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Unformatted text preview: ECON301: Intermediate Macro Problem Set #2 Solutions S ECTION 1: M ULTIPLE C HOICE Q UESTIONS 1. The money demand curve will shift to the left when which of the following occurs? (a) a decrease in income (b) an increase in the interest rate (c) an open market sale of bonds by the central bank (d) an increase in income (e) a reduction in the interest rate 2. The crowding out effect is zero if (a) The LM-curve is horizontal (b) The LM-curve is vertical (c) The central bank conducts open market sales following fiscal expansion (d) Income is stimulated via a tax cut rather than an increase in government spending (e) The IS-curve is horizontal 3. The non-institutional civilian population is 250 million, of which 100 million are employed and 10 million are unemployed. Based on this data, the unemployment rate is (a) 4% (b) 6.6% (c) 9.1% (d) 10% (e) 11.1% 4. Suppose workers and firms expect the overall price level to increase by 5%. Given this information, we would expect that: (a) the nominal wage will increase by less than 5% (b) the nominal wage will increase by exactly 5% (c) the nominal wage will increase by more than 5% (d) the real wage will increase by 5% (e) the real wage will increase by less than 5% 5. Suppose that increased international trade makes product markets more competitive in the U.S. Given this information, we would expect to observe which of the following? (a) an upward shift in the WS curve (b) a downward shift in the WS curve (c) an upward shift in the PS curve (d) a downward shift in the PS curve (e) none of the above 6. The aggregate demand curve will shift to the right when which of the following occurs? (a) a reduction in the money supply (b) a reduction in consumer confidence (c) a rise in the price level (d) a reduction in taxes (e) a decrease in the price level 7. Assume the economy is initially operating at the natural level of output. Now suppose that individuals reduce their marginal propensity to save. We know with certainty that which of the following will occur in the short run as a result of decreased desire to save? (a) greater investment (b) less investment (c) an increase in the nominal wage (d) higher output and lower investment (e) no change in the economy at all 8. The aggregate demand has its particular shape because of which of the following explanations? (a) an increase in the money supply will cause a reduction in the interest rate, an increase in investment, and an increase in output (b) an increase in the aggregate price level will cause an increase in the interest rate and a reduction in output (c) an increase in the aggregate price level will cause a reduction in the real wage, an increase in employment, and an increase in output (d) as the aggregate price level decreases in a closed economy, goods and services become relatively cheaper and individuals respond by increasing the quantity demanded of goods and services (e) an increase in the money demand will cause an increase in the interest rate and a decrease in output ECON301: Intermediate Macro Problem Set #2 Solutions 2 9. At the current level of output, suppose the actual price level is greater than the price level that individuals expect (i.e., Pt > Pte ). We know that: (a) output is currently below the natural level of output (b) the interest rate will tend to rise as the economy adjusts to this situation (c) the nominal wage will tend to decrease as individuals revise their expectations of the price level (d) the AS curve will tend to shift down over time (e) the LM curve will tend to shift down over time 10. An example of a stock variable would be (a) real GDP. (b) savings. (c) investment. (d) the amount of money in circulation. (e) income S ECTION 2: F REE R ESPONSE Q UESTIONS 1. Clearly explain what “crowding out” refers to and its overall effects. Graphically illustrate the level of crowding out in an IS-LM model. Explain in detail how the interest elasticity of investment affects the level of crowding out. Be sure to explain why this is the case. Note: This question requires lengthy dialogue and a corresponding graph. Be sure to answer all parts of the question. Answer: Crowding out refers to the decrease in investment and the corresponding decrease in real GDP that results from an increase in government expenditures. Specifically, the increase in government spending causes aggregate expenditure to rise. When aggregate expenditure increases, the equilibrium level of GDP also rises. This result causes the IS curve to shift out to the right to (i∗0 , Y1 ) as output rises given a fixed level of interest rates. The increase in the nominal interest rate from i∗0 to i∗2 causes a decrease in investment in the aggregate expenditure model. As a result, real GDP only rises to Y2∗ instead of Y1 (the level of output that would have been attained had interest rates remained unchanged). Thus, the new equilibrium point will become (i∗2 , Y2∗ ) (be sure you know how the economy reaches the new equilibrium). If investment is interest rate elastic, then small changes in the interest rate will lead to large changes in the level of investment. Similarly, if investment is interest rate inelastic, then large changes in the interest rate will lead to small changes in the level of investment. The higher the interest rate elasticity of investment, the greater the magnitude of the change in equilibrium output. Since the slope of the IS curve is determined by the response of output to changes in the nominal interest rate, the more interest rate elastic is investment, the more elastic the IS curve. When the IS curve is elastic the crowding out effect will be significant, because as interest rates rise to i∗2 , investment decreases significantly causing a relatively ECON301: Intermediate Macro Problem Set #2 Solutions 3 large decrease in real GDP. When the IS curve is inelastic the crowding out effect will be low, because as interest rates rise to i∗2 investment decreases only a small amount causing a relatively small decrease in real GDP. In general, the amount of crowding out is equal to Y1 − Y2∗ . i LM i*1 i*0 Crowding Out IS’ IS Y0* Y1 Y1* Y 2. Consider first the goods market model with constant investment that we saw in Chapter 3. Consumption is given by C = c0 + c1 (Y − T ) and I, G, and T are given. (a) Solve for equilibrium output. What is the value of the multiplier? Now let investment depend on both sales and the interest rate: I = b0 + b1 Y − b2 i (b) Solve for equilibrium output. At a given interest rate, is the effect of a change in autonomous spending bigger than it was in part (a)? Why? (Assume c1 + b1 < 1.) Next write the LM relation as M/P = d1 Y − d2 i (c) Solve for the equilibrium output. (Hint: eliminate the interest rate from the IS and LM relations.) Derive the multiplier (the effect of a change in one unit in autonomous spending on output). ECON301: Intermediate Macro Problem Set #2 Solutions 4 (d) Is the multiplier you obtained in part (c) smaller or larger than the multiplier you derived in part (a)? Explain how your answer depends on the parameters in the behavioral equations for consumption, investment, and money demand. Answer: (a) Using the fact that Y =C +I +G in a closed economy, the above consumption function can be written as Y = I + G + c0 + c1 Y D = I + G + c0 + c1 (Y − T ) Solving for Y then yields Y = 1 [c0 − c1 T + I + G] 1 − c1 The multiplier is the coefficient on autonomous expenditures: 1/(1 − c1 ). (b) From part (a), Y = I + G + c0 + c1 (Y − T ) = b0 + b1 Y − b2 i + G + c0 + c1 (Y − T ) Solving for Y then yields Y = 1 [b0 − b2 i + c0 − c1 T + G] 1 − b1 − c1 The multiplier is 1/(1 − c1 − b1 ). Since the multiplier is larger than the multiplier in part (a), the effect of a change in autonomous spending is bigger than in part (a). This is due to the fact that an increase in autonomous spending now leads to an increase in investment as well as consumption. (c) First solve the IS relation for the nominal interest rate, i, to obtain d1 1 M Y − d2 d2 P Substituting for the interest rate in the answer to part (b) gives   b2 d 1 b2 M 1 Y = b0 + c 0 − c 1 T + G − Y + 1 − b1 − c 1 d2 d2 P     b2 d 1 1 1 b2 M → 1+ Y = b0 + c 0 − c 1 T + G + d 2 1 − b1 − c 1 1 − b1 − c 1 d2 P i= Solving for Y then yields   b2 M Y = b 0 + c0 − c1 T + G + 1 − b1 − c1 + b2 d1 /d2 d2 P 1 The multiplier is 1/(1 − c1 − b1 + b2 d1 /d2 ). ECON301: Intermediate Macro Problem Set #2 Solutions 5 (d) The multiplier is greater (less) than the multiplier in part (a) if (b1 − b2 d1 /d2 ) is greater (less) than zero. The multiplier as measured in part (c) measures the marginal effect of an increase in autonomous spending on equilibrium output. As such, the multiplier is the sum of two effects: a direct effect of output on demand and an indirect effect of output on demand via the interest rate. The direct effect is equivalent to the horizontal shift of the IS curve. The indirect effect depends on the slope of the LM curve (since the equilibrium moves along the LM curve in response to a shift of the IS curve). The direct effect is captured by the sum c1 + b1 , which measures the marginal effect of an increase in output on the sum of consumption and investment demand. As this sum increases, the multiplier gets larger. The indirect effect is captured by the expression b2 d1 /d2 and tends to reduce the size of the multiplier. The ratio d1 /d2 is the slope of the LM curve, and the parameter b2 measures the marginal effect of an increase in the interest rate on investment. Note that the slope of the LM curve becomes larger as money demand becomes more sensitive to income (i.e., as d1 increases) and becomes smaller as money demand becomes more sensitive to the interest rate (i.e., as d2 increases). 3. Suppose the markup of goods prices over marginal cost is 5%, and that the wage setting equation is W = P (1 − u) where u is the unemployment rate. (a) What is the real wage, as determined by the price setting equation? (b) What is the natural rate of unemployment? (c) Suppose that the markup of prices over costs increases to 10%. What happens to the natural rate of unemployment? Intuitively explain the logic behind your answer. (d) In general, if the unemployment rate is very low, how easy is it for firms to find workers to hire? How easy is it for workers to find jobs? What do your answers imply about the relative bargaining power of workers and firms when the unemployment rate is low? What do your answers imply about what happens to the wage as the unemployment rate gets very low? Answer: (a) Using the price setting equation, the real wage is given by 1 1 W = = = 0.952 P 1+µ 1.05 (b) To find the natural rate of unemployment, equate the price setting and wage relations to obtain 1−u= 1 = 0.952 → u = 4.8% 1+µ ECON301: Intermediate Macro Problem Set #2 Solutions 6 (c) When the markup over prices rises to 10%, the real wage falls to W 1 1 = = = 0.91 P 1+µ 1.10 Thus, the natural rate of unemployment increases to u = 1 − 0.91 = 9% The increase in the markup lowers the real wage. Algebraically, from the wage-setting equation, the unemployment rate must rise for the real wage to fall. Thus, the natural rate increases. Intuitively, an increase in the markup implies more market power for firms, and therefore less production, since firms will use their market power to increase the price of goods by reducing supply. Less production implies less demand for labor, so the natural rate rises. (d) When the unemployment rate is rather low, it is relatively difficult for firms to find workers to hire and much easier for workers to find jobs. As a result, the bargaining power of workers rises considerably when the unemployment rate is very low. Therefore, the nominal wage rate rises as the unemployment rate gets very low. ECON301: Intermediate Macro Problem Set #2 Solutions 7 4. Show and fully explain the short run and medium run effects of the monetary authority deciding to decrease the nominal money stock. In order to receive full credit, you must utilize both the IS-LM and AD-AS graphs. In explaining your answer you must take into account price level effects and thoroughly explain all economic reactions. Be sure to state the overall impact on output, prices, the nominal interest rate, and investment in both the short- and medium-runs. Answer: LM’ LM’’ LM i i2 B i1 i0 A’ A (A’’) IS Y1 Y2 YN Y P AS AS’ P0 P1 P2 B A A’ A’’ AD AD’ Y1 Y2 YN Y Before the change in the nominal money stock, M , assume the AS-AD market is in medium run equilibrium, denoted by point A. Now suppose the M decreases to M 0 < M . This decreases the real money stock, causing the equilibrium interest rate to rise in the money market. As a result, the LM curve shifts up to LM’, leading to lower equilibrium output in the short-run (denoted as point A” in the IS-LM model). This causes the AD curve to shift to the left, which drives down the price level since the AS curve is upward sloping. As the price level falls, real money balances rise partially offsetting the effect of the decrease in M and causing the LM curve to fall to LM”. Now at point (P1 , Y2 ) in the ADAS model and point (i1 , Y2 ) in the IS-LM model, both of which are denoted as point A’. Thus, in the short-run, output and prices are lower and the nominal interest rate is higher, implying that the effect on investment is ambiguous. Since output is below the natural level, the price level is lower than wage-setters expected. Thus, in the medium run, wage setters revise their expectations downward causing the AS curve to shift down to AS’. As the AS curve shifts down, prices continue to fall, which leads to further increases in the real money stock. Thus, the LM curve continues to shift down. Eventually, the LM curve returns to where it was located before the decrease in the nominal money stock. Now at point (P2 , Y N ) in the AD-AS model, denoted as point A”, and point (i0 , Y N ) in the IS-LM model, denoted as point A. Thus, in the medium run, output and the nominal interest rate are left unchanged, while the price level is lower, implying that there is no effect on investment. ECON301: Intermediate Macro Problem Set #2 Solutions 8 ...
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