Lesson 8: Aggregate demand; consumption, investment, public expenditure and taxation.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 1 Lesson 8: Aggregate demand; consumption, investment, public expenditure and taxation. 8.1 Consumption As we saw in the circular flow diagram presented in Lesson 7, in a closed economy the three components of demand are: Consumption (C), Investment (I), and Government purchases (G). If the economy was open (with imports and exports) there would be a fourth component, net exports. Here we will make the simplifying assumption that the economy is closed and will therefore ignore net exports. Aggregate demand can therefore be defined as: Y=C+I+G When we eat food, wear clothing, have a hair cut or go to a movie we are consuming part of the current output (GDP) produced by the economy. As we saw in Lesson 6, this is a considerable part: about two thirds of GDP. What does consumption depend on? Households receive income from their labour and from the ownership of capital. The income households receive is the totality of the economy s output (Y) Part of this income goes to the Government in the form of taxes (T). The remainder, we call disposable income (Y-T). Then, out of this disposable income,

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 2 households decide how much to consume (C) and how much to save (S). Therefore, we define consumption as a function of disposable income (Y-T). C = C(Y-T) This is the consumption function. We will assume that consumption depends positively on disposable income; the higher disposable income is, the higher the level of consumption. C Slope: Marginal propensity to consume Consumption function (Y-T) The increase in consumption per unit increase in disposable income is the marginal propensity to consume, and it is expressed by the slope of the consumption function.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 3 Slope C = = Y Marginal propensity to consume (MPC) Usually, out of a given increase in income, people do not consume the whole of it. A part goes to consumption and the rest to saving. We therefore assume that the MPC is greater that zero (that is, increases in income elicit increases in consumption) but less than one (that is, an increase in income of one euro elicits and increase in consumption of less than one euro). If the MPC is, say, 0.7, then an increase in income of 1 will generate an increase in consumption of 70 cents and an increase in savings of 30 cents. 8.2 Investment Both firms and household demand investment goods. Firms buy machines and buildings out of their internally generated resources, or financed by resources that they obtain from the financial markets. Households also demand investment goods when for instance they buy a new house. Investment demand is around 15% of GDP, although in some growing economies it can be much higher.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 4 The quantity of investment goods demanded depends on the interest rate, which measures the cost of the funds used to finance investment. For an investment project the value of the future revenue it generates must exceed its cost. And this comparison depends on the interest rate, whether the firm borrows funds to finance this investment or pays it out of its own resources. The higher the interest rate is, the lower the demand for investment goods. That is, the investment function I = I(r) is a negative relationship between investment and the rate of interest. Why should investment depend negatively on the interest rate? This is an interesting question, the answer to which requires a small detour on the issue of how to compare resources at different moments in time. Suppose you are considering the possibility of undertaking an investment project which costs 100 now and will give 108 next year. Is this investment project worth doing? Clearly this involves comparing the two figures 100 and 108. A first quick answer would be: yes, do the project, because the benefits are greater than the

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 5 costs (108>100). However, thinking a bit more about this, we see that we are comparing two heterogeneous things: money today with money next year. These are not the same thing: Money today is something that I can spend now; money next year is something else; I do not even now for sure that next year I will be alive to enjoy the 108. So we need some method to convert these heterogeneous things into homogeneous entities that can be compared. Economists do that by translating money at one given moment in time into money at another moment in time. And the instrument that allows us this translation is precisely the rate of interest. Is 100 today more or less than 108 next year? We can do two things to make this comparison: either we put the two quantities in terms of next year s money, or we put the two quantities in terms of today s money. Let us make the comparison in terms of next year s money. How much will 100 today be worth next year? If there is a financial market and the rate of interest is, say, 5%, I could put this money into a saving account and next year I would obtain the 100 I initially deposited plus 5 of interest (=0.05*100). So, if the rate of interest is 5%, 100 today is equivalent to 105 next year.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 6 [Parenthesis: The above argument can be applied whatever the time period considered. In three years time, 100 would be worth the following: After 1 year: 100(1+0.05)=105 After 2 years: 100(1+0.05)(1+0.05)=100(1+0.05) 2 =110.25 After 3 years: 100(1+0.05)(1+0.05)(1+0.05)=100(1+0.05) 3 =115.76 So, in three years, 100 today would be worth 115.76. In general, if the rate of interest is r, x today, after n years, will be worth y, where y is y = x(1 + r) n End of parenthesis] Let us now make the comparison in terms of today s money. If the rate of interest is 5%, how much is 108 next year worth today? To answer this question, we ask ourselves another slightly different question: How much money (x) would I have to put today in a savings account, to get 108 next year? Clearly the answer is x(1+ 0.05) = 108 108 x = = 102.9 (1+ 0.05) So, if the rate of interest is 5%, 108 next year are worth 102.9 this year.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 7 [Parenthesis. Convince yourself that the above argument can also be generalized. In general, if the rate of interest is r, the value today of y in n year s time is x, where x is y x = (1 + r) n End of parenthesis] Now that we have converted, under two different methods, heterogeneous things into homogeneous things, we can answer the question as to whether the investment project is worth doing or not. Comparison in terms of next year s money The return of the project (108 ) is greater than its cost (105 ), so do the project. (108>105) Comparison in terms of today s money The return of the project (102.9 ) is greater than its cost (100 ), so do the project. (102.9>100) Both methods give the same answer: DO the project. Now, see that the answer above depends on the value of the interest rate. Suppose that the interest rate instead of being 5%, was 10%. Would it be worthwhile to do the project in question?

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 8 If you apply the same argument but now with this higher interest rate (do it!), you will find that Comparison in terms of next year s money Benefit: 108; Cost: 110; 108<110; therefore DO NOT do the project. Comparison in terms of today s money Benefit: 98.2; Cost: 100; 98.2<100; therefore DO NOT do the project. Conclusion: A project that was worthwhile when the interest rate was 5%, it is not worthwhile if the interest rate rises to 10%. So there is a negative relationship between investment and the interest rate. The investment function can therefore be graphically represented as follows: r Investment function I=I(r) I

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 9 8.3 Public expenditure and taxation In a civilized society a government is needed. Someone has to define the rules of the game and check that they are obeyed. All civilized societies need a judicial and a police system. Governments are also needed to provide some goods and services that might not be adequately provided by the market (roads, education, health, etc.). The purchases that the government (in all its levels, central, autonomic and local) makes (G) in order to fulfil these duties (services of judges, of teachers, of public officers in general, guns, roads, etc.) account for about 18% of GDP in Spain. Governments also incur in another type of spending: transfer payments to households, such as pensions, welfare payments, unemployment subsidies, etc. These are transfer payments (Z); the only thing they do is to take money away from the private sector through the tax system, and return this money back to the private sector through these different programs. They do no use up resources currently produced by the economy (they only transfer resources), and are therefore not included in G. Quantitatively, these expenditures may be even more important than those included in G. Taking them into account, total government expenditures (G+Z) represent near 50% of GDP.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 10 To finance all these expenditures, the government obtains resources from the private sector through total taxes (TT). The taxes that we have considered above, in the definition of disposable income, are less than these total taxes. Households pay out a total amount of taxes equal to TT, but receive back an amount of transfers equal to Z. The T considered above should be interpreted as taxes net of transfers, which is the net detraction that the household sector as a whole experiences as a result of the action of the government. This may be seen more clearly in formal terms. If the government has a balanced budget (total expenditure equals total revenue), then G+Z=TT Government purchases plus transfers must equal total taxes. But the above equation can be rewritten as G=TT-Z=T So, in terms of our notation, a balanced budget means that government purchases must equal taxes net of transfers, and that the taxes considered in the definition of disposable income are also taxes net of transfers. Having cleared this up, we will revert to our previous notation and, in other to avoid cumbersome denominations, we will call T simply taxes rather than net taxes. If government expenditures exceed taxes (G>T), the government incurs in a public deficit. In this case we

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 11 say that the government has a negative saving (it needs to borrow resources from the financial market). If government expenditures are less than taxes (G<T), the government generates a public surplus. In this case the government saves (it contributes resources to the financial market). In the real world, public deficits are more prevalent than public surpluses. The model we are considering here does not try to explain how taxes and government expenditures are determined, so we will suppose that both of them are fixed at the levels G and T. G = G and T = T The model, however, does investigate how changes in government expenditures and taxes affect consumption, investment and the rate of interest. 8.4 A model of the whole economy. The concept of savings and the role of the interest rate Putting all these things together, we can define aggregate demand by means of the following system of equations

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 12 Y = C + I + G C = CY ( T) I G T = Ir () = G = T Substituting the last four equations into the first, we have Y = CY ( T) + Ir () + G This is the aggregate demand function of this economy. Observe that it does not give us a solution, but rather a relationship between output and the rate of interest. To determine these two variables (and therefore consumption and investment), we have to consider aggregate supply. From Lesson 7 we know that in this simple model, aggregate supply is given by the available quantity of productive factors and by the technology reflected in the production function. Since we consider these three elements given, aggregate supply is Y = Y Equilibrium is reached when aggregate demand equals aggregate supply. So, the solution to the whole model is obtained when Y is substituted for Y in the aggregate demand expression.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 13 Y = CY ( T) + Ir () + G Observe that the only variable that has not been predetermined is the rate of interest. This is the variable that will ensure that aggregate demand equals aggregate supply. What this equation says is that in this model the rate of interest will adjust so that aggregate demand equals aggregate supply. This feature can be seen more clearly looking at the model from a slightly different perspective. Instead of concentrating on demand and supply, let us look at saving and investment. We define saving (S) as the output that remains after the demands of consumers and the government have been satisfied. We can use this concept in the model above rewriting the final equation as follows Y CY ( T) G = Ir () (1) The left hand side of the equation (1) is the saving of this economy, which will also be predetermined since all the intervening variables are given. Given aggregate output, Y, predetermined from the supply side of the economy, consumption, C, predetermined by the consumption function and the exogenously fixed levels of output and taxes, and

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 14 government purchases, G, also exogenously fixed, saving is also predetermined at the level S. S = Y CY ( T) G (2) Saving in this economy does not depend on the rate of interest, but will change when income, taxes and government purchases change. We could represent this graphically in the following manner: r Saving function S S The right hand side of equation (1) is the investment function, which we already know (Section 8.2) that relates negatively savings and investment. Putting these two relationships togheter, which is what equation (1) does, we have a representation of the equilibrium in the market for loanable funds (the financial market).

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 15 S = Y CY ( T) G = S (2) I S = Ir () (3) = I Saving is the amount of resources left over after consumption and government purchases. It represents the supply of loanable funds of this economy available for investment. Investment represents the demand for loanable funds to finance investment projects. The reason why there is a market that puts together these two sides is because the agents of the economy that save are not necessarily the same as the agents that invest. Most of the saving is done by households, while most of the investment is done by firms. The interest rate is the price in this market, and if we assume that this is a flexible market, the interest rate will adjust until demand and supply are equal. This is achieved at r. This is the equilibrium rate of interest, that makes investment equal to the predetermined level of savings. In other words, r is the interest rate that makes the demand for loanable funds to be equal to the existing supply of loanable funds.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 16 r Saving function. Supply of loanable funds r Investment function. Demand for loanable funds S S, I What is nice about this model (and what makes it so simple) is that this equilibrium interest rate, which equates the demand and supply of loanable funds, is also the instrument that equates the aggregate demand for goods and services to the available supply of these goods and services. The effect of changes in fiscal policy The government may want to intervene in the economy by changing the levels of taxes (T) or government purchases (G). We call changes in these variables, fiscal policy. As we can see from equation (2), if the government does that, the level of available savings in the economy will also change. Let us consider the two possible changes one at a time.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 17 Increase in taxes (holding government purchases constant) If the government rises taxes, disposable income will go down and therefore consumption will decrease. From equation (2) we see that if consumption decreases, the level of savings in the economy will rise. In the graph of the financial market below we represent this rise by a displacement to the right of the saving function from S to S. Consequently, the equilibrium of the market goes from point A to point B, and the equilibrium rate of interest falls from r to r. So, in the final equilibrium point, we would have that: a) consumption would have decreased (due to the increase in taxes and fall in disposable income); b) investment would have increased (due to the fall in the interest rate; c) the government would have generated a budget surplus (due to the increase in taxes for the same quantity of government purchases); and d) output would have remained the same, since capital, labour and the technology have stayed unchanged. In this model, therefore, an increase in taxes ( T ) has the effect of redistributing the available quantity Y out of consumption of output of the economy ( ) ( C ) and into investment ( ) I.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 18 r Saving function with taxes equal to T Saving function with taxes equal to T r A r B Investment function S S I, S Increase in government purchases (holding taxes constant) If the government increases its purchases from G to G, we see from equation (2) that saving will go down. Consumption remains the same, as nothing has changed as far as income or taxes are concerned (disposable income therefore stays put), but since total output is fixed and government purchases increase, the level of savings of the economy will go down. In the graph below we represent this fall by a shift to the left of the saving function from S to S.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 19 Consequently, the equilibrium of the market goes from point A to point B, and the equilibrium rate of interest increase from r to r. In the final equilibrium point, we would therefore have that: a) consumption remains the same (due to the fact that disposable income does not change); b) investment decreases (due to the rise in the interest rate; c) the government generates a budget deficit (due to the increase in government purchases for the same level of taxes); and d) output remains the same, since capital, labour and the technology do not change. In this model, therefore, an increase in government G has the effect of redistributing the purchases ( ) available quantity of output of the economy ( Y ) out of investment ( I ) and into government purchases ( ) G. This is known as the crowding out effect of public expenditure: government purchases crowd out private investment.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 20 r Saving function with government purchases equal to G Saving function with government purchases equal to G r B r A Investment function S S I, S Exercises for the practical class 1. What would be, under this model (the classical model), the effects of both an increase in government purchases and an increase in taxes of the same amount ( G = T)? Hint: See that taxes influences saving through the consumption function and that the marginal propensity to consume is less than one.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 21 2. What would be the effects of an increase in the amount of capital available to the economy? [Parenthesis: The saving defined so far is the total saving of the economy. Sometimes it is called national saving. This total saving is the sum of the saving done by the private sector (private saving) and the saving done by the public sector (the government) (public saving). If you want, from the above definition of saving you can derive an expression that shows explicitly how these two concepts are defined. We have defined total saving (S) as S = Y C G Adding and substracting T to this equation, we have, ( ) ( ) S = Y T C + T G Total saving= Private Saving + Public Saving Private Saving Public Saving ( Y T C) ( T G) = = Private saving is income minus taxes and minus consumption. Public saving is taxes minus government purchases. Public saving is in fact the public balance of the government budget. If T-

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 22 G=0, the budget is balanced (the government does not save or disave); if T-G>0, the budget is in surplus (the government saves); and if T-G<0, the budget is in deficit (the government disaves). End of parenthesis] A real world description of the financial system The financial system, which plays such an important role in the previous model, is in reality a complex set of institutions that exist in modern economies to coordinate saving and investment decisions. As we have said before, this market exists because usually savers and investors are different people. The purpose of the financial market is to move the economy s scarce resources from savers (people who spend less than they earn) to borrowers (investors) (people who spend more than they earn). People save because they expect in a future date to get back the amount saved plus interest. That is, they expect to get a larger amount of money in the future. People invest because they think they have projects that will have returns over and above the amount invested. That is why they are not afraid

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 23 of borrowing money: they think that with the return of the project they will be able to pay back the loan plus the interest and still obtain some benefit. Institutions that form the financial system a) Financial markets b) Financial intermediaries Financial markets i) The bond market ii) The stock market Financial intermediaries i) Banks ii) Mutual funds 8.5 Long run equilibrium and short run fluctuations The model discussed in this lesson is very simple. As we said before, it can be taken as a model that represents an economy where prices are flexible (in this simple case the only price is the rate of interest) and that therefore manages to utilize all its resources.

Introduction to Economic Analysis. Antonio Zabalza. University of Valencia 24 This may be a reasonable model if we want to analyse the long run response of an economy to some policy change, but not if our interest is to trace this response in the short run. In the short run, prices tend to be less than flexible and this may cause that some resources are not fully utilized. Also, the economy considered in this model is an economy in which there is no money. All variables considered are real variables; or to put it otherwise, the price level is constant and can therefore be ignored. This is not the case in real monetary economies. There the price level fluctuates over time and this may cause that, even for a given quantity of productive factors, aggregate supply is not fixed and depends positively on the price level. Another way to put this is that the model above may be a fair representation of the long run tendency of the economy, but that we may also be interested in knowing how the economy behaves on its way to this long run tendency. In reality, we see that economies do not grow in a steady fashion, but rather they fluctuate around a given tendency. The study of these fluctuations is another important topic of macroeconomics. All these complications will be taken up when you do Macroeconomics I in your third year.