c. A decline in autonomous investment spending by firms reduces aggregate demand at each level of inflation, shifting the AD curve to the left.

Transcription

1 Homework Answers Chapters 28 and 20 Chapter 28 Questions 1. What two variables are related by the aggregate demand (AD) curve? Explain how real balances (i.e., the purchasing power of people s holdings of money) are related to movements along the curve. List and discuss two other factors that lead the curve to have a negative slope. The AD curve shows the relationship between the inflation rate and shortrun equilibrium output in the economy. As the inflation rate rises, given the rate of growth of the money supply, real balances (M/P) fall. This tends to raise the interest rate, which reduces autonomous expenditure and in turn, short-run equilibrium output. Therefore, along the AD curve, as the inflation rate rises, the output level falls, leading to a downwardsloping curve (with inflation on the vertical axis and output on the horizontal axis). There are four other factors listed in this chapter that could lead to this downward slope: (1) inflationary effects on the behavior of the Fed, (2) inflationary effects on the redistribution of income and wealth, which in turn affect consumption, (3) inflationary effects on investment spending, and (4) inflationary effects on net exports (for a given exchange rate). 2. State how each of the following affects the AD curve and explain a. An increase in government purchases b. A cut in taxes c. A decline in planned investment by firms d. A monetary expansion, i.e., a decision by the Fed to increase the money supply. a. For given levels of inflation and the real interest rate, an increase in government purchases raises aggregate demand and short-run equilibrium output. Thus an increase in government purchases shifts the AD curve to the right. b. Because it leads consumers to spend more, a cut in taxes stimulates aggregate demand at each level of inflation, shifting the AD curve to the right. c. A decline in autonomous investment spending by firms reduces aggregate demand at each level of inflation, shifting the AD curve to the left.

2 d. For each level of inflation, a lower real interest rate stimulates consumption and investment spending, raising aggregate demand and output. Thus, an expansionary monetary policy shifts the AD curve to the right. Chapter 28 Questions 3, 4, 5, and 6 p Prices of commodities are set continuously in auction markets and therefore can adjust quickly to changes in supply or demand. However, most prices are not determined in auction markets but are set only periodically. In setting prices or wages for a longer period, individuals expectations of future inflation are important; the higher is expected inflation, the higher the future wage or price must be set in order to maintain the desired level of purchasing power. But expectations of inflation in turn depend in part on recent experience with inflation. So we have a vicious (or virtuous circle), as high inflation leads to high expectations of inflation, which in turn leads to high actual inflation (and the reverse if inflation is low). Together with long-term contracts that lock in prices and wages for a period of time, expectations of inflation contribute to inflation inertia, or stickiness. 4. Expansionary gaps tend to raise inflation, and recessionary gaps tend to reduce it. If an expansionary gap exists, for example, firms are producing above normal capacity. Eventually they will respond by attempting to raise their relative price (that is, raising their own price faster than the rate of inflation). As all firms try to do this, inflation will tend to speed up. Likewise, a recessionary gap implies that firms are producing below normal capacity. To stimulate demand for their products, firms will try to reduce their relative prices, leading to an overall slowdown in inflation. Graphically, the link between output gaps and inflation is captured by movements of the short-run aggregate supply (SRAS) line. If an expansionary gap exists at the current intersection of the SRAS line and the AD curve (which determines short-run equilibrium output), inflation rises and the SRAS line moves upward. If a recessionary gap exists in short-run equilibrium, inflation falls and the SRAS line moves downward. Inflation and the SRAS line adjust until the economy reaches long-run equilibrium at the intersection of the AD curve and the long-run aggregate supply (LRAS) line. See Figures 28.6 and Short-run equilibrium occurs at the intersection of the AD curve and the SRAS line. When short-run equilibrium output is greater than potential output (that is, equilibrium is to the right of the LRAS line), an expansionary gap

3 exists. The expansionary gap leads inflation to rise over time; the SRAS line, which shows the current rate of inflation, therefore also rises over time. The SRAS line continues to rise until it intersects the LRAS line and AD curve at point B. At point B, called the long-run equilibrium point, output equals potential output and the inflation rate is stable. (See below, and see figure 28.6 in the text for the example with a recessionary gap). Long-run aggregate supply LRAS Inflation B * SRAS OutputY* Y A A D SRAS 6. The answer is ambiguous, as whether stabilization policy is useful depends largely on the speed at which self-correction takes place. The more slowly the economy adjusts, the more likely it is that stabilization policy will be useful. Thus if the economy has many long-term contracts or other barriers to rapid adjustment, or if the economy is initially far from full employment, then stabilization policy is more likely to be useful. How does a tight monetary policy, like that conducted by the Volcker Fed in the early 1980s, affect output, inflation, and the real interest rate in the short run? In the long run? Assume for concreteness that the economy starts at full employment, but with an inflation rate higher than the Fed would like. To reduce inflation, the Fed tightens monetary policy, shifting the AD curve leftward. In the short run inflation is unchanged (the SRAS line has not shifted), output is lower (a recession), and the real interest rate is higher (tighter money means that the Fed raises the real interest rate at any given level of inflation). The

4 recessionary gap implies that over time inflation will fall; graphically, the SRAS line shifts downward until long-run equilibrium is restored at the intersection of the AD curve, the LRAS line, and the SRAS line. In the long run inflation is lower and output returns to full employment. The real interest rate declines as inflation falls; indeed, in the long run it returns to its original full-employment value, consistent with equilibrium in the market for saving and investment. Most central banks place great value on keeping inflation low and stable. Why do they view this objective as so important? Moderate and high rates of inflation can impose significant costs to the economy, in particular with respect to long run growth. Low and stable inflation helps reduce uncertainty for businesses and helps to encourage greater investment, which in turn leads to higher productivity and faster growth of potential output (higher standards of living). High and moderate inflation has been shown empirically to retard economic growth, thus policymakers attempt to keep inflation low, even though at times following this policy may lead to short-run costs in terms of higher unemployment and lower output. Exercises 3, 4, 5, 6, 7, and 8 3. a. In the short run, the equilibrium inflation rate and output level are given by the intersection of the SRAS and AD curves. Algebraically, the short run equilibrium level of output is found by substituting the current inflation rate into the AD equation. Thus, in the short run, Y = 13,000 20,000(.04) = 12,200 and inflation = 4%, the current level of inflation. b. In the long run, the equilibrium inflation rate and output level are given by the intersection of the LRAS and AD curves. Algebraically, the long-run equilibrium inflation rate is found by substituting the level of potential output into the AD equation. Thus, in the long run, 12,000 = 13,000 20,000 1,000 = 20,000 1,000 = =.05 = 5% 20,000 and the long-run level of output equals 12,000, the potential output level.

5 4. a. In the short run, the equilibrium inflation rate is simply the current inflation rate, 10%, and output equals Y = 1,000-1,000(.10) = 900. Thus, the economy is experiencing a recessionary gap, since Y < Y*. In the long run, the equilibrium output level is the level of potential output, 950. The long run equilibrium inflation rate is found by substituting Y* for Y in the AD curve equation and solving the inflation rate: 950 = = =.05 = 5% 1000 b. The initial values for the inflation rate and the output level are listed below in the row labeled Quarter 0. The resulting inflation rate and output level for each quarter (1 through 5) are listed. Note that in this example, this quarter s inflation rate is determined from last quarter s inflation rate and the difference between actual and potential output from the previous quarter (i.e. inflation occurs with a lag). Note that over time the inflation rate appears to be converging on the long run equilibrium inflation rate, 5%. Note also that the recessionary gap gets smaller each quarter as the economy moves toward potential GDP. Quarter Inflation Rate Y Y* Y*-Y In each part below, point A in the diagram corresponds to the initial situation, and point B shows the short-run effects of the change. From point B, the SRAS line adjusts up or down as needed to achieve long-run equilibrium (adjustment not shown). Long-run equilibrium in each figure is labeled point C. a. From A, an increase in autonomous consumption shifts the AD curve right, increasing output in the short run to point B. In the long run, inflation rises to a higher level and output returns to potential, in point C. Long-run aggregate supply LRAS Inflation * SRAS SRAS

6 C A B b. A reduction in taxes increases consumer spending and hence aggregate demand. The graph and the results in the short run and the long run are the same as in part a. c. An easing of monetary policy lowers the real interest rate set by the Fed at each level of inflation. The aggregate demand curve shifts right. The graph and results are the same as in part a. d. A sharp drop in oil prices is a favorable inflation shock. The SRAS line shifts downward, reducing inflation and raising output, going to point B. If potential output is unchanged, an expansionary gap exists and inflation will begin to rise. In the long run the economy returns to output and inflation as originally, point A=C. Long-run aggregate supply LRAS Inflation A, C B SRAS SRAS AD e. Increased government purchases raise aggregate demand and shift the AD curve right. The graph and results are the same as in part a. 6. Refer to the figure below: Initially the economy is at equilibrium where a recessionary gap exists. If no action is taken, inflation will slow, the SRAS curve will fall to SRAS, and output will return to potential output at the long-run equilibrium on the LRAS. If the self-adjustment process plays out in 18 months or less, then by the time the tax cut is put in place the economy will already be back to full employment. The tax cut, which shifts the AD curve right, will thus cause the economy to overshoot full employment, leading to an expansionary gap. Output Y* Y Inflation A LRAS SRAS B SRAS

7 7. The economy is initially at equilibrium (at point A) when it is hit by both an inflation shock (shifting SRAS up to SRAS ) and a shock to potential output (reducing Y* and shifting LRAS leftward to LRAS ). The AD curve is unchanged. The short-run equilibrium is at the intersection of AD and SRAS at point B. Inflation has risen and output has declined. LRAS LRAS Inflation B C A SRAS SRAS SRAS Y * Y* Output I ve drawn it so that the new equilibrium is to the left of LRAS, so that there is a recessionary gap even relative to the new, lower level of potential output. (This need not be the case; if the inflation shock is smaller, the short-run equilibrium could be to the right of LRAS, though still to the left of LRAS.) The short-run effect of the combination shock is a fall in output plus higher inflation. In the long run, inflation and the SRAS curve will adjust as needed to bring the economy to long-run equilibrium at point C. Note that at the new equilibrium output is permanently lower than it was at the initial equilibrium, as potential output has dropped. With no change in aggregate demand, inflation is also permanently higher. Output in the long run will equal the new, lower level of potential output, whether the Fed responds or not (monetary policy cannot affect potential output and thus cannot affect output in the long run). If the Fed tries to fight the recession, it will end up achieving nothing but higher inflation. AD

8 But, unless the Fed does something, long-run Inflation will be higher than originally. If the Fed responds to the oil price increase by tightening policy, the AD curve will shift left, along with the leftward shift of LRAS and the upward shift of SRAS. Inflation will not increase as much in the long run, but the short-run decline in output will be even worse. In the short run, the economy moves to point D. If the Fed does respond, the accentuated short-run recession will lead to lower inflation, now at point E. Inflation D LRAS B C E LRAS Y * A Y* Output 8. a. If the Fed eases its monetary policy, this will reduce the real interest rate at any level of inflation. Thus, for any inflation, there will be an increase in autonomous expenditure (due to the Federal Reserve s reducing interest rates), shifting the AD curve to the right. Shifting the AD curve to the right to close the recessionary gap reduces the unemployment rate and increases the output level. However, the cost is that the inflation rate will remain at its current level, rather than falling in response to the recessionary gap. LRAS AD SRAS SRAS Inflation A B AD SRAS Y Y * Output b. If the Fed takes no action, the economy will continue with a recessionary gap longer, meaning that unemployment rates will be higher and output lower, for a longer period than if the Fed had reduced interest rates (as in part a) this is the cost of taking no action. However, over time, the inflation rate will fall and the Fed will then respond (along its monetary policy reaction

9 function) by reducing interest rates, leading to a move down and to the right along the AD curve. The economy will eventually return to a long run equilibrium at potential GDP, with a lower inflation rate than in part a (the benefit). See figure Chapter 20 Questions 1, 2, 3, 4, 5, 6 p Since 1870 real GDP per person has grown more than tenfold in the U.S. and many other industrial countries; and by 25-fold in Japan. These large increases in output per person have led to substantial increases in the material standard of living of the average person. 2. Real GDP per person (a basic determinant of living standards) equals average labor productivity times the share of the population that is employed. The share of the population that is employed can only rise so far; it can never exceed 100%. Thus, large long-term gains in output per person (and hence living standards) generally must come from increases in average labor productivity. (What we can consume depends on what we can produce!) 3. Human capital is the talents, education, training, and skills of workers. Human capital is important because workers with more human capital are more productive, implying higher levels of output per worker and higher living standards. New human capital is created through investment in people, as when individuals spend time and money acquiring an education, or an employer devotes resources to training workers. 4. To get the most output (in terms of ditches dug), you should give the first shovel to the strongest worker, the next shovel to the second strongest worker, and so on until you run out of shovels. Because a stronger worker can make better use of a shovel than a worker who is less muscular, this strategy is consistent with the low-hanging fruit principle, that limited resources should be devoted first to their most productive uses. Since workers without shovels produce nothing, the more shovels you have, the more total output and output per worker will be produced; thus extra capital (shovels) enhances average labor productivity. However, because an extra shovel will be used by a worker who is weaker than those who already have shovels, the extra output made possible by each additional shovel is declining (diminishing returns to capital). 5. Entrepreneurs are people who create new business enterprises. By combining workers with new and more productive technologies, or by

10 having them produce more highly valued products and services, entrepreneurs increase the productivity of any given set of workers. Effective managers (who oversee the day-to-day operations of businesses) also increase productivity, through activities such as improving the organization of production, finding the best matches of workers and jobs, obtaining necessary financing, and coordinating the firm s activities and needs with those of its suppliers and customers. 6. Among the policies that governments can use to promote growth are encouraging the development of human capital (for example, by support of education); encouraging high rates of saving and investment (for example, through tax breaks); public investment in infrastructure (such as highways, bridges, and communications networks); and support of basic research. A particularly important function of government is to provide a political and legal environment conducive to growth, including a stable political system, well-defined property rights, free and open exchange of ideas, and a tax and regulatory system favorable to entrepreneurship and other economically productive activities. Exercises 1, 3, 6, 8, and After one year, Richland s real GDP per person equal 10,000*(1.01), after two years it equals 10,000*(1.01)*(1.01) = 10,000*(1.01) 2, and so on. After ten years, Richland s GDP per person equal 10,000*(1.01) 10 = 11,046, and after twenty years it equals 10,000*(1.01) 20 = 12,202. Poorland s GDP per person after ten years is 5,000*(1.03) 10 = 6720, and after twenty years it equals 5000*(1.03) 20 = So after twenty years Poorland has gone from half the level of income of Richland to about three-quarters the level. Below is an MS Excel sheet that makes these calculations.

11 1% 3% Richland Poorland 0 $10,000 $5,000 =B3*(1+$B$1) =C3*(1+$C$1) 1 $10,100 $5,150 2 $10,201 $5,305 3 $10,303 $5,464 4 $10,406 $5,628 5 $10,510 $5,796 6 $10,615 $5,970 7 $10,721 $6,149 8 $10,829 $6,334 9 $10,937 $6, $11,046 $6, $11,157 $6, $11,268 $7, $11,381 $7, $11,495 $7, $11,610 $7, $11,726 $8, $11,843 $8, $11,961 $8, $12,081 $8, $12,202 $9,031 =B3*(1+$B$1)^$A$26 =C3*(1+$C$1)^$A$ $14,215 $14,216 Suppose that GDP per person in Richland and Poorland are equal after t years; our objective is to find t. After t years Poorland s GDP per person is 5000*(1.03) t, and Richland s GDP per person is 10,000*(1.01) t. Setting these two expressions equal, and dividing both sides by 5000, we get (1.03) t = 2*(1.01) t By solving the above equation for t (algebraically, graphically, or by trial and error), we find that Poorland catches up in between 35 and 36 years. The easiest (and most exact) algebraic solution is to use the properties of logarithms: (1.03) t = 2*(1.01) t [(1.03)/(1.01)] t = 2 divide both sides by (1.01) t log[(1.03)/(1.01)] t = log2 take logs of both sides t log[(1.03)/(1.01)] = log2 a property of logs says that log(y x )=xlogy t = log2/{log[(1.03)/(1.01)]} divide both sides by log[(1.03)/(1.01)] t= 35.35

12 3. Real GDP per person is average labor productivity times the share of the population that is employed. Hence, in 2000 real GDP per person was $66,588*0.489, or $32,562. What will real GDP per person be in 2040 if productivity grows by the same amount as in but the share of the population that is employed falls to the 1960 level? Between 1960 and 2000 average labor productivity grew from $35,836 to $66,588, a gain of 85.8%. i. Given a participation rate of 0.489, real GDP per person was $32,561 in If productivity grows by the same percentage over the period , in 2040 it would equal ( )*$66,588, or $123,721. To find real GDP per person in 2040, multiply this number by the share of the population that is employed, which we assume will be 0.364, the same as in Doing this multiplication we find real GDP per person in 2040 to be $45,034, about $12,472 or 38.3% higher than in So in this scenario output per person will be higher in 2040, relative to 2000, but by much less than implied by the increase in labor productivity. The projected decline in the share of the population that is working implies that output per person will grow more slowly than average labor productivity. An alternative interpretation of the book s phrase productivity grows by the same amount as in is to think that ALP will increase by the same amount (as opposed to the same proportion, which is what the previous paragraph assumes). Between 1960 and 2000, ALP increased by $66,588 - $35,836 = $30,752. $30,752 plus 2000 s $66,588 equals $97,340 = ALP o This implies that ALP would have increased by 46%. This ALP, times the share of the population employed in 2040 (0.364) gives us 2040 s output per person: ALP 2040 x N/Pop = Y/N $97,340 x = $ Then output per person would have increased by 8.8%. The huge increase in ALP (nearly 50%) gets nearly cancelled out by the fall in the share of population employed. 6 a. With four employees and two lanes, both lanes have a checker and a bagger. Total output is 80 customers per hour. Average labor productivity is 80/4 = 20 customers per hour per worker. b. A bagger increases output by 15 customers per hour (the difference between the 40 customers serviced by a checker and a bagger and the 25 customers served by a checker only). If there is an empty lane available, a checker increases output by of 25 customers. So the best strategy is to take one of the baggers and make him or her a checker in the new lane. Total output is = 90 customers per hour, and average labor productivity is 22.5

13 customers per hour. Note that adding capital (the extra lane) increases both total output and average labor productivity. c. With four lanes, all four employees become checkers. Total output is 100 customers and average labor productivity is 25 customers per hour. Because there are only four employees, a fifth lane adds no output (average labor productivity remains 25 customers per hour). Lanes Output/hour Average Labor Productivity /4 = /4 = /4 = /4 = 25 We do observe diminishing returns to capital, but only for the fifth lane: Adding a third lane increased output by 10 customers per hour, as did adding a fourth lane. However, adding a fifth lane does not increase output further. Why didn t we observe diminishing returns to capital in the 3 rd and 4 th lanes? Because here we assumed that jobs are heterogeneous (that is, different from one another. Sorry for the jargon.). The job of bagger is not as productive as the job of checker: more capital allows us to use labor in a more productive way. If all jobs are homogeneous, that is, all the same or at least very similar (say, the identical job of digging ditches, even if the workers themselves are different) then we would observe diminishing returns to capital from the first additional lane. 8 a. Zero, as that will allow her stock of fish to double by next year. b. Maximizing the growth of her stock of fish has the disadvantage that it allows Hester no current income to spend. In other words, Hester can have the benefit of a very high income and consumption next year only at the cost of starving herself this year. Analogously, the more a country is willing to starve itself this year, by saving and investing its resources in new capital goods rather than consuming, the faster it will grow. c. To maximize her current income Hester should sell all her fish this year, realizing $5000. The problem with this strategy is that it leaves no source of income for the future. d. If Hester harvests none of her fish this year, she has no income this year; and if she harvests all of her fish this year, she has no income next year. Having very low or zero income in either year is very unpleasant for Hester. A better choice is to sell some fish this year, allowing for a reasonable level of current income and consumption, while leaving enough fish in the hatchery to provide for reasonable income in the future as well. In the same way, a country should choose a rate of economic growth that balances the cost of sacrificing consumption today against the benefits of higher income and consumption in the future.

14 10. A good answer will cite some statistics from the U.S and other countries on such issues as saving rates, public capital formation, and spending on research and development.