# Introduction to Economics, ECON 100:11 & 13 Multiplier Model

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1 Introduction to Economics, ECON 1:11 & 13 We will now rationalize the shape of the aggregate demand curve, based on the identity we have used previously, AE=C+I+G+(X-IM). We will in the process develop a more quantitative model of macroeconomics. Recall first the notion that expenditure on the aggregate in the economy, translates into production, which in turn translates into income. The main idea is that whatever you spend has to derive from earned income. So if we were to put this on a diagram, i.e. draw a relationship between real production and real income/output/gdp, it must be a 45 degree line extending out from the origin. I will refer to this curve as AE=Y. Now we recall all the elements of AE individually, and graph them. First recall consumption by consumers in the economy is dependent on their disposable income. Second, investment, government, taxes, exports are autonomous, which means it is not dependent on the system, i.e. it is decided by something, someone. Let us write each relationship down. 1. Consumption: C = a + by D, where YD = Y T. a is called the autonomous aspect or portion of consumption. Think of it as some level of subsistence consumption. b is called the marginal propensity to consume (MPC), and describes the proportion of disposable income an individual would consume. Note that Y is real income, and T is taxes. Then another way we can think about the consumption relationship with real income in the economy is that b is just the slope of the consumption function. The question is should it be steeper than the 45 degree line or gentler. Consider the following, if it is steeper, it would mean that the value of consumption is always greater than real income which is not possible. This then mean that it must be flatter than the 45 degree line, i.e. a slope of 1. Another way to think about it is that because we never spend every cent we have, since we save, the slope, or the marginal propensity to consume is always less than 1. Note 1

2 Introduction to Economics, ECON 1:11 & 13 that another way to write the consumption equation in terms of Y and T is C = a + by bt. This means that the greater tax T, the lower the consumption line. a and b are both positive numbers/constants. Diagramatically, C = a + by D There is also in addition an interesting point. Note that what you do not consume, you save, which means 1- the marginal propensity to consume give you the marginal propensity to save. 2. Investment, and Government spending are all autonomous. What this means is that it is a constant at every level of real income. Let the current level be I = I and G = G for investment and government spending respectively. Diagrammatically, they are just horizontal lines as below. 2

3 Introduction to Economics, ECON 1:11 & 13 I = I G = G 3. We lastly examine international trade. Recall that we think of exports as autonomous. Let the level of export, dependent on our trading partner s national income be E = E. However, imports is dependent on our own national income. Although in our earlier discussion, we have not included an autonomous aspect of imports, but in general, due to specialization, there is an autonomous aspect to imports, since an economy cannot produce everything they need. Let the relationship that describes imports be IM = c + dy. This means that c can be thought of as autonomous imports, and d as the marginal propensity to import. Note that the equation says imports are dependent on real income. As in consumption, necessarily the diagrammatic representation of the line/relationship must be gentler than the 45 degree line. Note that c and d are both positive constants and d is a constant that is less than 1. Why? Note that the marginal propensity to consume (b) plus d cannot be greater than 1. That is because we know the economy saves, and given that, they cannot consume more than what they have. 3

4 Introduction to Economics, ECON 1:11 & 13 ( c dy ) X IM = X + 4. Since we know that aggregate expenditure is the sum of all these above elements from point 1 to 3. To depict the relationship, all we need is to perform vertical summation. Why? First, let us sum autonomous G, and I to consumption C. C + I + G C + I C I = I G = G To include net exports, simply do the same. However, note that X IM = X ( c + dy ) is downward sloping with respect to real income, since as income rises the marginal propensity to import rises. This means that the slope of the AE line is gentler. What is the slope of the AE curve? 4

5 Introduction to Economics, ECON 1:11 & 13 C + I + G + C + I + G ( X IM ) ( c dy ) X IM = X + What does the intersection mean? It is of course not possible that aggregate demand not equating with real income. This means that the point the economy spend, the AE is at the point at which it intersects with the 45 degree line. Each level of aggregate expenditure is dependent on the autonomous variables, and the price level. Then as price level rises, necessarily aggregate expenditure AE falls, while if price level falls, AE rises. How can we describe this algebraically? At the intersection, AE must equate with real income, which means: Y = C + I + G + X IM Y Y + dy by Y Y Y = a + by bt ( ) a c bt + I + G = 1+ d b 1 = 1+ d b = + I + G = a c bt { a c bt + I + G + X } + X + I + X c dy + G + X ( autonomous expenditure multiplier) ( autonomous expenditure) What does this tell you? 1. An increase(decrease) in autonomous variables, government spending (G), exports (X), investments (I) would lead to an increase(decrease) in aggregate expenditure and hence real income. 2. The change in the autonomous variables does not lead to, in general, a \$1 for \$1 change in real income, and consequently aggregate expenditure. Why? Consider 1 this, if b is greater than d, then 1 + d b is less than 1, and greater than 1+ d b 1. When that happens, a \$1 increase(decrease) in any of the autonomous variables listed above (C,I,G) leads to a more than \$1 increase(decrease) in aggregate 5

6 Introduction to Economics, ECON 1:11 & 13 expenditure, and consequently real income. Note that a change in taxes change aggregate expenditure and hence real income in the opposite direction. This is what we learned earlier about multiplier effect, and this is the reason why we call this the multiplier model. What happens when d is greater then b (Consider an economy with little own production, and hence to rely on imports)? When would there be no multiplier effect; that is a \$1 change lead to a \$1 change? Deriving AD curve Now we can show how we can use the AE curve to derive the AD curve we learned earlier. First each AE is given a level of price. A change in prices alters the real income (the real value of money, and hence how much you can consume and import), however all the autonomous variables of AE remains unchanged. The diagrammatic relationship is below, 6

7 Introduction to Economics, ECON 1:11 & 13 AE(P 1 ) AE(P 2 ) AE(P 3 ) / GDP Price Level P 3 P 2 P 1 AD Output/ GDP Since each AD is drawn given a level of autonomous expenditures, when those autonomous expenditures changes, we get a whole new set of AE lines, and consequently a new AD curve. This explains how AD can be shifted, and allows us to examine how government policy depending on the type of action shifts the AD and brings about a new equilibrium in the aggregate economy. 7

9 Introduction to Economics, ECON 1:11 & 13 will not affect her spending/consumption habits. But of course it is more common that if the deviation is quite substantial, such as a lottery winning, we would expect here to raise current consumption quite a bit immediately. This idea is know as the Permanent Hypothesis which says that expenditures are based on permanent of lifetime income, and not transitory changes in income. When this happens the MPC out of current income is zero, and the multiplier is 1, ignoring the effect out of importing. 9

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