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304L Homework 7 Solutions

304L Homework 7 Solutions - Economics 304L Principles of...

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Unformatted text preview: Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Homework 7 Solutions The following problems refer to the “Problems and Applications” section at the end of Chapter 20 of Mankiw (pp. 469 ‐ 471). 1. No. 1. a. The current state of the economy is shown in the figure above. The aggregate‐demand curve and short‐run aggregate‐supply curve intersect at the same point on the long‐run aggregate‐ supply curve (the intersection of AD1 and SRAS1 is the initial long run equilibrium). A stock market crash leads to a leftward shift of aggregate demand. The equilibrium level of output and the price level will fall. Because the quantity of output is less than the natural rate of output, the unemployment rate will rise above the natural rate of unemployment (the intersection of AD2 and SRAS1 is the short run equilibrium, which involves a recession in this problem since output is now below the natural rate associated with LRAS). If nominal wages are unchanged as the price level falls, firms will be forced to cut back on employment and production. Over time as expectations adjust, the short‐run aggregate‐supply curve will shift to the right, moving the economy back to the natural rate of output (the intersection of AD2 and SRAS2 is the new long run equilibrium). This is the Keynesian “self‐ correcting mechanism,” which occurs in the long run. Of course, Keynes himself was not an advocate of just waiting for the economy to self‐correct in the long run. Instead, Keynes advocated active government policy in response to a recession. No. 3 (Note that increases in the money supply increase AD. One way that they do so is by reducing interest rates, thereby increasing investment expenditures by firms. Decreases in the money supply reduce AD because interest rates increase and investment expenditure falls. We elaborate on this in Chapter 21). The current state of the economy is shown in the figure below. The aggregate‐demand curve and short‐run aggregate‐supply curve intersect at the same point on the long‐run aggregate‐ supply curve (point A). b. c. 2. a. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Price Level LRAS AS2 AS1 C B A AD2 AD1 Natural Rate of Output Quantity of Output b. c. d. e. f. If the central bank increases the money supply, aggregate demand shifts to the right (to point B). In the short run, there is an increase in output and the price level. The mechanism that delivers this outcome will be discussed in Chapter 21. Over time, nominal wages, prices, and perceptions will adjust to this new price level. As a result, the short‐run aggregate‐supply curve will shift to the left. The economy will return to its natural rate of output (point C). According to the sticky‐wage theory, nominal wages at points A and B are equal. However, nominal wages at point C are higher, since firms and workers will have negotiated new contracts with higher nominal wages as a response to the higher price level. According to the sticky‐wage theory, real wages at point B are lower than real wages at point A (nominal wages are fixed, but the price level has risen). However, real wages at points A and C are equal. Yes, this analysis is consistent with long‐run monetary neutrality. In the long run, an increase in the money supply causes an increase in the nominal wage, but leaves the real wage unchanged. Note: normally, we would address a problem like the above by assuming that the economy begins in a recession (output below natural rate) or expansion (output above the natural rate). Below is a diagram of the economy in a recession, with short run equilibrium output below the natural rate. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler In this situation, if the government does nothing and allows the economy to “self correct,” then over time, SRAS will shift out until the economy returns to long run equilibrium, as shown below. Each of the three theories of SRAS tells a different story about how this occurs. We discussed the sticky wage theory story in class, and details on the other two are given in the text. If instead of allowing the economy to self correct, the government can intervene with fiscal or monetary policy that causes spending to increase. Instead of waiting for SRAS to shift, the AD curve will then shift right. If the policy gets it right, then the economy will return to long run equilibrium as shown in the diagram below. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler 3. a. No. 5 The statement that "the aggregate‐demand curve slopes downward because it is the horizontal sum of the demand curves for individual goods" is false. The aggregate‐demand curve slopes downward because a fall in the price level raises the overall quantity of goods and services demanded through the wealth effect, the interest‐rate effect, and the exchange‐rate effect. The statement that "the long‐run aggregate‐supply curve is vertical because economic forces do not affect long‐run aggregate supply" is false. Economic forces of various kinds (such as population and productivity) do affect long‐run aggregate supply. The long‐run aggregate‐supply curve is vertical because the price level does not affect long‐run aggregate supply. The statement that "if firms adjusted their prices every day, then the short‐run aggregate‐ supply curve would be horizontal" is false. If firms adjusted prices quickly and if sticky prices were the only possible cause for the upward slope of the short‐run aggregate‐supply curve, then the short‐run aggregate‐supply curve would be vertical, not horizontal. The short‐run aggregate supply curve would be horizontal only if prices were completely fixed. The statement that "whenever the economy enters a recession, its long‐run aggregate‐supply curve shifts to the left" is false. An economy could enter a recession if either the aggregate‐ demand curve or the short‐run aggregate‐supply curve shifts to the left. No. 6. According to the sticky‐wage theory, the economy is in a recession because the price level has declined so that real wages are too high, thus labor demand is too low. Over time, as nominal wages are adjusted so that real wages decline, the economy returns to full employment. b. c. d. 4. a. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler According to the sticky‐price theory, the economy is in a recession because not all prices adjust quickly. Over time, firms are able to adjust their prices more fully, and the economy returns to the long‐run aggregate‐supply curve. According to the misperceptions theory, the economy is in a recession when the price level is below what was expected, because firms do not have perfect information and some will perceive that the fall in their price was due to a fall in their relative price, which encourages them to cut back on production . Over time, as firms realize the lower price is due to a general fall in demand with a lower overall price level, P, and not a change in their relative price, their expectations adjust, and the economy returns to the long‐run aggregate‐supply curve. The speed of the recovery in each theory depends on how quickly price expectations, wages, and prices adjust. b. The following problems refer to the “Problems and Applications” section at the end of Chapter 21 of Mankiw (pp. 495 ‐ 496). 5. a. No. 2 The increase in the money supply will cause the equilibrium interest rate to decline, as shown in the first figure below. Households will increase spending and will invest in more new housing. Firms too will increase investment spending. This will cause the aggregate demand curve to shift to the right as shown in the second figure. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler Price Level Short-run Aggregate Supply P2 P1 AD 2 AD 1 Y1 Y2 Quantity of Output b. c. d. e. As shown in the previous figure, the increase in aggregate demand will cause an increase in both output and the price level in the short run. When the economy makes the transition from its short‐run equilibrium to its long‐run equilibrium, short‐run aggregate supply will decline, causing the price level to rise even further. The increase in the price level will cause an increase in the demand for money, raising the equilibrium interest rate. Yes. While output initially rises because of the increase in aggregate demand, it will fall once short‐run aggregate supply declines. Thus, there is no long‐run effect of the increase in the money supply on real output. No. 8 The initial effect of the tax reduction of $20 billion is to increase aggregate demand by $20 billion x 3/4 (the MPC ) = $15 billion. Additional effects follow this initial effect as the added incomes are spent. The second round leads to increased consumption spending of $15 billion x 3/4 = $11.25 billion. The third round gives an increase in consumption of $11.25 billion x 3/4 = $8.44 billion. The effects continue indefinitely. Adding them all up gives a total effect that depends on the multiplier. With an MPC of 3/4, the multiplier is 1/(1 – 3/4) = 4. So the total effect is $15 billion x 4 = $60 billion. Another way to derive this is to use the tax multiplier we introduced in class. For a tax change of ΔT, the change in output is given by the tax multiplier, –MPC/(1‐MPC), so ΔY = (‐MPC/(1‐MPC)) × ΔT . Government purchases have an initial effect of the full $20 billion, because they increase aggregate demand directly by that amount. The total effect of an increase in government purchases is thus $20 billion x 4 = $80 billion. So government purchases lead to a bigger effect on output than a tax cut does. The difference arises because government purchases affect aggregate demand by the full amount, but a tax cut is partly saved by consumers, and therefore does not lead to as much of an increase in aggregate demand. 6. a. b. c. Economics 304L: Principles of Macroeconomics Spring 2010 Sadler d. 7. a. The government could increase taxes by the same amount it increases its purchases. No. 9 If the marginal propensity to consume is 0.8, the spending multiplier will be 1/(1‐0.8) = 5. Therefore, the government would have to increase spending by $400/5 = $80 billion to close the recessionary gap. With an MPC of 0.8, the tax multiplier is (0.8)(1/(1‐0.8)) = (0.8)(5) = 4. Therefore, the government would need to cut taxes by $400 billion/4 = $100 billion to close the recessionary gap. If the central bank was to hold the money supply constant, my answer would be larger because crowding out would occur. They would have to raise both government spending and taxes by $400 billion. The increase in government purchases would result in a boost of $2,000 billion, while the higher taxes would reduce spending by $1,600 billion. This leaves a $400 billion rise in aggregate spending. No. 12 Tax revenue declines when the economy goes into a recession because taxes are closely related to economic activity. In a recession, people's incomes and wages fall, as do firms' profits, so taxes on these things decline. Government spending rises when the economy goes into a recession because more people get unemployment‐insurance benefits, welfare benefits, and other forms of income support. If the government were to operate under a strict balanced‐budget rule, it would have to raise tax rates or cut government spending in a recession. Both would reduce aggregate demand, making the recession more severe. b. c. d. 8. a. b. c. ...
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