WEBVTT NOTE 4.09. Some Fallacies Relating to Utility 1 00:00:00.000 --> 00:00:02.000 9. 2 00:00:02.000 --> 00:00:05.340 Some Fallacies Relating to Utility 3 00:00:05.340 --> 00:00:12.180 A doctrine commonly held by writers on utility is that the consumer acts so as to bring the 4 00:00:12.180 --> 00:00:20.580 marginal utility that any good has for him into equality with the price of that good. 5 00:00:20.580 --> 00:00:26.820 To understand this thesis, let us examine the preference scale of Mr. Jones in contemplating 6 00:00:26.820 --> 00:00:28.820 The Theory of Money and Credit 7 00:00:56.820 --> 00:01:07.060 2.9 grains, followed by 2.8 grains, followed by a third suit, followed by 2.7 grains. 8 00:01:07.060 --> 00:01:15.320 And suppose also that the market price is 2.9 grains per suit. Jones will buy not one 9 00:01:15.320 --> 00:01:22.740 or three, but two suits. He will buy up to the last unit at which the diminishing marginal 10 00:01:22.740 --> 00:01:36.860 We are omitting possible shifts in rank resulting from the increasing utility of money which 11 00:01:36.860 --> 00:01:40.180 would only complicate matters unduly. 12 00:01:40.180 --> 00:01:41.660 This is obvious. 13 00:01:41.660 --> 00:01:48.980 Now if a writer couches the exposition in terms of highly divisible goods, such as butter, 14 00:01:48.980 --> 00:01:55.540 and in terms of small units of money such as pennies, it is easy to leap unthinkingly 15 00:01:55.540 --> 00:02:02.500 to the conclusion that the consumer for each good will act in such a way as to equalize 16 00:02:02.500 --> 00:02:09.060 at the market price the marginal utility of the sum of money and the marginal utility 17 00:02:09.060 --> 00:02:10.700 of the good. 18 00:02:10.700 --> 00:02:16.860 It should be clear, however, that there is never any such equalization. 19 00:02:16.860 --> 00:02:22.820 In the case of the suit, the rank of the second suit is still considerably above the rank 20 00:02:22.820 --> 00:02:28.180 of the 2.9 grains, so there is no equalization. 21 00:02:28.180 --> 00:02:33.780 Even in the case of the most divisible of goods, there will still be a difference in 22 00:02:33.780 --> 00:02:38.620 rank, not an equalization, between the two utilities. 23 00:02:38.620 --> 00:02:45.820 A man may buy 11 ounces of butter at 10 cents an ounce, until there is nothing ranking between 24 00:02:45.820 --> 00:02:54.020 In the 11th ounce and the 10 cents on his utility scale, yet there is still no equality, 25 00:02:54.020 --> 00:03:00.700 but a difference in rank, with the last ounce bought ranking higher than the last sum of 26 00:03:00.700 --> 00:03:02.460 money spent. 27 00:03:02.460 --> 00:03:09.180 Of course, the consumer tries to spend his money so as to bring the two as close as possible, 28 00:03:09.180 --> 00:03:12.220 but they can never be equal. 29 00:03:12.220 --> 00:03:22.220 Furthermore, the marginal utility of each particular good after the purchases are made differs in rank from that of every other. 30 00:03:22.220 --> 00:03:28.220 Thus, let us take one grain of gold as the monetary unit under consideration. 31 00:03:28.220 --> 00:03:34.220 Let us say that the given market prices of various goods are as follows. 32 00:03:34.220 --> 00:03:37.220 Eggs, one dozen per grain. 33 00:03:37.220 --> 00:03:40.220 Butter, one pound per grain. 34 00:03:40.220 --> 00:03:47.220 Bread, one loaf per grain. Candy, one bar per grain. 35 00:03:47.220 --> 00:04:00.220 Now each individual will purchase each commodity until the last point at which the marginal utility of the unit exceeds the marginal utility of a grain of gold. 36 00:04:00.220 --> 00:04:09.220 For one man, this might mean the purchase of five pounds of butter, three loaves of bread, two bars of candy, etc. 37 00:04:09.220 --> 00:04:20.220 This would mean that either a sixth pound of butter or a fourth loaf of bread would have a lower marginal utility than a grain of gold foregone. 38 00:04:20.220 --> 00:04:32.220 However, the marginal utility of each good will still differ in rank from that of every other, and will not be equal to that of any other. 39 00:04:32.220 --> 00:04:44.720 Another, even more curious doctrine holds that in equilibrium the ratio of the marginal utilities of the various goods equals the ratio of their prices. 40 00:04:44.720 --> 00:05:00.220 Without entering in detail into the manner by which these writers arrive at this conclusion, we can see its absurdity clearly, since utilities are not quantities and therefore cannot be divided. 41 00:05:00.220 --> 00:05:14.220 These fallacies stem from a related one, the idea that an individual will act so as to equalize the marginal utility that any good will have in each of its uses. 42 00:05:14.220 --> 00:05:24.220 Applied to money, this would imply that the marginal utility of a unit of money is equal for each field of expenditure for each person. 43 00:05:24.220 --> 00:05:33.220 This is incorrect, as we have just seen that the marginal utilities of the various goods are not equalized. 44 00:05:33.220 --> 00:05:43.220 Successive units of a good are allocated to the most desired end, then to the next most desired satisfaction, etc. 45 00:05:43.220 --> 00:05:49.220 If there are several uses for the good, each one involving many possible units, 46 00:05:49.220 --> 00:05:57.220 The marginal utility of a unit in each use continues to decline as the supply increases. 47 00:05:57.220 --> 00:06:03.220 As goods are purchased, the marginal utility of each good purchased diminishes, 48 00:06:03.220 --> 00:06:11.220 and a man may allocate his money first to one use, then to another, and then to the first use again. 49 00:06:11.220 --> 00:06:18.220 However, in no case is there any equalization of marginal utilities. 50 00:06:18.220 --> 00:06:25.420 The dogma of the equalization of marginal utilities may best be illustrated in the following passage 51 00:06:25.420 --> 00:06:31.020 from perhaps the originator of this line of argument, Stanley Jevons. 52 00:06:31.020 --> 00:06:38.620 Let S be the whole stock of some commodity and let it be capable of two distinct uses. 53 00:06:38.620 --> 00:06:46.220 Then we may represent the two quantities appropriated to these uses by X1 and Y1, 54 00:06:46.220 --> 00:06:52.220 It being a condition that x1 plus y1 equal s. 55 00:06:52.220 --> 00:06:59.220 The person may be conceived as successively expending small quantities of the commodity. 56 00:06:59.220 --> 00:07:08.220 Now it is the inevitable tendency of human nature to choose that course which appears to offer the greatest advantage at the moment. 57 00:07:08.220 --> 00:07:13.220 Hence, when the person remains satisfied with the distribution he has made, 58 00:07:13.220 --> 00:07:27.220 It follows that no alteration would yield him more pleasure, which amounts to saying that an increment of commodity would yield exactly as much utility in one use as in another. 59 00:07:27.220 --> 00:07:41.220 Let delta U1, delta U2 be the increments of utility which might arise respectively from consuming an increment of commodity in the two different ways. 60 00:07:41.220 --> 00:07:49.220 When the distribution is completed, we ought to have delta U1 equals delta U2. 61 00:07:49.220 --> 00:07:57.220 The same reasoning will evidently apply to any two uses, and hence to all uses simultaneously, 62 00:07:57.220 --> 00:08:06.220 so that we obtain a series of equations less numerous by a unit than the number of ways of using the commodity. 63 00:08:06.220 --> 00:08:18.220 The general result is that the commodity, if consumed by a perfectly wise being, must be consumed with a maximum production of utility. 64 00:08:18.220 --> 00:08:33.220 The chief errors here consist in conceiving utility as a certain quantity, a definite function of an increment in the commodity, and in treating the problem in terms of infinitely small steps. 65 00:08:33.220 --> 00:08:59.220 Both procedures are fallacious. Utilities are not quantities, but ranks, and the successive amounts of a commodity that are used are always discrete units, not infinitely small ones. If the units are discrete, then the rank of each unit differs from that of every other, and there can be no equalization. 66 00:08:59.220 --> 00:09:09.220 Many errors in discussions of utility stem from an assumption that it is some sort of quantity, measurable at least in principle. 67 00:09:09.220 --> 00:09:21.220 When we refer to a consumer's maximization of utility, for example, we are not referring to a definite stock or quantity of something to be maximized. 68 00:09:21.220 --> 00:09:27.220 We refer to the highest ranking position on the individual's value scale. 69 00:09:27.220 --> 00:09:33.840 scale. Similarly, it is the assumption of the infinitely small added to the belief in 70 00:09:33.840 --> 00:09:41.320 utility as a quantity that leads to the error of treating marginal utility as the mathematical 71 00:09:41.320 --> 00:09:48.980 derivative of the integral total utility of several units of a good. Actually, there is 72 00:09:48.980 --> 00:09:56.260 is no such relation, and there is no such thing as total utility, only the marginal 73 00:09:56.260 --> 00:10:00.100 utility of a larger sized unit. 74 00:10:00.100 --> 00:10:06.540 The size of the unit depends on its relevance to the particular action. 75 00:10:06.540 --> 00:10:12.500 This illustrates one of the grave dangers of the mathematical method in economics, since 76 00:10:12.500 --> 00:10:18.820 this method carries with it the bias of the assumption of continuity, or the infinitely 77 00:10:18.820 --> 00:10:20.820 is a really small step. 78 00:10:20.820 --> 00:10:27.820 Most writers on economics consider this assumption a harmless but potentially very useful fiction, 79 00:10:27.820 --> 00:10:31.820 and point to its great success in the field of physics. 80 00:10:31.820 --> 00:10:38.820 They overlook the enormous differences between the world of physics and the world of human action. 81 00:10:38.820 --> 00:10:45.820 The problem is not simply one of acquiring the microscopic measuring tools that physics has developed. 82 00:10:45.820 --> 00:10:53.820 The crucial difference is that physics deals with inanimate objects that move but do not act. 83 00:10:53.820 --> 00:11:00.140 The movements of these objects can be investigated as being governed by precise, 84 00:11:00.140 --> 00:11:06.860 quantitatively determinate laws, well expressed in terms of mathematical functions. 85 00:11:06.860 --> 00:11:12.140 Since these laws precisely describe definite paths of movement, 86 00:11:12.140 --> 00:11:21.140 There is no harm at all in introducing simplified assumptions of continuity and infinitely small steps. 87 00:11:21.140 --> 00:11:30.840 Human beings, however, do not move in such fashion, but act purposefully, applying means to the attainment of ends. 88 00:11:30.840 --> 00:11:40.440 Investigating causes of human action, then, is radically different from investigating the laws of motion of physical objects. 89 00:11:40.440 --> 00:11:47.320 In particular, human beings act on the basis of things that are relevant to their action. 90 00:11:47.320 --> 00:11:51.800 The human being cannot see the infinitely small step. 91 00:11:51.800 --> 00:11:57.240 It, therefore, has no meaning to him and no relevance to his action. 92 00:11:57.240 --> 00:12:03.800 Thus, if one ounce of a good is the smallest unit that human beings will bother distinguishing, 93 00:12:03.800 --> 00:12:11.240 Then the ounce is the basic unit, and we cannot simply assume infinite continuity in terms 94 00:12:11.240 --> 00:12:14.860 of small fractions of an ounce. 95 00:12:14.860 --> 00:12:21.560 The key problem in utility theory neglected by the mathematical writers has been the size 96 00:12:21.560 --> 00:12:23.160 of the unit. 97 00:12:23.160 --> 00:12:28.300 Under the assumption of mathematical continuity, this is not a problem at all. 98 00:12:28.300 --> 00:12:34.580 It could hardly be when the mathematically conceived unit is infinitely small and therefore 99 00:12:34.580 --> 00:12:37.100 literally sizeless. 100 00:12:37.100 --> 00:12:43.740 In a praxeological analysis of human action, however, this becomes a basic question. 101 00:12:43.740 --> 00:12:50.140 The relevant size of the unit varies according to the particular situation, and in each of 102 00:12:50.140 --> 00:12:55.820 these situations this relevant unit becomes the marginal unit. 103 00:12:55.820 --> 00:13:02.460 There is none but a simple ordinal relation among the utilities of the variously sized 104 00:13:02.460 --> 00:13:04.540 units. 105 00:13:04.540 --> 00:13:11.940 The tendency to treat problems of human action in terms of equality of utility and of infinitely 106 00:13:11.940 --> 00:13:18.420 small steps is also apparent in recent writings on indifference maps. 107 00:13:18.420 --> 00:13:24.900 Almost the entire edifice of contemporary mathematical economics in consumption theory 108 00:13:24.900 --> 00:13:28.900 has been built on the indifference assumption. 109 00:13:28.900 --> 00:13:35.820 Its basis is the treatment of large-sized classes of combinations of two goods between 110 00:13:35.820 --> 00:13:40.540 which the individual is indifferent in his valuations. 111 00:13:40.540 --> 00:13:46.900 Furthermore, the differences between them are infinitely small, so that smooth lines 112 00:13:46.900 --> 00:13:49.500 and tangents can be drawn. 113 00:13:49.500 --> 00:13:56.080 The crucial fallacy is that indifference cannot be a basis for action. 114 00:13:56.080 --> 00:14:02.280 If a man were really indifferent between two alternatives, he could not make any choice 115 00:14:02.280 --> 00:14:07.520 between them, and therefore the choice could not be revealed in action. 116 00:14:07.520 --> 00:14:11.780 We are interested in analyzing human action. 117 00:14:11.780 --> 00:14:16.980 Any action demonstrates choice based on preference. 118 00:14:16.980 --> 00:14:26.980 There is, therefore, no role for the concept of indifference in economics or in any other 119 00:14:26.980 --> 00:14:29.520 praxeological science. 120 00:14:29.520 --> 00:14:37.220 If it is a matter of indifference for a man, whether he uses 5.1 or 5.2 ounces of butter, 121 00:14:37.220 --> 00:14:43.160 for example, because the unit is too small for him to take into consideration, then there 122 00:14:43.160 --> 00:14:48.400 There will be no occasion for him to act on this alternative. 123 00:14:48.400 --> 00:14:54.040 He will use butter in ounce units instead of tenths of an ounce. 124 00:14:54.040 --> 00:14:59.740 For the same reason, there are no infinitely small steps in human action. 125 00:14:59.740 --> 00:15:04.040 Steps are only those that are significant to human beings. 126 00:15:04.040 --> 00:15:09.480 Hence, they will always be finite and discrete. 127 00:15:09.480 --> 00:15:15.740 The error in reasoning on the basis of indifference is the failure to appreciate the fact that 128 00:15:15.740 --> 00:15:23.860 a problem important in the field of psychology may have no significance in the realm of praxeology 129 00:15:23.860 --> 00:15:27.300 to which economics belongs. 130 00:15:27.300 --> 00:15:34.040 Psychology deals with the problem of how or why the individual forms value scales, and 131 00:15:34.040 --> 00:15:40.740 And for this question it is relevant to consider whether the individual is decisive or inclined 132 00:15:40.740 --> 00:15:45.920 to be indifferent between various alternatives. 133 00:15:45.920 --> 00:15:52.120 Praxeology however is a logical science based on the existence of action per se. 134 00:15:52.120 --> 00:15:59.160 It is interested in explaining and interpreting real action in its universal sense, rather 135 00:15:59.160 --> 00:16:02.380 than in its concrete content. 136 00:16:02.380 --> 00:16:09.060 Its discussion of value scales is therefore a deduction from the nature of human action, 137 00:16:09.060 --> 00:16:14.400 and not a speculative essay on the internal workings of the mind. 138 00:16:14.400 --> 00:16:20.900 It is consequently irrelevant, for praxeology, whether a man, in having to decide between 139 00:16:20.900 --> 00:16:28.380 alternatives A and B, makes a choice firmly and decisively, or whether he decides by tossing 140 00:16:28.380 --> 00:16:29.780 a coin. 141 00:16:29.780 --> 00:16:33.700 This is a problem for psychology. 142 00:16:33.700 --> 00:16:40.020 Praxeology is concerned only with the fact that he chooses, for example, A rather than 143 00:16:40.020 --> 00:16:47.820 B, and that therefore A ranked higher in his preference scale than B. Utility theory is 144 00:16:47.820 --> 00:16:55.540 not concerned with psychology or the internal operations of the mind, but is part of a separate 145 00:16:55.540 --> 00:17:03.300 science based on the logical consequences of the simple existence of action. 146 00:17:03.300 --> 00:17:08.000 Neither is praxeology based on behaviorist psychology. 147 00:17:08.000 --> 00:17:14.780 In fact, insofar as praxeology touches on psychology, its principles are the reverse 148 00:17:14.780 --> 00:17:17.080 of those of behaviorism. 149 00:17:17.080 --> 00:17:23.680 As we have seen, far from simply observing action in the same way as we observe and record 150 00:17:23.680 --> 00:17:30.280 the Movement of Stones, Praxeology is based on a fundamental distinction between human 151 00:17:30.280 --> 00:17:37.760 action and the motion of inorganic matter, namely that human action is motivated toward 152 00:17:37.760 --> 00:17:40.860 the achievement of certain ends. 153 00:17:40.860 --> 00:17:45.480 Means and resources are used for the achievement of these ends. 154 00:17:45.480 --> 00:17:52.200 Far from leaving mind out of the picture, praxeology is the basic axiom of action, action 155 00:17:52.200 --> 00:18:22.200 The Theory of Money and Credit The Theory of Money and Credit The Theory of Money and Credit 156 00:18:22.200 --> 00:18:30.280 Maps by Means of Questionnaires. These attempts, besides being open to the stricture that indifference 157 00:18:30.280 --> 00:18:39.280 is not praxeologically valid, fail to realize that value scales can and do change continually, 158 00:18:39.280 --> 00:18:45.360 and that therefore such questionnaires have no relevance to the business of economics. 159 00:18:45.360 --> 00:18:51.500 Economics is interested not in value scales professed in response to questionnaires, but 160 00:18:51.500 --> 00:18:55.900 in the Values Implied by Real Action. 161 00:18:55.900 --> 00:19:01.940 As Ludwig von Mises states, with regard to all attempts to separate value scales from 162 00:19:01.940 --> 00:19:08.200 action, the scale of value is nothing but a constructed tool of thought. 163 00:19:08.200 --> 00:19:13.460 The scale of value manifests itself only in real acting. 164 00:19:13.460 --> 00:19:18.620 It can be discerned only from the observation of real acting. 165 00:19:18.620 --> 00:19:25.740 It is, therefore, impermissible to contrast it with real acting and to use it as a yardstick 166 00:19:25.740 --> 00:19:28.520 for the appraisal of real actions. 167 00:19:28.520 --> 00:19:36.580 Dr. Harro Bernardelli justly says, If someone asks me in abstracto whether my love for my 168 00:19:36.580 --> 00:19:43.120 country is greater than my desire for freedom, I am somewhat at a loss how to answer. 169 00:19:43.120 --> 00:19:49.680 But actually having to make a choice between a trip in my country and the danger of losing 170 00:19:49.680 --> 00:19:57.540 my freedom, the order of intensities of my desire becomes only too determinate. 171 00:19:57.540 --> 00:20:03.920 Since indifference is not relevant to human action, it follows that two alternatives for 172 00:20:03.920 --> 00:20:09.620 choice cannot be ranked equally on an individual's value scale. 173 00:20:09.620 --> 00:20:15.740 If they are really ranked equally, then they cannot be alternatives for choice, and are 174 00:20:15.740 --> 00:20:18.740 therefore not relevant to action. 175 00:20:18.740 --> 00:20:25.700 Hence not only are alternatives ranked ordinarily on every man's value scale, but they are 176 00:20:25.700 --> 00:20:33.660 ranked without ties, that is, every alternative has a different rank. 177 00:20:33.660 --> 00:20:39.420 The famous illustration used by the indifference theorists to demonstrate the relevance of 178 00:20:39.420 --> 00:20:44.460 Indifference to Human Action is the case of Buridan's ass. 179 00:20:44.460 --> 00:20:51.380 This is the fable of the ass who stands hungry, equidistant from two equally attractive bales 180 00:20:51.380 --> 00:20:56.780 of hay, or thirsty, equidistant from two water holes. 181 00:20:56.780 --> 00:21:03.300 Since the two bales or water holes are equally attractive in every way, the ass can choose 182 00:21:03.300 --> 00:21:06.960 neither one, and must therefore starve. 183 00:21:06.960 --> 00:21:12.960 This example is supposed to prove the great relevance of indifference to action, and to 184 00:21:12.960 --> 00:21:19.080 be an indication of the way that indifference is revealed in action. 185 00:21:19.080 --> 00:21:26.140 Compounding confusion, Schumpeter refers to this ass as perfectly rational. 186 00:21:26.140 --> 00:21:31.560 In the first place, it is of course difficult to conceive of an ass or a person that could 187 00:21:31.560 --> 00:21:33.600 be less rational. 188 00:21:33.600 --> 00:21:39.960 He is confronted not with two choices, but with three, the third being to starve where 189 00:21:39.960 --> 00:21:41.520 he is. 190 00:21:41.520 --> 00:21:47.240 Even on the indifferentist's own grounds, this third choice will be ranked lower than 191 00:21:47.240 --> 00:21:50.560 the other two on the actor's value scale. 192 00:21:50.560 --> 00:21:54.620 He will not choose starvation. 193 00:21:54.620 --> 00:22:00.660 If both the left and right waterholes are equally attractive, and he can find no reason 194 00:22:00.660 --> 00:22:06.660 For those who prefer one or the other, the ass or the man will allow pure chance, such 195 00:22:06.660 --> 00:22:10.720 as a flip of a coin, to decide on either one. 196 00:22:10.720 --> 00:22:14.500 But on one, he must and will decide. 197 00:22:14.500 --> 00:22:22.420 Again, we are interested in preference as revealed through choice, and not in the psychology 198 00:22:22.420 --> 00:22:24.140 of preferences. 199 00:22:24.140 --> 00:22:30.260 If the flipped coin indicated the left waterhole, then the left waterhole was finally placed 200 00:22:30.260 --> 00:22:57.500 Another way of attempting a justification of the indifference analysis is to suppose 201 00:22:57.500 --> 00:23:04.700 Suppose that a man, Jones, chooses each of two alternatives, A and B, about 50 percent 202 00:23:04.700 --> 00:23:08.740 of the time, upon repeated opportunities. 203 00:23:08.740 --> 00:23:14.500 This shifting is alleged to be a demonstration that Jones is really indifferent as between 204 00:23:14.500 --> 00:23:16.780 the two alternatives. 205 00:23:16.780 --> 00:23:19.660 Yet what is the reasonable inference? 206 00:23:19.660 --> 00:23:26.460 Clearly that in some cases A was preferred to B on Jones' value scale, and that in the 207 00:23:26.460 --> 00:23:32.320 and the others, the positions were shifted, so that B was preferred to A. 208 00:23:32.320 --> 00:23:38.020 In no case was there indifference between the two alternatives. 209 00:23:38.020 --> 00:23:44.420 The shift of choice indicates a shift in the preference scale, and not indifference on 210 00:23:44.420 --> 00:23:47.020 a constant value scale. 211 00:23:47.020 --> 00:23:52.900 Of course, if we were dealing with psychology, we could enter into a discussion of intensities 212 00:23:52.900 --> 00:24:00.100 of Preferences, and opine that the man, with respect to his underlying personality, was 213 00:24:00.100 --> 00:24:07.060 relatively indifferent, rather than intensely biased as between the two alternatives. 214 00:24:07.060 --> 00:24:13.100 But in praxeology we are not interested in the concrete content of his value scales, 215 00:24:13.100 --> 00:24:16.100 nor in his underlying personality. 216 00:24:16.100 --> 00:24:20.860 We are interested in value scales as revealed through choice.