CHAPTER 23 - THE SHORT-RUN MACRO MODEL PROBLEM SET 2. a. Real GDP Autonomous Consumption MPC x Disposable Income Consumption = Autonomous Consumption + (MPC x Disposable Income) $0 $30 $0 $30 $100 $30 $85 $115 $200 $30 $170 $200 $300 $30 $255 $285 $400 $30 $340 $370 $500 $30 $425 $455 $600 $30 $510 $540 b. Real GDP Consumption Planned Investment Government Net Exports $0 $30 $40 $20 -$15 $75 $100 $115 $40 $20 -$15 $160 $200 $200 $40 $20 -$15 $245 $300 $285 $40 $20 -$15 $330 $400 $370 $40 $20 -$15 $415 $500 $455 $40 $20 -$15 $500 $600 $540 $40 $20 -$15 $585 c. Aggregate Expenditures d. $500 billion is the equilibrium level of real GDP.
e. If the actual level of real GDP in this economy is $200 billion, then the economy will expand. This is because aggregate expenditure ($245 billion) is greater than real GDP ($200 billion), so firms find their inventories falling, and will expand output, leading to a higher real GDP in the future. f. If planned investment falls to $25 billion, the equilibrium level of real GDP will fall from $500 billion to $400 billion. 4. a. Inventories will fall unexpectedly, sending firms a signal to produce more output. GDP A is not sustainable because the extra production will move the economy to the right along the horizontal axis. b. Inventories will rise unexpectedly, sending firms a signal to produce less output. GDP B is not sustainable because cut in production will move the economy to the left along the horizontal axis. 6. a. Real GDP and total employment will increase. b. Real GDP and total employment will increase. c. Real GDP and total employment will decrease. 8. a. In the table in Problem 1, the second column (C) would be affected; each number in the column would become smaller, since households would spend less at each level of income. b. The change in saving is the vertical distance between the two aggregate expenditure lines.
c. Real Aggregate Expenditure (C + I + NX) 1 (C + I + NX) 2 45 Y 2 Y 1 Real GDP 10. a. If the MPC is 0.95, then the expenditure multiplier is 20. Therefore, the change in real GDP is 20 x $7,500 = $150,000. b. If the MPC is 0.65, then the expenditure multiplier is 2.86. Therefore, the change in real GDP is 2.86 x -$300,000 = -$857,143. c. If the MPC is 0.75, then the expenditure multiplier is 4. Therefore, the change in real GDP is 4 x -$5 billion = -$20 billion.
12. Round increase in I in each round Total Initial Increase in Investment 1000 1000 1000 2 90 690 1690 3 62 476 2166 4 43 329 2495 5 30 227 2721 The final change in GDP would be higher than $2,500 billion, because further rises in investment act as a de-stabilizer, thus increasing the multiplier. 14. Y = [a (b T) + I P + G + NX] / (1 b) = [600 0.75) = 7,200. At this equilibrium, C = a + b(y T) = 600 + 0.75(7,200 400) = 5,700. Therefore, in equilibrium, we have aggregate expenditure = C + I P + G + NX = 5,700 + 600 + 700 + 200 = 7,200, which is equal to equilibrium real GDP. MORE CHALLENGING QUESTIONS 16. Initially, the economy is in equilibrium at point E, with real GDP and aggregate expenditure (AE) both equal to $10 billion per day. Then, due to pessimism, the AE line shifts down to AE 2 on day 2, and people (for the moment) don t yet realize that the lower level of spending will cause their income to drop as well. That is, they believe they will continue to earn income of $10 billion on day 2, so their spending is at point H (the point on AE 2 associated with an expected income of $10 billion). But actual income on day 2 is equal to total spending (because income on day 2 is earned only from services that are actually bought on day 2). So with spending at point H, actual income on day 2 will be equal to height of point H. To measure day 2 s actual income along the horizontal (GDP) axis, we go leftward to the 45-degree translator line (point K). So income on day 2 is found at point K. On day 3, people believe they will earn income of Y 2 (the same as they actually earned on day 2), so they will spend at point L. This lower level of spending will reduce their actual income on day 3 to the height of point L. To measure day 3 s actual income along the horizontal (GDP) axis, we go leftward to the 45-degree translator line, and so on. Continuing in this way, we make smaller and smaller movements that bring us closer and closer to the new equilibrium at point J, where AE 2 intersects the 45-degree line. This is the same equilibrium GDP we would reach in an economy that produced only goods, in which inventory changes would cause the movements toward equilibrium GDP.
AE 1 F Aggregate expenditure per day AE 2 K H J L 45 0 New equilibrium income Income on day 2 $10 billion Real GDP per day