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that it does so, Chapter 7 Petty’s Idea 2/3/16 di HOUSE_OVERSIGHT_011070
February 6, 2026 at 10:18 PM
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young. If all mothers invest preferentially in their own, or maximize Hamilton’s standard rb>c , healthier mothers will produce more young with higher doses of the antidote genes, while sicklier mothers will produce less with less. Here it is females who compete to prove the same better genes that males just proved in the tournaments or beauty contests. The race against parasites speeds up again with Trivers’ fine insight about healthier mothers choosing to dial up the ratio of sons to daughters (“primary sex ratio”), and to expand the reproductive period at both ends with shorter birth spacing for more male offspring still. (Some of this may be my idea rather than his.) Nature proves best current genes twice. Fathers prove them by duking it out or strutting their stuff. Mothers carrying the same best genes prove it by winning the breeding contest against other mothers after. The ex ante/ ex post distinction counts as much in biology as in economics. Here it accelerates the selection process. Offspring carrying the antidote gene to meet current parasites will generally not on that account cost more ex ante invested consumption to raise. If they are males, who can turn that advantage into many offspring, the ex post value of that same investment can be far higher. The converse works for offspring lacking the gene. Their mothers can make the best of it by producing females who will find breeding opportunities anyhow with mates carrying the gene, since she knows which they are and males always have cheap sperm to spare, and will so keep their own genes in the gene pool. Parasites got the last laugh by killing Hamilton on research in Africa a few years after I met him. I never knew well enough to call him Bill. Bob Trivers called him the deepest thinker in the world. That couldn’t be wrong by much. Parasites and Demes Ernst Mayr, Bob Trivers’ doctoral advisor at Harvard, defined a deme as a race or subpopulation that intrabreeds at least 95% of the time. I hypothesize
February 6, 2026 at 10:18 PM
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higher frequencies of the antidote gene than others. They will tend to be healthier, and so able to invest more energy in more Chapter 7 Petty’s Idea 2/3/16 10 HOUSE_OVERSIGHT_011069
February 6, 2026 at 10:18 PM
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added the mechanics. Nassau Senior made that principle his first axiom in his Outline of 1836. The biological imperative lapsed from attention when the first generation of marginalists, led by Jevons and Menger, with Walras soon to follow, thought it unscientific to explain or justify tastes. It reemerged a century later in bioeconomics, much of which looked for economic implications of Hamilton’s rule. We will see how it might clarify pure consumption and the maximand. Enlightened Kin Selection Hamilton’s rule needs completion because the quarterback and his genes have figured out that the bench is better than the hospital. What really happens, | think, is a long-range example of Bob Trivers’ “reciprocal altruism” of 1971 as generalized by Richard Alexander. Bob wrote that creatures might invest in non-kin if the investment were expected to be repaid with interest. Alexander added that the repayment could be to the investor’s kin with equal genetic benefit if Hamilton’s hurdle rb>c were cleared from the investor's perspective. The quarterback yields to special teams on fourth down, and they to the defense until possession changes again, for the best interests of each and all in the long run. The interest they receive in turn for deferring to non-kin is the cost of maintaining themselves on the bench. It does not accrue and compound because it is paid out continuously. It is an insurance cost that each temporary winner dares not trim. Group selection is enlightened kin selection. Three or four decades ago, this much acknowledgement of group selection would have met more resistance than I expect now. It shouldn’t have. Half the beauty of the Hamilton-Zuc scenario is in explaining allelic diversity as a result of agonistic rather than lethal competition. Zack and Jack and their genotypes are rivals now because they are teammates in the big picture. Kin selection is a help until it crosses the line and becomes a hindrance. Some mothers in the source deme will carry
February 6, 2026 at 10:17 PM
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replacing the work force, which is trusted to spend it on both. Malthus’ population principle in 1798 and 1801 Chapter 7 Petty’s Idea 2/3/16 9 HOUSE_OVERSIGHT_011068
February 6, 2026 at 10:17 PM
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peacock’s tail feathers are an encumbrance in running from predators. And why give the expensive displays mostly to males? Why do males exist at all in species where they contribute genes but no care? We just saw the answer to the first. Answers to the second two again build on an insight of Trivers in 1973. Males produce cheap sperm carrying genes alone. Females produce eggs packed with costly nutrients. A male can pass genes to many descendants through many mates if they approve his signs. That speeds up the fight against parasites. Nature evolved males and their self-promoting signs and their contests for fastest spread of antidote genes to catch up to shifts in parasite load. Where Do Losers Go? A key point in the Hamilton-Zuk theory is that losers’ genes in the beauty contest are typically not driven to extinction. They are driven to low frequencies until needed again. Kin selection, up to a point, helps maintain genic diversity by preserving current losers within the gene pool. Selection pressures punish and restrain kin selection when it conflicts with preservation of other genes whose time will come again. I met Hamilton at a conference in Squaw Valley, where Bob Trivers had helped us attract him, and told him this reason why I thought his 1982 paper helped complete and qualify his 1964 paper. He was the absent-minded professor to perfection. Moody, distracted, profound. He smiled, a rare thing for him, and said “It’s been a long search.” This explains what I mean by lineage survival or fitness. Much of this book assumes its maximization even among modern humans, who create our own urban environments in place of the ancestral savanna for which we were adapted. And much of economic history, although written in cities by city-dwellers, appears to assume the same. Chapter 2 listed some examples. Let’s review them. There was Petty’s of 1662. The similar equilibrium wage theories of Smith and Ricardo expected pay to converge to the level maintaining and
February 6, 2026 at 10:17 PM
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glance to hinder fitness? A Chapter 7 Petty’s Idea 2/3/16 8 HOUSE_OVERSIGHT_011067
February 6, 2026 at 10:17 PM
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Hamilton’s Parasite Theory My take on Hamilton’s 1982 paper, which I consider his masterpiece, is a blend of his thoughts, Bob Trivers’ from a decade before, Richard Alexander’s, and maybe mine. Mine sees a population arranged in local “demes” which intrabreed in most cases for best adaptation to local pressures including pathogens and parasites. A local strain to which the local deme is adapted might spread to other demes which are not. Hosts in the invaded demes become sick. Female ones there intuit the degraded conditions, breed less often, and breed mostly females (mothers can choose) because males with their now ill-adapted anti-parasite (histocampatability) genes will find few willing mates. This begins the part from Trivers. I’ll come to Alexander’s later. Mothers in the source deme see an opposite picture. Conditions are not necessarily better than before, but they are better than in the invaded demes. They intuit this, breed more often, and breed mostly males. The males migrate to those invaded demes, carrying histocompatibility genes pre-adapted to the invaders, and find willing mates there if they can show the signs. The idea that mothers choose to breed mostly males in prosperous conditions is the other half of Trivers’ idea. The idea that the invading parasite and the males with antidote genes might tend to originate from the same deme may be mine. That presupposes that females can trust the signs. Nature makes sure they can. She provides resistant males with hard-to-feign ones to prove it. This was one of Hamilton’s key insights. His idea has been called the “truth in advertising” theory. Symmetrical antlers, deep croaks, accurate songs and bright colors where they should be tell the females whose genes can be trusted. Parasites and pathogens would fake them in afflicted host males if they could. It seems they can’t. Hamilton, I believe, had solved three nagging puzzles at once. Why does nature waste resources on beauty displays that seem at first
February 6, 2026 at 10:16 PM
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and the team than being carried to the hospital. He realizes that other players are best for punts or field goals or defense until he gets the ball again. Selection pressures do not favor the same traits and genes every time. Chapter 7 Petty’s Idea 2/3/16 7 HOUSE_OVERSIGHT_011066
February 6, 2026 at 10:16 PM
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holds frequencies under ten percent, and those frequencies are constantly shifting. The flux proves that losers are allowed mating opportunities too, though not as much, and leave young to compete in the next generation. Hamilton explained why that could make sense in a paper published with Marlene Zuk in 1982. George Williams in 1976 and John Tooby in 1980 had argued that fittest genes in one generation might not be fittest in the next if niche pressures varied to counter current gene choices. Tooby had pointed to parasites and pathogens, particularly single-cell ones whose life cycle runs less than an hour. They could evolve new strains to outflank our old defenses and call for new ones. Hamilton and Zuk continued this theme. They suggested that genes might have long memories, put in human terms, and might have seen the same parasites and pathogens pull such tricks before. If some individuals in the host population still carried the antidote gene that worked the last time the same unexpected strain arose, or something close enough to it, hosts collectively could weather the threat if that antidote gene could be identified and spread fast enough. Then how? Hamilton and Zuk proposed that what winning males display in contests of singing or croaking or agility or symmetry, or bright colors in the right places, was possession of the genes needed to counter the current strains of pathogens and parasites. Losers in the same contests carried genes that had proved best against strains of the past and might come back in the future. Nepotism practiced by winners would speed up the spread of the current antidote. But losers carried genes that had worked against other strains that might recur. A way had to be found to keep all those potential antidotes somewhere in the medicine cabinet. Current losers had to be saved for later. Gene diversity was the key to group survival in the long run. The quarterback trots to the bench on fourth down because that is better for himself
February 6, 2026 at 10:16 PM
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to fixity, and its rivals to extinction, within a few generations if selection favored it consistently. Their argument was Malthus’ insight: breeding success is geometric. Yet there is rich allelic diversity wherever we look. There are some gene sites in some species where the most common allele Chapter 7 Petty’s Idea 2/3/16 6 HOUSE_OVERSIGHT_011065
February 6, 2026 at 10:16 PM
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her chimps at Gombe. I think I have seen it among the pack of dogs, led by my father’s favorite “Sean”, at Sutton Place. That would count as one of the practical constraints. Too little support for family over equally deserving others is seen as a fault, and too much as another. The reason is obvious. Jack’s ambitions for kin will eventually conflict with Zack’s, just as with ambitions for food and nest sites and mating opportunities. Not everyone’s firstborn can be king of the hill. Social creatures evolve agonistic rules to settle such conflicts peacefully. Losers in mating tournaments, or in contests where males display and females choose, usually survive to compete again next year. The contest is in the group interest because the traits of strength and skill proved in the winner will be those passed on. Our genes tell us to compete as best we can for the sake of a fair test, and to stop when the verdict seems clear. And soon enough it does. The quarterback tries his best for three downs to move the yardsticks, but trots to the sidelines on fourth down for the sake of another chance later. If genes can encode this farsighted strategy for those other kinds of competition, why not for nepotistic competition too? For decades, biologists wondered why genes need so much selecting in species long established. Shouldn't earlier contests have selected the fittest genes once and for all, with no need for further ones but to screen out recent and harmful mutations? Shouldn’t the best traits have become clear millennia ago? Why need males contest in tournaments or beauty contests every breeding season, with mostly the same contestants, when best genes ought to have proved themselves soon after the species began? Then there would be no genetic diversity except for recent mutations not yet screened out. Population genetists such as Fisher, J. B.S. Haldane and Sewall Wright had written mathematical models showing that even the slightest selection pressures should drive a gene
February 6, 2026 at 10:16 PM
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self-replication might for that reason hurt chances of achieving it. We know this happens. Human tradition everywhere resists and punishes nepotism when it crosses a line. Jane Goodall reported the same for Chapter 7 Petty’s Idea 2/3/16 5 HOUSE_OVERSIGHT_011064
February 6, 2026 at 10:15 PM
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parameter typically fluctuates around zero and group fitness holds about where it started. Hamilton’s rule, applied to diploids like us where closest relatedness r absent inbreeding is %, forbids investment where fitness gained (benefit) is less than twice fitness given up (cost). I see no escape from the inference that fitness would double with each generation, or more to account for cases where relatedness fell below ¥%. I see no relief in an interpretation, say, that each successive generation cures this imbalance by investing only half or less of its fitness and letting the rest lapse. Fitness is likelihood of leaving descendants of equal fitness. It is not strictly conserved, because likelihood is generally not identical to outcome. There is ex ante and ex post fitness. But the ex ante kind is meaningless unless potency, in Aristotle’s terms, is expected to converge to act. Hamilton’s rule should not have escaped this critique for half a century. It clearly has merit, but needs some different expression. Such a reformulation might treat rb/c as a maximand within practical constraints. We can see how it might be by looking at the context. Darwin’s idea is a competition for breeding success. This biological imperative is a powerful predictor in nature. It predicts that traits are selected for successful reproduction to the exclusion of all else. Evidence is impressive. “Semelparous” creatures who breed only once and do not invest postpartum care, like salmon and soybeans, die within hours. An octopus mother breeds only once, cares for her young a few weeks, and dies as they disperse. Nature is on a tight budget. Resources wasted soon become resources lost to thriftier lineages. Hamilton saw this. He was right in stressing the role of competition among individuals and individual heritable traits. Darwin did the same. One thing Hamilton’s rule leaves out, which is not to claim that he overlooked it, is that traits and their genes best at prioritizing
February 6, 2026 at 10:15 PM
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implicitly constant at the population scale unless there is population growth (Fisher’s “Malthusian parameter”). For creatures other than us, the Chapter 7 Petty’s Idea 2/3/16 4 HOUSE_OVERSIGHT_011063
February 6, 2026 at 10:15 PM
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and Ricardo and Malthus and Mill, until the marginalist revolution shifted focus from objectives to the mechanics in supply, demand and price. Bioeconomics awoke a century later, largely it seems in response to the challenge of Hamilton’s rule. Now I will look at it too. My term “lineage survival” is unusual. It is meant not to take sides between “kin selection” and “group selection.” The kin selection idea was another word for Hamilton’s rule from his doctorial thesis in 1964. It said that genes encoding investment in close kin encode investment in likeliest sharers of those genes, and should tend to entrench and perpetuate themselves. His condition for investment was r)bc.r here meant relatedness: % for offspring or siblings, % for nephews or nieces or grandoffspring, and so forth. b meant benefit to the donee, and c meant cost to the investor. The sign > means “greater than”. The cost and benefit were measured in fitness itself, meaning chances to survive and breed. But that too meant “inclusive fitness” where investing in kin counted as breeding when adjusted for relatedness. The idea was that I give up some of my chances if | can increase yours to my net genic advantage in the long run. Hamilton allowed for exceptions including meiotic drive, which sometimes forecloses gene competition. His rule prevailed because it made mostly good predictions. Humans and creatures in general usually care for their own young first, if they have any, and for closely related young if not. Hamilton made it clear that cost c and benefit b in his hurdle rb>c respectively meant fitness given up by the investor and fitness grained by the investee. He further made it clear that fitness could be measured as R. A. Fisher’s “reproductive value” V(x) published in 1930 and 1957. V(x) meant likelihood at age x of reaching each successive age times expected offspring at that age. V(x), or Bob Trivers’ “reproductive success” RS, which simplifies V(x) to expected remaining offspring, is
February 6, 2026 at 10:15 PM
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tended to reason explicitly or implicitly from the biological imperative, meaning what I call “ends” in lineage survival, from Petty through Smith Chapter 7 Petty’s Idea 2/3/16 3 HOUSE_OVERSIGHT_011062
February 6, 2026 at 10:14 PM
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I confess that this book casts me as that little boy crashing the economic party, and maybe the evolutionary biology one too, in trust that outsiders might have better chances to spot the obvious unseen. What else was the pay rule? I derived it easily from doctrines already accepted, | think, and anyhow hard to refute. Those were the total return turism and Ben-Porath’s equation for human growth. The maximand rule or deadweight loss rule would prove it as well. How could Becker have missed that what holds for investment in job training by employers holds for any investment by anyone in anything? How could students of the age-wage problem have missed the obvious solution? Investment implies expected recovery with interest, by the investor or a chosen donee, and recovery means recovery of depreciation. I belabor this point because tradition dies hard, and naturally tends to circle wagons under attack. I doubt that my surprise attack will meet the resistance Darwin’s found. Darwin’s met resistance founded on faith. I took pains to show that my version requires only selection for lineage survival, and that a benign Artificer might ordain the same. Evolutionary Biology and Hamilton's Rule Economics, meaning any quantitative rationale of choice, normally describes humans and human choice. That goes for this book too. But some treatments of economics including this one are meant to fit other creatures as well. My axioms have kept that in mind. The mortal and reproducing population need not be human. Much of the animal kingdom, I think, shows convergent tastes and predictions or acts as if it did. The biological imperative is meant to apply to all. All, as I see it, own capital of both factors. Even protozoans own (“monopolize”) the nutrients they assimilate and the space they occupy. Humans are exceptional in their cultural accumulations of learning and technology shown in our secular (lasting) growth. But I did not make those features axioms. I argued that economics
February 6, 2026 at 10:14 PM
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how tradition and mind-sets and in-groups might sometimes need a look from outside. Peer review is not enough. Sometimes it perpetuates nonsense. The little boy was not a peer, but he could tell clothes when he saw them. (“Peer”, as any theorist knows, means someone who pees on your theory.) Chapter 7 Petty’s Idea 2/3/16 2 HOUSE_OVERSIGHT_011061
February 6, 2026 at 10:14 PM
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selection should probably do as well. We are all at peace with the fact that people and other creatures care for their young. Economics and evolutionary biology are much the same. Helen Keller, born blind and deaf, might still have reasoned her way through much of both. Hamlet would have loved them. I love them most when they test the limits of logic, and consult the data only at the end. The theme from which both reason, as Herbert Spencer taught in the nineteenth century, is what he called “survival of the fittest.” Another philosopher, Karl Popper, found fault with this idea a century later. Popper was one of those I mentioned who disapprove of truisms. I haven’t read Popper, but gather that he thought it improper to define fitness as potential survival, and then measure it as survival. That objection is close to being understandable from an anti-truism viewpoint. But the reason why it is not quite a truism is instructive. Measurement implies an “empirical” world of data in external and observable reality. Spencer’s insight, really his paraphrase and generalization of Darwin’s, is not quite a truism because it carries the hypothesis that “potential” has an empirical meaning. Aristotle’s idea that potency precedes and explains act is called causality. Adam Smith’s friend and fellow Scotsman David Hume scarcely doubted causality, but argued correctly (I think) that it cannot be proved either by logic or by experiment. The fittest prove themselves such by surviving if and only if Aristotle was right. Natural selection simply means the untestable but little-doubted theory of causality. Spencer or Darwin or Gertrude Stein might be faulted for insulting our intelligence by stating the obvious. That shoe would fit Gertrude Stein. But Spencer and Darwin, like the little boy in Hans Christian Andersen’s The Emperor’s New Clothes, were stating the obvious unseen. Andersen’s point was that intelligence was not the thing lacking or what the little boy supplied. It was about
February 6, 2026 at 10:14 PM
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selection, divine Chapter 7 Petty’s Idea 2/3/16 al HOUSE_OVERSIGHT_011060
February 6, 2026 at 10:13 PM
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CHAPTER 7: PETTY’S IDEA How We Got to this Point I said that if] had any sense, I would have left the worms in the can by pretending to believe (4.1) as Mill did and as the rest of the world seems to do. Charts and tables confirm his prediction in his and their terms as well as mine. But Piketty’s argument was rightly criticized for leaving human capital out. Someone might or might not have faulted mine on the same ground if I had stopped at the end of Chapter 4. Whether they would have or not, every composer knows that the critic to hear is the one inside. What that critic told me was to gamble a case already won, open the can, and follow the argument and worms wherever they lead. That’s why my title promised other surprises. I risked following it past clarification into digression when I argued the pay rule. I since tried to justify the digression, if there was some, by showing how that rule could explain Piketty’s data for pay/net profit ratios in the twentieth century. And I tried to show how the pay rule and depreciation theory combined, making pay all human depreciation and no realized work at the end, gives the only convincing explanation of age-wage profiles showing rising or steady pay as human capital grades smoothly to zero. Risk theory reinforced this argument by revealing time discount rates for human capital as those made plain for physical capital owned by the same ageing cohorts. Every step was an adventure, and every step led to the next one. But I opened other questions and cans along the way, and the same critic tells me to follow the worms a little farther. I said that the cost of survival is adult consumption for the sake of investment in the next generation, that pure consumption is more or less the same, and that we will understand the maximand when we understand pure consumption. These threads lead into evolutionary biology, which reasons how traits are selected for lineage survival. The faithful need not take alarm. Although I mean natural
February 6, 2026 at 10:13 PM
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support this hypothesis too, as the constancy of pay differences to the end would otherwise be improbable. I made it the Darwinian axiom: maintenance is exhausted in satisfying our taste for survival. Ben-Porath’s life cycle was adjusted to express these features. Factor risk theory argued that human capital is the riskier and higher-return factor because capital of any kind takes on the risk characteristics of its owners and human capital is owned disproportionately by the risk-tolerant young. The Y rule contradicts the Y = | + C equation, while the pay rule contradicts the dogma that output equals pay plus work. National accounts are founded on both. That means I can expect tough resistance. I have tried to prepare for it by adding a little more to each argument with each chapter. Throughout this chapter, and throughout this book, I have bent over backwards to distinguish logical certitudes from falsifiable hypothesis. Economics needs both. But it needs to know which is which. The pay and Y rules, for example, are each certitude in part. The certain part is the heretical one. The present value and maximand rules follow from definitions, and compel expected recovery of human depreciation in pay. | then relied on the convergence axioms to infer actual recovery as a norm, not a invariable outcome, and on the new axiom of the biological imperative, as well as evidence from age-wage profiles, to infer that maintenance consumption is exhausted rather than recovered in pay as well. Chapter 6: Parallels with the Firm 2/4/16 25 HOUSE_OVERSIGHT_011059
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taste satisfaction. These are all ex post descriptions of realized outcomes rather than intentions. Together they give output = investment + invested consumption + positive self-invested work — human depreciation + net transfer + exhaust = investment + invested consumption + self-invested work — recovered human depreciation + net transfer + exhaust. (6.24) This much is certitude. I now apply (5.9), which includes consumption = invested consumption + pure consumption, to reach the Y rule in its general form: output = investment + consumption + self-invested work — human depreciation + net transfer. (6.25) The net transfer term disappears at the collective scale. Although (6.24) is logical certitude infered from definitions, (5.9) and consequently (6.25) are not. cannot rule out the possibility of a third kind of consumption recovered in work products as per Quesnay. I hope that my interpretation of age- wage profiles in the light of the boss-secretary parable has revealed that as improbable. The same holds for my derivation of the pay rule through Ben-Porath’s equation and (6.18). (6.18), my inference that human cash flow equals less invested consumption, also trusts that all maintenance consumption is exhausted in satisfying tastes. Summary Accounting for human capital is much like accounting in a firm. Expected recovery of human depreciation in pay is logical certitude illustrated in age-wage profiles and in the boss-secretary parable. The pay rule is not entirely logical certitude, however, as it also asserts that maintenance consumption is not recovered. Age-wage profiles Chapter 6: Parallels with the Firm 2/4/16 24 HOUSE_OVERSIGHT_011058
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Where Keynes and Kuznets and macroeconomic tradition have been right is in reasoning that pay and gross profit, meaning gross of depreciation, sum to the “expenditure” spent on consumption and gross investment. This fact of arithmetic is the logic behind Say’s law: pay plus profit are always enough to buy what is produced. We saw that this truism gives cold comfort when calamity or misjudgment make profit negative, as with the subprime houses of 2008. What it certifies, anyhow, is expenditure = pay + gross profit = consumption + gross investment. (6.21) We can subtract depreciation to reach pay + profit = consumption + investment. (6.22) Now (6.19) can be corrected as a whole to show income = pay + profit + self-invested work - human depreciation = output = consumption - investment + self-invested work - human depreciation. (6.23) My main goal in this book has been to further the work of Solow in exogenizing growth, and also the work of Ben-Porath in endogenizing human capital as something produced within the economy. It was in that spirit that I derived the Y rule in Chapters 2 and 5 by putting human capital inside. I reached output = investment + human capital growth + cash flow. Here “ex post net” is understood before output and investment, so that investment means physical capital growth. (6.16) applies the growth truism to human capital. The cash flow truism shows that cash flow is net transfer plus exhaust realized in Chapter 6: Parallels with the Firm 2/4/16 23 HOUSE_OVERSIGHT_011057
February 6, 2026 at 10:12 PM