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- 1. Keynes’s Analysis of Capitalist Depressions Throughout the remainder of the General Theory, Keynes consistently assumed that the rate of utilization of the productive capacity of physical capital declined sharply in times of depression, and the number of employed workers declined sharply as well. Keynes’s theory was addressed to those obvious realities of depression in an insightful and coherent manner. But because it is an equally obvious fact of capitalist depressions that the real wages of workers did not increase when employment decreased, Keynes’s adherence to the marginal productivity theory that wages were always equal to the workers’ marginal productivity contradicted the rest of his theory. As we have frequently pointed out in this book, the contradictions in a great thinker’s theory (and Keynes was a logician of the first order) give the best insights into the thinker’s ideological orientation. Keynes wished to furnish capitalist governments with theoretical insights that would help to save capitalism. In doing so, it was necessary for him to abandon some tenets of neoclassical theory. But, as we will see, he wanted to retain as much neoclassical ideology as possible. So he adhered to both the marginal productivity theory of distribution and the belief that the free market efficiently allocated resources (once full employment was attained), despite the fact that both these tenets of neoclassical ideology were logically tied to the belief that the free market automatically created a full employment, Pareto optimal situation. Even with theorists having the extraordinary logical ability of Keynes, ideology very frequently wins out over logic. Keynes rejected the notion that if a capitalist economy started from a situation of full employment, then the rate of interest would automatically equate saving and investment and thus keep aggregate demand equal to aggregate supply. His major departures from the doctrines that comprised the neoclassical
- 2. theory of automaticity were twofold: First, although he accepted the neoclassical notion that saving was influenced by the rate of interest, he insisted that the level of aggregate income was a far more important influence on the amount of saving than was the rate of interest. Second, he argued that saving and investment did not determine the rate of interest. The interest rate was a price that equalized the demand and supply of money— something quite different from (although not unrelated to) investment and saving. These were very important departures indeed, because, although Keynes was unaware of it, they destroyed not only the neoclassical theory of the automaticity of the market but also the two other pillars of neoclassical ideology—the marginal productivity theory of distribution and the theory that a free, competitive market will result in a Pareto optimal allocation of resources. Keynes wanted to achieve the first result (the destruction of the belief in the automaticity of the market) but leave the other two concepts intact. The principle that underlay his departure from the neoclassical theory of saving was referred to by Keynes as the “consumption function.” He insisted that the level of consumption and the level of saving were primarily a “function of the level of income,” that is, they were determined primarily by the level of income. He admitted that “substantial changes in the rate of interest … may make some difference”17 in the level of saving, but this influence was much less important than the influence exerted by the level of income: For a man’s habitual standard of life usually has first claim on his income, and he is apt to save the difference which discovers itself between his actual income and the expense of his habitual standard. … It is also obvious that a higher absolute level of income will tend, as a rule, to widen the gap between income and consumption. For the satisfaction of the immediate primary needs of a man and his family is usually a stronger motive than the motives toward accumulation. … These reasons will lead, as a rule, to a greater proportion of income being saved as real
- 3. income increases.18 The consumption function depicted the relation of saving and consumption to the level of income. The relationship between a change in income and the resultant change in saving (or the ratio of the change in saving to the change in income) was defined as the “marginal propensity to save.” The relationship between a change in income and the resultant change in consumption (or the ratio of the change in consumption to the change in income) was defined as the “marginal propensity to consume.” The marginal propensity to consume and the marginal propensity to save were both assumed to be less than one, and neither was primarily determined by or among the primary determinants of the rate of interest. Keynes’s second major departure from the neoclassical theory of the automaticity of the market was his rejection of the neoclassical theory of the determination of the interest rate: The propensity to consume … determines for each individual how much of his income he will consume and how much he will reserve [save] in some form of command over future consumption. But this decision having been made, there is a further decision which awaits him, namely, in what form he will hold the command over future consumption. … Does he want to hold it in the form of immediate liquid command (i.e., in money or its equivalent)? Or is he prepared to part with immediate command for a specified or indefinite period of time …? In other words, what is the degree of his liquidity-preference—where an individual’s liquidity preference is given by a schedule of the amounts of his resources … which he will wish to retain in the form of money in different sets of circumstances? … It should be obvious that the rate of interest cannot be a return to saving or waiting as such. For if a man hoards his savings in cash, he earns no interest, though he saves just as much as before. On the contrary, the mere definition of the rate of interest tells us in so many words that the rate of interest i s the reward for parting with liquidity for a specified period. For the
- 4. rate of interest is, in itself, nothing more than the inverse proportion between a sum of money and what can be obtained for parting with control over the money in exchange for debt for a stated period of time. Thus the rate of interest at any time, being the reward for parting with liquidity, is a measure of the unwillingness of those who possess money to part with their liquid control over it. The rate of interest is not the “price” which brings into equilibrium the demand for resources to invest with the readiness to abstain from present consumption. It is the “price” which equilibrates the desire to hold wealth in the form of cash with the available quantity of cash. … If this explanation is correct, the quantity of money is the other factor, which, in conjunction with liquidity preference, determines the actual rate of interest in given circumstances.19 The rate of interest was determined, then, by the demand for and supply of money. At any given time the supply of money was constant at a level determined by the actions of the central bank or the monetary authorities. The demand for money— which was the same as the liquidity preference—was, according to Keynes, determined by three motives: (i) the transactions motive, i.e. the need for cash for the current transaction of personal and business exchanges; (ii) the precautionary motive, i.e. the desire for security as to the future cash equivalent of a certain proportion of total resources; and (iii) the speculative motive, i.e. the object of securing profit from knowing better than the market what the future will bring forth.20 The portion of demand for money that arose from the speculative motive was related to the rate of interest. To understand this relationship, we must understand how the price of a bond (or a security, or any kind of interest-paying I.O.U.) reflects the rate of interest. If we purchase a bond that promises to pay us $1,000 in one year, and the rate of interest is 3 percent, then the current value of that bond is approximately $970 (the extra $30 being the interest we will earn in one year).
- 5. If, however, the day after we purchase that bond, the rate of interest rises to 6 percent, then the value of a $1,000 bond falls to approximately $940 (the extra $60 being the interest that can be earned at 6 percent). It is obvious that if we are then forced to sell the bond, we will suffer a loss. Moreover, even if we do not anticipate being forced to sell the bond, but we do expect the interest rate to rise to 6 percent, then we are better off not to buy the bond when the interest rate is 3 percent. If we instead hold the cash and wait for the interest rate to go up, then (if our expectation about the change in the interest rate proves to be correct) we can buy the bond for $940 rather than $970, and apply the extra $30 toward the purchase of another bond with which to earn more interest. Therefore, in Keynes’s view, a portion of the demand for money depended on expectations about what will happen to the interest rate in the future. When the interest rate was very high (in relation to previous rates, or what was considered a normal rate), very few people would expect it to go even higher in the future; consequently, very few people would hold cash for speculative purposes. At lower interest rates, more people would be inclined to believe that the interest rate would increase; consequently, more money would be held for speculative purposes by those who expected the interest rate to rise in the future. Therefore, the amount of money demanded for speculative purposes declined as the interest rate rose, and increased as the interest rate fell. Figure 15.3 illustrates Keynes’s theory of the interest rate and its relation to saving and investment. It can be contrasted to the orthodox neoclassical view illustrated in Figure 15.2. In part (a) of the figure, the demand for money reflects in part the speculative motive and hence declines as the interest rate rises. With the original supply of money (determined by the monetary authorities) r1 was the interest rate that equated the demand for and supply of money. But at r1 there was an excess of saving over investment, as illustrated in part (b). If this situation persisted, then aggregate demand would be less than aggregate
- 6. supply. All output could not be sold. Businesses, unable to sell all that they had produced, found that their inventories of unsold goods were increasing. Each business saw only its own problem: that it had produced more than it could sell. It therefore reduced production in the next period. Most businesses, being in the same situation, did the same thing. The results were a large reduction of production, a decrease in employment, and a decline in income. With the decline in income, however, even less would be spent on goods and services in the next period. So businessmen again found that even at the lower level of production, they were unable to sell all they had produced. They again cut back production, and the downward spiral continued. Under these circumstances, businesses had little or no incentive to expand their capital goods (because excess capacity already existed), and, therefore, investment fell drastically. Expenditures of all types plummeted. As income declined, saving declined more than proportionately. This process continued until the declines in income had reduced saving to the point where it no longer exceeded the reduced level of investment. At this low level of income, equilibrium was restored. Leakages from the income-expenditure flow were again equal to the injections into it. The economy was stabilized, but at a level where high unemployment and considerable unused productive capacity existed. But the problem, as posed in Figure 15.3, was easily remedied. The monetary authorities could increase the supply of money to the point where was the prevailing rate of interest (in Figure 15.3). At that interest rate, saving equaled investment, aggregate demand equaled aggregate supply, and there was no problem. There were some situations, in Keynes’s view, in which monetary policy (increasing or decreasing the money supply) was sufficient to maintain full employment. But there were also some situations in which monetary policy was not sufficient. Keynes was more interested in these situations because he believed them to be more realistic characterizations
- 7. of the actual conditions that both precipitated and sustained depressions in capitalist economies. The first such situation occurred when the distribution of income was so unequal (thereby increasing saving by putting more income into the hands of the wealthy, who saved much more than did workers) and the full-employment level of output and income was so high that, regardless of how low the rate of interest sank, saving and investment could not be equated. This situation is illustrated in Figure 15.4, which is self-explanatory. But Keynes did not believe that it required such a drastic discrepancy between saving and investment to create a situation in which monetary policy was unable to prevent a disastrous depression. It was possible, he argued, that if the rate of interest that would equate the full-employment levels of saving and investment was very low, monetary policy might not be able to lower the interest rate sufficiently. If monetary authorities pushed the rate of interest so low that nearly everyone expected the interest rate to rise significantly in the future, then people would prefer to hold cash rather than securities even when the monetary authorities dramatically increased the amount of money in the system: Circumstances may develop in which even a large increase in the quantity of money may exert a comparatively small influence on the rate of interest. … Opinion about the future of the rate of interest may be so unanimous that a small change in present rates may cause a mass movement of cash [into private hoards].21 Such a situation is depicted in Figure 15.5. It can be seen that when the rate of interest approaches some minimum point, the demand for money flattens out, indicating that even with large increases in the supply of money, most of the increased money supply will be held in private hoards. In Figure 15.5, a large increase in the money supply results in a very small decline in the rate of interest and still leaves an excess of saving over investment. In either of the situations depicted in Figures 15.4 and 15.5, the
- 8. free, competitive market would lead society into a disastrous depression; monetary policy would be useless in preventing the social calamity. It was obvious that something more fundamental and more powerful was needed. Keynes’s analysis was not, in its essentials, drastically different from those offered by Marx (Chapter 9) and Hobson (Chapter 13). The principal cause of a depression was, in the opinion of all three thinkers, the inability of capitalists to find sufficient investment opportunities to offset the increasing levels of saving generated by economic growth. Keynes’s unique contribution was to show how the relation of saving to income could lead to a stable but depressed level of income, with widespread unemployment. Marx had believed the disease to be incurable. Hobson had prescribed measures to equalize the distribution of income and thereby reduce saving as a cure. Could Hobson’s prescription work? This probably is not a very meaningful question. In most industrial capitalist countries, wealth and economic power determine political power, and those who wield power have never been willing to sacrifice it to save the economic system. In the United States, for example, out of 300,000 nonfinancial corporations existing in 1925, the largest 200 made considerably more profit than the other 299,800 combined. The wealthiest 5 percent of the population owned virtually all the stocks and bonds and received in excess of 30 percent of the income. Needless to say, this 5 percent dominated American politics. In these circumstances, speculating about what would happen if the income and wealth were radically redistributed amounts to mere daydreaming. Keynes’s answer to the problem was more realistic. Government could step in when saving exceeded investment, borrow the excess saving, then spend the money on socially useful projects that would not increase the economy’s productive capacity or decrease the investment opportunities of the future. This government spending would increase the injections into the spending stream and create a full-employment equilibrium. In doing so, it would not add to
- 9. the capital stock. Therefore, unlike investment spending, it would not make a full-employment level of production more difficult to attain in the next period. Keynes summarized his position thus: Ancient Egypt was doubly fortunate, and doubtless owed to this its fabled wealth, in that it possessed two activities, namely, pyramid-building as well as the search for precious metals, the fruits of which, since they could not serve the needs of man by being consumed, did not stale with abundance. The Middle Ages built cathedrals and sang dirges. Two pyramids, two masses for the dead, are twice as good as one: but not so two railways from London to York.22 What type of expenditures ought the government to make? Keynes himself had a predilection toward useful public works such as the construction of schools, hospitals, parks, and other public conveniences. He realized, however, that this would probably benefit middle- and lower-income recipients much more than it would the wealthy. Because the wealthy had the political power, they would probably insist on policies that would not redistribute income away from them. He realized that it might be politically necessary to channel this spending into the hands of the large corporations, even though little that was beneficial to society would be accomplished directly. If the Treasury were to fill old bottles with banknotes, bury them at suitable depths in disused coal mines which are then filled up to the surface with town rubbish, and leave it to private enterprise on well-tried principles of laissez faire to dig the notes up again … there need be no more unemployment. … It would indeed be more sensible to build houses and the like; but if there are political and practical difficulties in the way of this, the above would be better than nothing.The Military Economy Between 1947 and the mid-1970s, the American government spent nearly $2 trillion (numbers of that magnitude are hard to conceptualize: that figure is 2,000 billions of dollars) on military expenditures.25 The total expenditures for wars and
- 10. preparation for potential wars, past, present, and future, including both warfare and related expenditures, grew from $27.9 billion per year in 1947 to $112.3 billion in 1971.26 These figures represent a total of 12.2 percent of GNP in 1947 and 11.1 percent in 1971. Moreover, if one analyzes the “multiplier” effect of further aggregate demand created by these military expenditures, the impact was much larger. The most careful study of these effects resulted in two estimates, constituting lower and upper limits. The conservative estimate showed that, in 1947, military expenditures accounted, directly and indirectly (through the induced or multiplier effect), for 24.4 percent of aggregate demand in 1947 and 22.2 percent in 1971. Using the higher estimate, militarism accounted for 30.5 percent of aggregate demand in 1947 and 27.8 percent in 1971.27 In only a few of the intervening years was the figure very slightly lower, and in several of the intervening years the figure was higher. In the 1970s military spending grew at a somewhat lower rate but it virtually exploded in the 1980s. During the late 1970s many economists were predicting a severe recession was at hand. Indeed, at the time, the recession of 1981–82 was the worst since the 1930s. It was not, however, nearly as bad as most economists had predicted. The remaining years of the 1980s were years of economic prosperity. One does not have to look far to find the reason for this prosperity. Between 1980 and 1987, American military expenditures more than doubled. Defense spending was $134 billion in 1980 and had soared to $210 billion by 1983. During 1982 alone, the construction of two nuclear-powered aircraft carriers, two nuclear-powered attack submarines, and five warships; the procurement of the F-15 jet fighter; and the work of the B-1B and Stealth bomber and the MX missile created about 300,000 new jobs. General Dynamics hired 7,000 new employees to work on the M 1 tank project. Rockwell International added 4,000 additional employees to work on the B-1B bomber. Boeing, Lockheed, Raytheon, McDonnell Douglass, United Technologies, and General Electric all substantially increased
- 11. their workforces to produce new military hardware. The U.S. Defense Department increased its employment by 255,000 new jobs between 1981 and 1985.28 There can be no doubt that the prosperity of the 1980s was due primarily to the huge growth in militarism. President Bush’s budget proposal for the fiscal year 1991 included over $303 billion directly for defense and another $65 billion for “international affairs,” “science, space, and technology,” and “veterans’ benefits,” most of which are disguised military spending. Defense spending remained high from 1990 to 1999 averaging approximately $280 billion annually. Though looking back, the 1990s represent a sort of reprieve from the typical defense spending. According to the Office of Management and Budget (OMB) figures, the average growth in defense spending during the 1990s was nearly zero, compared to 9.6 percent a decade earlier. Moreover, defense spending as a percentage of total government expenditures actually decreased fairly consistently from 23.9 percent in 1990 to 16.1 percent in 1999, compared with an almost equally consistent increase from 22.7 percent in 1980 to 26.5 percent in 1989. Another way to consider the size of defense spending is in relation to GDP. Throughout much of the 1980s defense spending relative to GDP was in the high 5 percent to low 6 percent range, averaging 5.8 percent for the decade. This figure fell throughout the 1990s ending at 3 percent in 1999, with an average for the decade of 4 percent annually. Since 2000, however, these figures have all turned around. The annual growth in defense spending shot back up averaging 9.5 percent from 2000 to 2009 (a figure comparable to the 1980s). Defense spending as a percent of total government expenditures rose, again fairly consistently, from 16.5 percent in 2000 to an estimated 21.7 percent in 2009. The movement was similar for defense spending relative to GDP, rising from 3 percent at the beginning of the decade to an estimated 4.5 percent in 2009. From a longer historical perspective dating back to 1940, it appears that the 1990s represented a low in defense spending relative to the entire
- 12. budget and GDP. Unfortunately, the United States appears to be slowly returning to the more typical levels at the current time. Moreover, the correlation between changes in military spending and the cyclical instability of capitalism is very significant.29 There seems to be little question that militarism has been the contemporary capitalist equivalent to the pyramids of Egypt and the cathedrals of the Middle Ages. Has this militarism been a necessary response to international exigencies, or do military expenditures have unique features that make them particularly effective and desirable forms of government expenditures? A full answer to this question would necessitate an extensive discussion of the Cold War and its putative demise—something that cannot be done within the scope of this book. A growing body of historical literature has amassed considerable evidence, however, to show that the Cold War was the deliberate and fraudulent creation of American politicians, capitalists, and the capitalist-controlled press.30 If this position is correct, then the Cold War must be revived or a suitable substitute must be found. The wars in Iraq and Afghanistan might be the prototypes of a new world policing role for the United States. This could be our new Cold War. Whatever position one takes on the nature of the Cold War, however, two facts clearly emerge from the study of American militarism. First, militarism offers several unique and distinct advantages to capitalists over nearly any other form of government spending; and second, militarism has become so thoroughly enmeshed in the structure of the American economy that it is increasingly inconceivable that it can ever be extirpated short of a complete restructuring of the entire American social, economic, and political system. Militarism offers innumerable advantages to large corporations: (1) it stimulates aggregate demand without redistributing income from the rich to the poor; (2) there can never be too much elaborate weaponry; government-financed research constantly renders military hardware obsolete, and horror stories convince most of the public that continued escalation of
- 13. the arms race is absolutely necessary for survival; (3) the capital goods industry—the most volatile and unstable segment of a capitalist economy—is kept operating at near capacity by military production, and, yet, this does not increase the productive capacity of the capitalist economy. As a result, militarism does not worsen the persistent problem of excess aggregate productive capacity; (4) because virtually all military production is done by giant private corporations or subcontracted to smaller private corporations, it does not compete with private profit making; on the contrary, it reduces the anarchy of the free market by giving corporations a stable core of demand not subject to the vagaries of the market; (5) although precise statistics to substantiate this are unobtainable, most evidence points to military production being more profitable than production for the free market; (6) as Rosa Luxemburg pointed out, large military establishments are necessary to maintain and enlarge the worldwide “sphere of influence” of capitalist countries, in which profitable foreign investment and very favorable terms of trade can be assured; (7) as Veblen pointed out, jingoism, patriotism, and militarism are perhaps the most effective means of keeping workers docile and promoting the view among workers that their interests are in harmony with the interests of the capitalists. The price that we have paid for this militarism, however, is reflected in the evolution of the military-industrial complex, in which militarism has become a permanent, thoroughly integrated cancer in the very heart of the structure of American industry. Many of the largest and most powerful of American corporations are heavily dependent on military contracts. Equally important is the fact that a large number of cities, regions, and even whole states are heavily economically dependent on these corporations or on large military bases to support their local economies and maintain employment at a time when persistently high unemployment plagues the economy. A large reduction in the output of military hardware
- 14. or in the number or size of these military bases can economically ruin whole communities. Therefore, the slightest hint of a reduction in militarism brings powerful protests from military leaders, large corporations, politicians, and labor union leaders. In 1989 and 1990, there was a good deal of talk about the end of the Cold War. Because most East European economies, including the Soviet Union, were undertaking reforms that were pushing their economies toward market capitalism, it became difficult to use the horror of communism as a pretense for massive military expenditures. Yet, there is a powerful built-in resistance to the reduction of these expenditures, as seen in the return of higher growth and larger portions of the budget devoted to defense spending beginning again in 2000. If military expenditures are significantly reduced, the U.S. economy faces the prospect of stagnation and depression. It would appear as though the United States cannot allow the Cold War to “cool off” to a very great extent without finding some alternative to the “dangers of communism.” Iraq, Afghanistan, or any other nonindustrialized nation can never, by itself, replace the Soviet Union as the new enemy because they can be destroyed. The problem of finding an enemy to justify military expenditures is likely to grow worse. Problem 1: - work on this Astra Zeneca needs to understand if there is a discrepancy between how females (“F”) react to their COVID booster and how males (“M”) do. They sample ten thousand people for whether or not they've had no reaction to the booster (“-” : negative reaction) or an obvious reaction (“+” : positive reaction). In column A are the genders of the 10000 people, and in column B their reaction. Determine in cell E1 the number of males, in cell E2 the number of females, in cell E4
- 15. the number of positive reactions, and in cell E5 the number of negative reactions. Determine in cell E7 the number of positive reactions among males and in cell E8 the number of positive reactions among females. Determine in cell E10 the proportion of positive reactions among males, and in cell E11 the proportion of positive reactions among females. The operating hypothesis is that there is no difference between the proportion of positive reactions among males ( pm ) and females ( pf ). Construct a 90% confidence interval for the difference of true proportions ( pm- pf ), given sample, with the lower bound in E13 and upper bound in E14. If 0 is within the confidence interval enter “no discernable difference” in E16. If 0 is less than the lower bound we take that pm- pf in positive and say “men react worse” in E16, and if 0 is greater than the upper bound we take that pm- pf in negative and say “women react worse” in E16. Problem 2: A chip manufacturer observes that chips seem to be failing in two different ways. The manufacturer is trying to determine whether or not the two failures are independent, but believes that they are independent. After testing a thousand chips, give in E1 the number failures at site 1, and the number in E2 the number of failures at site 2, and at E3 the number of failures at both sites. If the two failures are independent, use the proportion of observed failures at site 1 and the proportion of observed failures at site 2 to give in E5 the number of chips expected to fail at both sites from a sample of size one thousand. We will compare the number of failures observed at both sites with the number expected.
- 16. Give the lower and upper bounds for a 90% confidence interval for the number of failures at both sites, assuming independence. If the observed number of failures at both sites is within this confidence interval display “YES” in E10, otherwise display “NO” Problem 3: Data is believed to be generated by an exponential random variable. A thousand data values are collected. Determine the average in C2 and compile the data into relative frequency bins (see E2:E5) in F2:F5. Using the average as mean, give in G2:G5 the proportions of data expected in each bin for an exponential process. Since the values in column G are proportions, determine in H2:I5 the upper and lower bounds of 90% confidence intervals for an average over a sample of size 1000 for Bernoulli random variables of these proportions (i.e. in H2 the lower bound for a 90% confidence interval for an average over a sample of size 1000 of a Bernoulli (G2) random variable, etc.). Then indicate whether the relative frequencies are within these confidence intervals with “YES” or “NO” in J2:J5. We accept that we do indeed have an exponential random variable if all four relative frequencies lie in their respective confidence intervals. Indicate whether we accept or reject the exponential random variable hypothesis with “ACCEPT” or “REJECT” in L2. Illustrate the relationship between the bounds and the relative frequency by plotting columns F:I against column E in C7:J22 with line plots.
- 17. gender reaction # of men in study 0.5154046487 M - # of women in study 0.9136065114 M - 0.9176842958 F - # of positive reactions F - # of negative reactions M - F - # of positive reactions among men M - # of positive reactions among women F - F - observed proportion of positive reactions among men F - observed proportion of positive reactions among women M -
- 18. M - lower bound for 90% confidence F - upper bound for 90% confidence M - M - gender disparity? F - M - M - F - M + F - M - F - M - M - F - M - F
- 573. - Site 1 Site 2 # of failures at site 1 0.1233931101 N N # of failures at site 2 0.0891696784 N N # of failures at both 0.1989457273 N N N N expected # of failures at both if independent N N N N lower bound for 90% confidence interval N N upper bound for 90% confidence interval N N Y N independent? N N N N Y
- 629. rel freq theory lower bound upper bound within range? accept/reject? 6.7772379848 0.99 [0, 5) 0.2519589369 0.7653389245 25.05 [5, 10) 0.9676871342 0.4754367766 3.83 [10, 15) 0.5732010645 0.882848873 2.41 [15, +∞) 0.3977676849 0.8980438132 7.68 0.8919743972 0.7190792523 3.21 0.422184712 0.9561023798 0 0.0011128183 0.6209694203 3.7 0.6558078579 0.7153364141 1.7