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Chapter 11: The Multiplier Model Chapter 11: The Multiplier Model Questions for Thought and Review 1. The multiplier model is more appropriate for large fluctuations in aggregate demand, when the economy tends to be subject to greater feedback effects and is less self-correcting. 2. Induced expenditures are $1,000. Autonomous expenditures are $1,000. 3. If planned expenditures are below actual production, income will decline. Here’s how: when planned expenditures are below actual production, firms will see that their inventories are building up faster than they’d like. In response, they cut production. As production falls, so does income. Consumption falls by a fraction of the decline in income, leading to a further decline in planned expenditures. This process continues until planned expenditures equal actual production. 4. At levels of output above equilibrium inventories are building up because planned expenditures are below actual production. People are not buying all that is produced. 5. The aggregate expenditures curve shifts down by the decline in autonomous expenditures. 6. The AE curve becomes steeper when the marginal propensity to expend increases. Equilibrium income rises. 7. Equilibrium income is $500 (300/.6= 500). 8. If the mpe is .8, then the value of the multiplier is 1/.2 or 5. If autonomous expenditures are $4,200, the equilibrium level of income in the economy is 5 x $4,200 = $21,000. This is demonstrated in the accompanying graph. Colander’s Economics, 8e. McGraw Hill © 2010 1 Chapter 11: The Multiplier Model 9. a. If the mpe is .66, the value of the multiplier is 3. A decrease in autonomous expenditures of $20 will likely result in a decrease in income of $60. b. This is demonstrated in the accompanying graph. 10. If withdrawals were immediately translated into expenditures, the size of the multiplier would be infinite since leakages from the economy would be zero. However, autonomous expenditures would no longer exist. In short, under these conditions the multiplier model would break down. 11. a. Given that the mpe is 0.8 and autonomous investment has risen by $20, income will increase by $100 (the multiplier is 1/.2 or 5, and 5 X 20 is 100). b. With an mpe of 0.5, the multiplier is now only 2 (1/.5), and so the change in investment causes income to increase by only $40. c. The decrease in exports and increase in investment cancel each other out so that autonomous expenditures in the aggregate are unchanged. d. See the graphs below. The graph on the left corresponds to (a) and the graph on the right corresponds to (b). The graph to (c) would show the AE curve not moving at all. (a) 12. (b) Given that the mpe is 0.6, I0 = 1,000; G0 = 8,000; C0 = 10,000; and (X0 - M0) = 1,000, then: a. Y = 10,000 + .6Y + 1,000 + 8,000 + 1,000. Y - .6Y = 20,000; 0.4Y = 20,000; Y = 50,000. Colander’s Economics, 8e. McGraw Hill © 2010 2 Chapter 11: The Multiplier Model Thus, the equilibrium level of income in the country is $50,000. b. If net exports increase by $2,000, income will increase by $5,000 (the multiplier is 2.5, or 1/.4). c. According to Okun’s rule of thumb, a one-percentage-point change in unemployment will cause a 2 percent change in income in the opposite direction. Thus, if income has increased by $5,000, which is a 10 percent increase, then unemployment should drop by 5 percentage points. d. If the mpe falls from 0.6 to 0.5, the multiplier decreases from 2.5 to 2. The answer to part (a) would now be $40,000; the answer to part (b) would be $4,000; and the answer to part (c) is that unemployment should still fall by 5 percentage points. 13. Shocks to aggregate expenditures are any sudden changes in factors that affect C, I, G, X, or M. This includes consumer sentiment, business optimism, foreign income, and government policy. It is possible that people could change their marginal propensities to consume and save, and this could also have an effect on the economy. 14. If the mpe is 0.5, then the multiplier is 2. Every $1 increase in autonomous expenditures will raise income by $2. To close a recessionary gap of $200 the government needs to generate $100 of additional autonomous spending. It can accomplish this by increasing government expenditures by $100, or by cutting taxes by $200 (assuming mpc = mpe). 15. Cutting taxes by $100 has a smaller effect on GDP than increasing expenditures by the same amount because people don’t spend the entire amount of the tax cut—they save some of it, too. The multiplier begins with the increased individual spending resulting from the tax cut, or the mpc times the tax cut. 16. a. This is shown as a shift down of the AE curve from AE0 to AE1 and a decline in real income. b. An improvement would be graphically represented by a shift up of the AE curve shown in the graph as the shift from AE1 to AE2 and a rise in real income. 17. Given that income is $50,000, the mpe is .75: a. To reduce unemployment by 2 percentage points (again, by Okun’s rule of thumb) requires a 4 percent increase in income, which in this case is $2,000. The multiplier is 4.0, calculated as [1/(1 - mpe)]. To generate a $2,000 increase in income, increase government spending by $500 or decrease taxes by $667. Colander’s Economics, 8e. McGraw Hill © 2010 3 Chapter 11: The Multiplier Model b. If the mpe is .67, the multiplier is about 3, which means that to generate a $2,000 increase in income, the government would have to increase spending by $667 or decrease taxes by $1,000. c. If the mpe is .5, then the multiplier is 2.0, which means that to generate a $2,000 increase in income, the government would have to increase spending by $1,000 or decrease taxes by $2,000. 18. a. If the mpe is .5, the multiplier is 2. Because there is a recessionary gap of $800, government would have to increase spending by $400 or decrease taxes by $800 to bring the economy back to long-run equilibrium. b. If the mpe is .8, the multiplier is 5. Because there is an inflationary gap of $1500, government would have to decrease spending by $300 or increase taxes by $375 to bring the economy back to long-run equilibrium. c. If the mpe is .2, the multiplier is 1.25. Because there is an inflationary gap of $1,200, the government should reduce expenditures by $960 or increase taxes by $4,800. d. If the mpe is .7, the multiplier is 3.33. Because there is a recessionary gap of $1,500, the government should increase expenditures by $450 or decrease taxes by $643. 19. a. If the mpe is .5, the multiplier is 2. To eliminate the inflationary gap, the government should undertake a contractionary fiscal policy. Since the economy is $36,000 above potential, we would advise decreasing government spending by $18,000 or increasing taxes by $36,000. b. Using Okun’s rule of thumb, since income falls by 6 percent, we would expect unemployment to rise by 3 percentage points to 8 percent. c. The multiplier now becomes 5, so we would advise decreasing government spending by $7,200 or increasing taxes by $9,000. We would not change our answer to b. 20. A circular flow diagram of the economy that would more accurately describe the multiplier model would include leakages of savings to investment that cause the diagram to pulsate as the economy continually overshoots equilibrium in response to shocks to the economy. 21. A mechanistic model states the equilibrium independent of where the economy has been or where people want it to be. A mechanistic model is used as a direct guide for policy prescriptions. An interpretive model is used as a guide that highlights dynamic interdependencies and suggests the possible response of aggregate output to various policy initiatives. 22. In the multiplier-accelerator model changes in output are accelerated because changes in investment depend on changes in income, not the level of income. This new interconnection accelerates the fall in demand and can possibly make the second shift larger than the first. In some cases output can be pushed into a freefall. Colander’s Economics, 8e. McGraw Hill © 2010 4 Chapter 11: The Multiplier Model Issues to Ponder 1. In mid-2009, the government budget was running a huge deficit and the state of fiscal policy was expansionary (low taxes and extremely high expenditures from the stimulus package) in an effort to spark a recovery from the deep recession that started in 2008. Economists differ on whether or not the recession has bottomed out and whether or not the stimulus will work. (This answer may change as the economy progresses.) 2. The effects of this invention on the economy would be manifold and in many ways unpredictable because such major shocks have social, institutional, and political effects, as well as economic effects. The obvious effect is that the demand for the pill would likely be tremendous (after people were sure it was safe), and so production of the pill would gear up to meet the demand. Market structure and pricing decisions will play a big role in determining the effect of the change. Alternative forms of transportation would suffer decreases in demand (cars, mass transit, airplanes, etc.), and levels of production of those goods and services would adjust, as would employment in those industries and related industries. Measured GDP might actually fall. 3. If there is a delay, it will mean that the initial multiplier effects can be small or non-existent, and then, suddenly, they become large and fast. Uncertain, changing, expectations can add to the ambiguity of the model’s result. Chapter 28: Appendix A 1. To determine precisely how much we would need to decrease taxes we must determine what the multiplier is. Assuming all other marginal propensities are zero, the multiplier is 5. The tax cut would initially affect the economy by only .8 times the tax cut, so to increase output by 400, we would decrease taxes by 100 (.8 X 100 X 5 = 400). 2. We would recommend increasing expenditures by 80 (80 X 5 = 400). 3. This makes the multiplier 3.57, which means that we would increase expenditures by about 112, or cut taxes by about 140. 4. This makes the multiplier 2.08, which means that we would increase expenditures by about 192 or cut taxes by about 213. Colander’s Economics, 8e. McGraw Hill © 2010 5 Chapter 11: The Multiplier Model 5. Making taxes and imports endogenous reduces the size of the multiplier because they increase the leakages from the expenditure flow. Because of taxes and imports, increases in income will lead to lower increases in expenditures than otherwise. 6. This would make the multiplier = 1/(1 - c + ct + m - mt). It would be a slightly higher multiplier. (The difference between the two assumptions is whether we are assuming government imports.) Chapter 28: Appendix B 1. a. As shown in the left-hand graph below, an increase in autonomous expenditures shifts the AE curve up and causes a movement along the AP curve to the right and results in a higher equilibrium income level twice the shift in the AE curve. b. As shown in the right-hand graph below, an increase in autonomous expenditures shifts the AD curve to the right by twice the increase in autonomous expenditures. Since the price level is fixed, real output increases by twice the rise in autonomous expenditures. Colander’s Economics, 8e. McGraw Hill © 2010 6 Chapter 11: The Multiplier Model c. Since prices are somewhat flexible, the rise in expenditures is split between an upward shift of the AE curve and a rise in prices that causes a downward shift of the AE curve that is smaller than the initial upward shift. The rise in income is less than twice the initial shock. This is shown in the graph to the right. In the AS/AD model, a flexible price means that the shift in the AD curve is split between increases in the price level and increases in real output. Real output rises by less than the multiplier times the increase in autonomous expenditures. 2. a. The AD curve will become steeper. b. An increase in the size of the multiplier makes the AD curve flatter because the effect of changes in the price level on aggregate demand will be augmented even more by the multiplier. c. An increase of $20 in autonomous expenditures has no effect on the slope of the AD curve; the increase only affects the position of the curve. d. A decline in the price level disrupting the financial market will make the AD curve steeper because it decreases the price-level interest rate effect. Colander’s Economics, 8e. McGraw Hill © 2010 7