Expenditure Real Private Gross Investment Real Government Expenditures!21

22 Fiscal Policy and Output in the Basic Keynesian Model Recall that there are two fiscal variables in the basic keynesian model. Government purchases G and taxes, net of transfers, T. How does fiscal policy affect output in the model? The impact can be deduced from their impact on autonomous spending D 0. An increase in government purchases G by $1 billion, increases autonomous spending by $1 billion as well. Hence, the effect on output is given by $(1/(1-c)) billions, because of the multiplier. An increase in taxes, net of transfers, by $1 billion, reduces autonomous consumption by $c billion, because consumers consume only c of their disposable income. Hence, the final effect on output is given by -$(c/(1-c)) billions, because of the multiplier. What if the government simultaneously increased spending and taxes by $1 billion. This is called a balanced budget fiscal expansion, because it has no effect on the government balance, which is defined by T-G. The increase in G by $1 billion increases autonomous spending and output by $(1/(1-c)) billions. The increase in T by $1 billion reduces output by $(c/(1-c)) billions. Hence the net effect on output in $ billions is given by, (1/(1-c))-(c/(1-c))=(1-c)/(1-c)=1 Thus, whereas an increase in government spending by $1 billion, financed by borrowing, increases aggregate demand and equilibrium output by $1/(1-c), i.e by the size of the multiplier of autonomous spending, an increase in government spending by $1 billion financed by taxes, increases aggregate demand and equilibrium output by $1. The balanced budget multiplier is equal to one.!22

23 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!23

24 A Summary of the Implications of the Basic Keynesian Model According to the basic keynesian model, output and income in the short run depend on aggregate demand, which depends on income, which is itself equal to output. An increase in aggregate demand, such as an increase in autonomous consumption, investment or government spending, leads to an increase in production and a corresponding increase in income. This increase in income leads to a further increase in demand through consumption, which leads to a further increase in production, and so on. The end result is an increase in output that is larger than the initial shift in demand, by a factor equal to the multiplier. Whereas an increase in government spending financed through borrowing increases aggregate demand and output by the size of the multiplier, an increase in government spending financed through an increase in taxes increases aggregate demand and output by the same amount. The balanced budget multiplier is equal to unity. The reason is that the increase in taxes reduces aggregate demand through the reduction in the disposable income of consumers. The size of the multiplier is directly related to the value of the marginal propensity to consume. The higher the marginal propensity to consume, the higher the multiplier. What is the value of the marginal propensity to consume in the United States today? To answer this question, and more generally to estimate behavioral equations and their parameters, economists use econometrics, a set of statistical methods appropriate for economics. A reasonable econometric estimate of the propensity to consume in the United States today is around 0.6. In other words, an additional dollar of disposable income leads on average to an increase in consumption by 60 cents. This implies that the multiplier is equal to 1/(1-c) = 1/(1-0.6) = 2.5.!24

Exercise 1 Output Determination, Aggregate Demand and Fiscal Policy

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