# Lesson 7 - The Aggregate Expenditure Model

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3 Lesson 7 - ECO 5- Master.nb 3 build to the total spending in the economy. The graph below demonstrates how consumption, investment, government spending, and net exports are added together to form the aggregate expenditures curve (AE). The 45 degree line is where real GDP (Y) equals aggregate expenditures (AE). The slope of the AE line is the MPC. Notice that when investment (I) is added to consumption it is a parallel shift and that the slope of the line does not change. The same occurs when government spending (G) and Net Exports (NX) are added. This is because we assume that investment, government spending, and net exports are a fixed amount that does not vary with changes in real GDP. The level of investment, government spending, and net exports can change and it will cause a shift in the AE curve, but it will not change the slope of the AE line. Deriving the Aggregate Expenditure Curve This graph demonstrates the derivation of Aggregate Expenditure AE. We start out with the consumption line C and add investment I, government purchases G, and then net exports NX. Aggregate Expenditure is equal to C+I+G+NX. Click on '+I' to add investment to the consumption. Click '+G' to add government purchases to consumption and investment. Then click +NX to add net exports and arrive at the aggregate expenditures line. Derive AE C +I +G +NX Reset Macroeconomic Equilibrium Macroeconomic equilibrium occurs where the AE line crosses the 45 degree line. In the graph above, you will notice it when the +NX button is pushed. Knowing that someone s expenditure is someone else s income, allows us to derive the mathematical equations necessary to reach equilibrium (Y*) in this model. We mathematically solve for macroeconomic equilibrium below. (Note: Remember that C = a + MPC*Y d and that Y d = Y - T.) Step-by-Step Solving for Macroeconomic Equilibrium (Optional). Output (GDP) = Income (Y) = Aggregate Expenditures (AE) (step ) 2. Y = AE of all sectors (step 2) 3. Y = C + I + G + NX (step 3)

4 4 Lesson 7 - ECO 5- Master.nb 4. Y = a + MPC(Y-T) + I + G + NX (step 4) 5. Collect like terms on one side: Y- MPC(Y) = a - MPC(T) + I + G + NX (step 5) 6. Y(- MPC) = a + I + G + NX - MPC(T) (step 6) 7. Y* = - MPC [a + I + G + NX - MPC(T)] (Equilibrium) (step 6) Try it out: Assume that C = *Y d, I = 50, G = 30, Exports = 40, Imports = 20, and T = 0. What is Y*? If we plug these numbers into the equation above then we get the following: Y* = [ (40-20) *(0)] = \$,70 This graph demonstrates the role of inventories in an economy, and how the economy gets back to equilibrium when the economy is not in equilibrium. The graph starts out at macroeconomic equilibrium. Click on the button AE > GDP. At this point spending (AE) is greater than production (GDP). Inventories unexpectedly decline. Firms order more goods and production increases. Click on the next button to the right. GDP increases and returns to equilibrium. Next, click on the button AE < GDP. At this point spending (AE) is less than production (GDP). Inventories unexpectedly accumulate. Firms order less goods and production decreases. Click on the next button to the right. GDP decreases and returns to equilibrium. Inventories Inventories can be an important indicator of future economic expansion or contraction. Inventories are goods that a business has on hand but they have not sold. The graph demonstrates the role of inventories in an economy, and how the economy gets back to equilibrium when the economy is not in equilibrium.

6 6 Lesson 7 - ECO 5- Master.nb producers have a certain level of inventories that they desire to have on hand, but that they do not want the stock of inventories to substantially grow or depleted. At GDP = 3,750, inventories would be piling up at the rate of 550 extra units of inventory each month! What would you do if you were running the economy and unwanted inventories were building up? Wouldn t that be a signal to you to reduce production? As you reduce production, output or the GDP, falls from GDP = 3,750 to GDP* = 2,850 (Click on Production ). To summarize, notice that in this model:. If spending is greater than production, inventories will be depleted and production will rise, and 2. If spending is less than production, inventories will accumulate and production will fall, SO Equilibrium is achieved where production exactly equals spending: Output (GDP) = Spending (AE) Section 2: Gaps and Multipliers Recessionary Gaps The reason the Aggregate Expenditures model is important to economists is that it demonstrates Keynes assertion that an economy can settle into an equilibrium position and stay there. Such an equilibrium position may or may not be at the level of real GDP where full employment exists, or in other words, at the level of real GDP where cyclical unemployment is zero. Thus, Keynes would assert that during the Great Depression, the economy had reached an equilibrium position far below its full employment level. Further, he would argue that since consumers were not spending, and since businesses would not hire and produce more output when their inventories were already high, the only other possible solution was to have government step in and create additional spending programs, even if the government had to borrow money to do so. A GDP gap exists when the equilibrium GDP is not equal to the level of full-employment GDP. These gaps take two forms. The first is called a Recessionary Gap, and is the amount of spending increase necessary to raise the AE curve in order to get an equilibrium position at the full employment level. As indicated by the name of the gap, the economy is often producing below its capabilities, and is usually in a recession when real GDP growth is negative or slowly growing in the 0-2 percent per year range. In the graphic below click on. Recessionary Gap. This will illustrate the recessionary gap. Notice that real GDP is at a level that is below full employment or potential GDP. If government spending were increased (click on Æ Government Spending ) it could shift the AE curve back to the AE* curve, then the economy's equilibrium output level would increase from GDP = 2,000 to GDP* = 2,850, where full employment could be achieved.

7 Lesson 7 - ECO 5- Master.nb 7 Recessionary and Inflationary Gaps This graph demonstrates recessionary and inflationary gaps. The graph starts out at full employment which is also potential GDP. Click on '. Recessionary Gap.' This shows the economy in equilibrium below full employment. The government can increase spending to move the economy back to full employment. Click the next button to the right to show this. On the other hand if the economy is performing beyond full employment there is an inflationary gap. Click on '2. Inflationary Gap.' To contract the economy, government spending will decrease. Click the next button to the right, and the economy moves back to full employment. Full Employment Reset Recessionary Gap. Recessionary Gap Æ Govt Spending Inflationary Gap 2. Inflationary Gap Govt Spending Inflationary Gaps A second type of gap exists when equilibrium real GDP actually exceeds the full employment level. This type of gap is known as an Inflationary Gap. In this situation, the economy is producing at very high levels, using its full capacity. For example, companies could be employing two or three shifts, many workers may be working weekends in addition to regular hours, and income levels would be very high. Further, capital equipment is fully utilized. In such a situation, there is tremendous pressure for prices to rise because income and spending levels are very high. In the graphic above click on 2. Inflationary Gap. This will illustrate the inflationary gap. Notice that real GDP is at a level that is above full employment or potential GDP. If government spending were decreased (click on Government Spending ) it could shift the AE 2 curve back to the AE* curve, then the economy s equilibrium output level would decrease from GDP = 3,750 to GDP* = 2,850, where full employment could be achieved. Thus the inflationary gap is the amount of spending reduction necessary to lower the AE curve in order to get an equilibrium position at the full employment level. The Expenditure Multiplier The model of Aggregate Expenditures that we are currently considering is often called a Keynesian Model because it was first formulated by British economist John Maynard Keynes in his General Theory of Employment, Interest, and Money, published in 936 at the height of the Great Depression. One of the central premises of Keynesian economics is the idea of a multiplier. Keynes hypothesized that a given increase in spending would cause output to

8 8 Lesson 7 - ECO 5- Master.nb increase by a multiple of the increase in spending. The multiplier plays an important role in the next step of our model which is to take the appropriate action in order to eliminate a GDP gap and restore equilibrium at the full employment level. As noted at the beginning of this topic, one person's expenditure becomes another person's income. The second person may save some of that income, but then spend the rest, which in turn becomes the income of the third person. To see how this concept can be applied to the elimination of a recessionary gap, we need to understand the Expenditure Multiplier. The expenditure multiplier is simply the multiple by which an initial change in aggregate spending will alter total output after all spending/income rounds. Deriving the Expenditure Multiplier Deriving the expenditure multiplier requires some math. When a business spends \$ on new plant or equipment it injects \$ into the economy. That \$ becomes income to someone (whoever built the machine or constructed the new plant) who spends a portion of it and saves the rest. The portion they spend and the portion they save depends on their MPC and their MPS. The portion that is spent becomes income to someone else who likewise spends a portion, which becomes income to another, who spends a portion, and so on. The spending stream can be characterized in the following way: Or \$ + \$(MPC) + \$(MPC)(MPC) + \$(MPC)(MPC)(MPC) + \$ + \$(MPC) + \$(MPC)2 + \$(MPC)3 + Which can be shown in its limit to equal. This is called the expenditure multiplier. As long as the MPC is less -MPC than, the multiplier will be greater than one. In fact, we can show that When the MPC is.9, the multiplier is 0 When the MPC is.8, the multiplier is 5 When the MPC is.75, the multiplier is 4 When the MPC is.6, the multiplier is 2.5 When the MPC is.5, the multiplier is 2 Therefore the formula for the multiplier is: Expenditure Multiplier = -MPC = MPS Example using the Expenditure Multiplier Let s look at an example on how the expenditure multiplier can be used. Suppose the MPC = 0.8, and there is a recessionary gap such that the difference between GDP * and GDP* at full employment and that this gap is \$300 billion dollars. We want to get from GDP * to the full employment GDP. In this case we want to see how much investment has to change to move the economy up to full employment equilibrium. Question: How much of an increase in gross private domestic investment (I) is required to close this gap? Answer: Since the multiplier is equal to -MPC =, which is equal to MPS 0.8 =, the multiplier is equal to Thus, the change in investment that is needed to bring about a \$300 billion change in real income is \$60 billion. In other words, when a business spends just \$, this expenditure becomes the income of someone else. Part of that income is saved in this case 20 for every dollar of income received while 80 is spent and becomes the income of person #3. Person #3 saves 6 and spends 64, creating more income for person #4, and so on. This same process happens for every one of the \$60 billion initial spent by business firms. Thus the initial investment spending

9 Lesson 7 - ECO 5- Master.nb 9 by the business firms multiplies throughout the economy, and grows it beyond the initial \$60 billion spending to where real incomes increase by \$300 billion bringing the economy into equilibrium at its full employment level. This is given mathematically as: DY or DRGDP = DInvestment x Multiplier For the example above, the math would be as follows: DY or DRGDP = \$300 billion DInvestment =? Multiplier = = DInvestment x 5 300/5 = DInvestment = \$60 billion Changes in GDP (Y) Previously we determined that equilibrium GDP or Y was found as follows. Y* = - MPC [a + I + G + NX - MPC(T)] You should notice that the term on front - MPC GDP or change in Y the equation looks as follows: DY* = - MPC [Da + DI + DG + DNX - MPC(DT)] is the multiplier. If you convert this equation to find the change in If you multiply the multiplier through the equation it looks as follows: DY* = Da + DI + DG + DNX - MPC(DT) - MPC - MPC - MPC - MPC - MPC Remember that a was the y-intercept for the consumption function. So a change in a is a change in consumption. For purposes of this model, we assume that we are changing only one of the elements at a time. If we are changing investment spending then changes in consumption (Da) will equal zero, changes in government spending (DG), and so on and so forth. Therefore we will be left with only: DY* = DI - MPC We will be doing this with all the rest of the elements below. Changes in Consumption Autonomous changes in consumption, or changes in consumption not resulting from changes in GDP, can also close recessionary and inflationary gaps. Using the formula just explained we see that a change in consumption can mathematically close recessionary and inflationary GDP gaps as follows: DY* = - MPC Da = Dreal GDP = Multiplier x DConsumption In this case the multiplier is the expenditure multiplier = -MPC.

10 0 Lesson 7 - ECO 5- Master.nb Changes in Investment In the example above there was a change in investment spending. At times the expenditure multiplier is called the investment multiplier. This is because there was an autonomous change in investment, or changes in investment not resulting from changes in GDP, that can help close the recessionary or inflationary gap. Using the formula just explained we see that a change in investment can mathematically impact GDP as follows: DY* = - MPC DI = Dreal GDP = Multiplier x DInvestment In this case the multiplier is the expenditure multiplier = investment multiplier = Changes in Government Spending -MPC. Autonomous changes in government spending, or changes in government spending not resulting from changes in GDP, can also close recessionary and inflationary gaps. When government spending is involved the multiplier is also called the government spending multiplier. Using the formula just explained we see that a change in government spending can mathematically impact GDP as follows: DY* = - MPC DG = Dreal GDP = Multiplier x DGovernment Spending In this case the multiplier is the expenditure multiplier = government spending multiplier = Changes in Net Exports -MPC. Autonomous changes in net exports, or changes in net exports not resulting from changes in GDP, can also close recessionary and inflationary gaps. Using the formula just explained we see that a change in net exports can mathematically impact GDP as follows: DY* = - MPC DNX = Dreal GDP = Multiplier x DNet Exports In this case the multiplier is the expenditure multiplier = Changes in Taxes -MPC. As mentioned before, the expenditure multipliers are all the same, even if they are called different names: -MPC. There is also a multiplier that is associated with a change in taxes. It is called the tax multiplier, and it is NOT the same as the spending multipliers. In fact, it is smaller than the spending multipliers. Why would the tax multiplier be smaller than the government spending multiplier? The answer lies in the fact that when a business or the government undertakes new spending, they inject the initial amount of that spending into the income stream and then it multiples through the economy. When the government decides to lower taxes, they are not injecting new money into the economy; they are simply deciding not to take money out of the economy that was already in the income stream. Individuals will then spend some portion of the money that they get to keep. So, if the government increases spending by \$ billion, the entire \$ billion is injected into the income stream. If they reduce taxes by \$ billion, only the MPC x \$ billion is injected into the income stream. Therefore, the impact of the tax multiplier is: \$(MPC) + \$(MPC)(MPC) + \$(MPC)(MPC)(MPC) + This progression can be shown to be equal to the spending multiplier times the MPC, or

11 Lesson 7 - ECO 5- Master.nb MPC x - MPC Which is simplified as MPC - MPC Since reducing taxes increases income and vice versa, the tax multiplier is negative, i.e. MPC - - MPC Let's look at some common values of the MPC and determine the tax multiplier for each. When the MPC is.9, the tax multiplier is -9 When the MPC is.8, the tax multiplier is -4 When the MPC is.75, the tax multiplier is -3 When the MPC is.6, the tax multiplier is -.5 When the MPC is.5, the tax multiplier is - Another way to look at this is using the equilibrium GDP formula we used when discussing changes in consumption, investment, government spending, and net export. When there is a change in taxes, note that the MPC is multiplied by that change. Also note that it is subtracting off of the other components of GDP. Therefore, increasing taxes will put downward pressure on GDP. We can see that when there is a change in taxes it is multiplied by the tax multiplier which is different than the expenditure multiplier. MPC DY* = - - MPC (DT) Tax Multiplier = - MPC - MPC In later lessons, we will discus what actions policy makers should take when facing a recession. Should they increase government spending or decrease taxes or do a combination of both? We will be incorporating discussions of the multipliers in that discussion. The Balanced-Budget Multiplier The final multiplier we want to consider in the Keynesian Model is called the balanced-budget multiplier. Essentially, this multiplier tells us what the impact will be on the GDP if you increase both government spending and taxes equally. For example, if the government wanted to increase government spending by, let's say, \$2 billion, but did not want to run a deficit, and therefore also increased taxes by \$2 billion. We'll look at each of these actions independently and then put them together to find a generalized answer. The equation for the balanced-budget multiplier is as follows: Balanced-budget multiplier = -MPC - MPC - MPC If the increase (decrease) in government spending is exactly equal to the increase (decrease) in taxes then the formula above simplifies as follows: -MPC -MPC =

12 2 Lesson 7 - ECO 5- Master.nb Therefore, if government spending and taxes go up by the exact same amount then GDP will go up by only that amount. The formula below can be used to show this. DY* = DG - MPC - MPC - MPC (DT) Assume the MPC is equal to 0.8. With an MPC of 0.8, the government spending multiplier is 5. If the government increases spending by \$2 billion, output will go up by \$0 billion. If the MPC is 0.8, the tax multiplier is -4. If the government increases taxes by \$2 billion, output will go down by \$8 billion. When these two things happen simultaneously, the net effect is to increase output by \$2 billion (\$0 billion - \$8 billion = \$2 billion). So an increase in government spending by \$2 billion and a simultaneous increase in taxes by \$2 billion will increase output by \$2 billion. In this case the balanced-budget multiplier is equal to and can be summarized as follows: when the government increases spending and taxes by the same amount, output will go up by that same amount. We can generally show that the balanced budget multiplier is equal to one, and that it is not dependent on the size of the MPC: when you sum the spending multiplier and the tax multiplier, you always get one, regardless of the MPC. Summary Key Terms 45 Degree Line AE Aggregate Expenditure Model Aggregate Expenditures Curve Aggregate Income Autonomous Changes in Consumption Autonomous Changes in Investment Autonomous Changes in Government Spending Autonomous Changes in Net Exports Balanced-Budget Multiplier Balanced-Budget Multiplier Formula C Constant Price Level Assumption Consumption Expenditure Multiplier Expenditure Multiplier Formula Exports Full Employment G GDP Gap Government Expenditures Government Spending Government Spending Multiplier Gross Private Domestic Investment I Imports Inflationary Gap Injection Inventories Investment

13 Lesson 7 - ECO 5- Master.nb 3 Investment Multiplier Keynesian Cross Model Leakage Macroeconomic Equilibrium Multiplier Model Net Exports NX Potential GDP Recessionary Gap Tax Multiplier Tax Multiplier Formula Y 203 by Brigham Young University-Idaho. All rights reserved.

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