Introduction In general, the poor have a lower budget for buying things, reflected in lower reserve prices (the maximum price that they can afford) and in decision-making rules sacrificing quality to price affordability. They select cheaper versions of goods, cheaper goods in a category, and skip entire categories of goods altogether. If they occasionally don't, their budget constraint hold even more stringently later on and for next purchases. In every case, they end up with a narrower and - possibly older - cumulative bundle of (mainly) low-quality goods.

However, this paper explores the particularly painful situation when the price paid for a certain good by a poor is higher than the prices paid by a rich for a comparable good. In this way, suggestions for potentially innovative powerful ways to combat poverty are devised. Policies aimed at fighting poverty should carefully consider these cases, because removing the sources might be particularly effective, especially in countries and in historical phases in which many people from the middle class go backwards and they are filling the rank of the poor. Synthesis The poor can well pay more than the rich for at least eleven main reasons: 1. the quantity of goods purchased; 2. the type and quality of the goods purchased; 3. the distribution channels used for purchases, also in connection with spatial localization of the poor; 4. the payment system; 5. the role of cumulative bundle, i.e. the stock of durables and semidurables available in the house and for the consumer; 6. the role of the family of origin, its friends and connections as well as of additional public advantages, such as being famous; 7. dangers, risks, death, insurance and bank-related issues; 8. the wider gap in performance to be closed; 9. discrimination from non-poor in jury and selection boards; 10. the sensitivity to public policies, including related to infrastructure; 11. the alignment of (highly paid) policy-makers to the interests of the rich. This list is not exhaustive, but it contains several situations where evolutionary economics can better explain reality than neoclassical assumptions, both in appreciative theory and in formal models. A. The quantity of goods purchased A.1. When selecting the size of a packaged goods (e.g. in grocery), the poor can easily be an item-price minimizer: by choosing the lowest absolute expenditure, the poor might choose a small package, whose price per kilo is larger than a bigger pack. A rich can buy the latter, thus turning out to behave as a kilo-price minimizer. We extensively covered such rules-of-thumb in a formal model presented in this paper and that you can download here. More in general, if wholesale or very large quantities can be accessed by the rich and not by the poor, the difference in price would hurt the poor, because, contrary to the neoclassical assumption of rising marginal costs, the dominant business practice is for firm to ask a lower price for a larger quantity demanded. Indeed, refusal to sell is never due to cost reasons. As a special case, when the rich purchases an expensive good he might receive a further good for free (or almost for free) as an additional benefit, whereas the poor, who has to purchase it separately, would pay the full cost of it. Again, this reflects the business practice of bundling goods and generating a profit margin from such an operation, which goes well beyond the static unrelated sales presented by neoclassical textbooks. B. The type and quality of the goods purchased B.1. In a vertically differentiated product, the low-end is made of cheap variant with the worst components and ingrediants, weakly assembled and manufactured. Defective and short-living products are cheaper at the time of purchase but their short life makes the poor pay more over time for the same level of need satisfaction, by compelling re-purchase. This market condition is the outcome of business rules that attract the rich to higher-priced good. If the low-end were qualitatively acceptable and working for the same duration as the higher priced versions, then also the rich, who have a higher reserve price, would skip down and buy the cheapest. In order to exploit their higher reserve price, firms explicitly provide worse good at the low end. For two paper in which such issues are framed, see here and here. In a similar vein, the cheapest food often are poor in presence of nutrient components, so the price per unit of such positive ingredients is extremely high. For instance natural vitamins in junk food are barely present, so by dividing the price for their weight, you get an extremely high price for the vitamins contained. More in general, high-value components in cheap goods are, if not totally absent, only present in very limited quantities. Conversely, the price paid for such components is much higher than the price paid when purchasing better goods. B.2. The poor can deliberately choose to buy expensive status symbols, in order to propel their self-esteem, to fake a belonging to a different social group, to send social signals for success, on which they rely to build a real success (e.g. getting a job, because in the job intervew the dress was part of the informal evaluation criteria). You can see this in the choice of the strange and visually impacting mobile phones by immigrants in low income ladder. B.3. The percentage allocation of income to categories of goods can differ between the rich and the poor, with the possibility that the percentage price increase might be higher in theirs. This study (2019) provides a confirmation of one of such cases: "prices have risen more quickly for people at the bottom of the income distribution than for those at the top a phenomenon dubbed 'inflation inequality'. An implication of this new finding is that we may be underestimating income inequality and poverty rates in the United States". C. The distribution channels used for purchases, also in connection with spatial localization of the poor C.1. The poor are often spatially segregated in marginal, rural or peri-urban areas where house rents are lower but transport to workplace takes longer and is more expensive, the more so if not well served by public transport.

In simple models where location of a commercial or service-providing premise requires an expected total margins over costs, rich neighbourhoods will see them mushrooming, whereas deprived neighbourhoods will remain under-served, with fewer competitors in each distribution category. Prices in neighbouring shops may thus be higher because of lack of competition. To be more precise, locally-produced goods (e.g. agricultural products) tend to be cheaper in rural areas, but there imported goods from any external area (including cities) would be offered in narrower spectrum of alternative varieties and for higher prices. Moreover, many types of shopping venues might be missing, because it's unprofitable to open them there. In sparse rural areas, the sheer number of potential consumers is so low that many distribution channels are not present. In concentrated sub-urban areas, it's the income level of the potential consumers, reflected in reserve price patterns, that would not allow for such presence. C.2. When, by contrast, the poor are mixed in rich cities and neighbourhood, the supply can be skewed towards better-quality higher priced goods, with place-related inflation hurting the poor. C.3. The rich can better escape high prices due to location, since can better afford transport. In an extreme case, by taking a flight the rich can go to countries where the prices are lower and make cheap purchase there. Innovation in distribution channel, including free and easy access to internet, in public transportation and urban regeneration could be venue for policies aimed at covering these issues. C.4. Certain high-level services, such as Universities, may be concentrated in cities and the rural poor may need to relocate if they want to attend, with corresponding higher costs. D. The payment system The rich tend to use more credit cards than the poor, which often prefer cash. Because of the business practice of charging the same nominal price, while the credit card issuer provides rewards to the card owner, the net price paid by the poor is higher. E. The role of cumulative bundle, i.e. the stock of durables and semidurables available in the house and for the consumer E.1. Over time, the rich buys and cumulates at home a much larger and differentiated stock of goods, which provides him and his family free services. By having a narrower cumulative bundle, the poor, if has a certain necessity, has to purchase new services and goods, wheras the rich simply draws on his own cumulative bundle for free. For longer discussion and a formal demonstration of this see here and here. E.2. Selling used assets is a source of revenue for the rich, but not for the poor (who haven't many and need all of them). The rich pays only the depreciation (from new to used quotations), the poor the full cost (because he does not resale). This interacts with the better quality and longer durability of goods purchased at the beginning by the rich, since their depreciation is much lower that bad quality goods of short use life. F. The role of the family of origin, its friends and social connections, as well as of additional public advantages, such as being famous F.1. The rich tend to have rich friends, whereas, for homogeneity social rules, the poor tend to have friends that are poor. Marriage follows the same regularity, at least in certain countries. Since all the rich have satiated their basic needs, they have plenty of opportunities to buy extravagant and specialised tools and objects, so the range of such thing is much wider for the rich (in connection with friends) than for the poor. The rich can obtain for free from his friends a number of occasional services (e.g. being hosted in a house in a foreing country), whereas the network of the poor, mainly constituted by peers, cannot offer such free opportunities. F.2. More fundamentally, since reciprocation is the key for a long flow of services freely offered to people, a person raised in a rich family can rely on getting favours by all people that were helped by his family in the past. He can be introduced in exclusive circles getting powerful people in a friendly athmosphere. He is subject to softer selection criteria, also because they expect his family to reciprocate any free help provided to him. F.3. We do not have to remind the strong legacy in terms of education that a rich family can provide to the children, especially where free public schools are inadequate. The parents of the rich could afford widely definied education trials and error (e.g. breaking things), the family poor could not afford. Without any determinism, and knowing that certain people could counterbalance these potential effects, one can expect that a child rising from a rich family may have been exposed to more non-standard, out-of -the box goods for free. If indeed such a child turns out to be smarter than average, then the time for him to learn to master skills and difficult tasks might be shorter, with future savings in getting knowledge and being equitably selected for jobs and responsibilities. F.4. Famous people are usually rich (or become rich because of notoriety). Famous people can mobilize and attract funds even without soliciting or doing anything special. For instance they can be paid to attend cerimonies and get things for free by people that would like to have a selfie with them. An example is Donald Trump getting unsolicited contributions to his presidential campaign in 2016 even if he stated that will self-fund it entirely. He also got the most of free earned media attention and didn't need to spend the money for advertising his name and policies: media reported what he was saying without paying (whereas other candidates, not to mention poor people, do not have - such - access to free media coverage).

G. Dangers, risks, death, insurance and bank-related issues G.1. Poor people accept more dangerous and less remunerative occupations, involving higher safety risks. They face higher probabilities of negative shocks in income (e.g. being fired or not paid after a performed job). They have more frequent and deeper negative shocks while starting nearer to minimal thresholds of income, so they have a disproportionately higher probability of going under. Meanwhile the rich are more frequently covered by insurance and they can afford a higher premium so the poor is less covered (or even totally uncovered), and has to pay more than the rich in the event of damage. G.2. The poor tend to have more illness and die younger. The time balance between "efforts to study and get productive" and "enjoying the gains from remuneration of efforts" is skewed against the poor: he has much less time to enjoy, so the price (in terms of efforts) is disproportionately higher than for the rich. For any unit of time spent enjoying, many more unit of time spent on efforts is requested from the poor than from the rich. Additionally, he and others will invest on his human capital less because of that. G.3. The poor are more risky loan bearers and are less creditworthy, so banks are reluctant to give credit and, if anything, they give smaller loans, because of lack or insufficiency in collateral, be it wealth or income (personal, of the family of origin or of friends). In such loans to the poor, the interest rate they require is higher than from the rich. Low and unregular income, coupled with negative shocks, may relatively frequently result in unpaid bills and negative balance in the bank account. Both lead to penalties, additional fees and further burdens. Except with microfinance, the poor has little access to credit and is credit rationed. Banks have routines linking past income to maximum credit ceilings. When they relax such routines, as it happened in USA with sub-prime loans for house purchases, it may well end up with the poor being unable to pay back the loan and put in motion a financial crisis. Contrary to the neoclassical theory, including many version of life-cycle theory, credit constraints are very effective in hindering poor people to invest. G.4. Everytime a purchase is an investment, whose upfront cost is higher for goods that are cheaper in operational expenditures and maintenance (O&M) and that last for longer time, the poor, who is cash- and credit-constrained, is at a disadvantage, ending up to choose cheaper goods, which are not the best investment, which immediately afterwards make the rich paying less than the poor. An example is in energy efficiency buildings: the poor usually live in very inefficient building and choose the cheapest versions of weatherisation, if anything at all, whereas the rich can afford (and the bank trust him for a loan to) buy the deepest renovation methods. More in general, a large upfront investment can open areas of low prices to those who can afford it, leaving the others with higher prices. G.5. When a not-so-legal behaviour reduces current costs but entails a small probability of getting caught (with a large fee), the rich, for which the fee is non-life-changing, can well decide to undertake the behaviour (thus saving as long as it is not cought). The poor, however, would be completely ruined by the fee, thus pay more and stay legal. On the same field, income tax fraud is larger by the rich since they have more to lose from taxation and can afford to pay the fixed amount of money requested by the tax accountant. G6. What said about the poor in a population is often true also for poor countries: their ratings are worse than the average, so the interest rate they pay on their international loan is higher as well. Under negative macroeconomic and governance shocks, they risk to enter into a spiral of high rates leading to currency depreciation, shrinking GDP (to some extent, their collateral) so, in the worst cases, defaulting. H. The wider gap in performance to be closed The poor starts from a low level of endowments and stock, so to reach the same level of performance they need to buy more and spend more. For instance to be healthy, he may have more medecine to use, if for many periods he could not afford a healthy lifestyle. If undernourished, he may need a trajectory of increasing food intake to recover. From a lower level of education, he might need to read more than his peers later on. Their house can easily be in worse conditions than the rich ones because of a lack of maintenance.

I. Discrimination from non-poor in selection boards and jury The more responsibility and entitlement to choice in an organization, the higher the wage. So a selection board, a jury or job interviewers is normally made by non-poor. They can easily discriminate the poor from a job, a task, an entitlement and to prefer their friends (or people rich enough to reciprocate in the future, either directly or through their social networks). At each career step, this cut off the poor from advancing. A poor has much higher probability of being jailed (and for longer time) than a rich having being suspected of the same crime (see e.g. here). L. Sensitivity to public policies, including related to infrastructure The rich has an endowment that often frees him from relying on public services. The poor, by contrast, is highly sensitive to the quantity and quality of accessible public goods and policies funded by public expenditure. Public transport, hospitals, schools, libraries, parks, and social opportunities in broad sense may represent a much larger share in actually consumed services and goods of the poor and, conversely, have a disproportionatly high share of poor in their user base, the more so as they are usually for free (we formally demonstrated that the higher the absolute level of price, the larger the share of the rich among its user base here). Bad quality, unreliable public services, provided by demotivated, badly-paid, and ineffectively monitored public servants hurt the poor and push them at the margin. Infrastructure, such as water pipes and railways, can be concentrated in cities and citycentres especially, leaving those living in the peripheries or in rural areas (which may well be poorer) in the need of owning and operating private solutions. For instance, purchasing water in bottles instead of from the tap (according to 2019 World Water Development Report editor-in-chief: "in cities, rich live in homes with piped water whereas poor people living in slums often have to buy water from trucks, kiosks and other vendors, spending roughly 10 to 20 times more". Ownership of car may be higher in rural areas where public transport is weaker, compelling an investment that, for certain households of city centres, may not be necessary. Needless to say, a car involves also insurance, maintenance, fuel costs, etc. M. The alignment of (highly paid) policy-makers to the interests of the rich Since also in the organization of the State, the higher the responsibility, the higher the wage, top-level policymaker are always very well paid, so their personal interest is aligned with the rich (e.g. in paying lower taxes). They choose, under any rhetorical justification, to implement decisions unfavourable for the poor. They have the decisive say on the provision of public goods, whose bad quality is instrumental to delegitimisation of public expenditure and to vocal requests of lowering taxes. They have a vested interest in blocking improvements. In the media, the same logics prevail, with bad practices being chastised but solutions are never given coverage. This is multiplied by funding mechanisms of electoral campaigns and all-around-the-clock lobbying pressures on legislative and bureacratic bodies by the networks of the wealthy. All this can easily raise the actual price paid by the poor for goods they are alone in purchasing, while tax loopholes may lead to the situation in which a boss is paying less taxes than his secretary. 4. Conclusion Many countries have been successful for several decades to improve the livelihood of the poor, to let the large majority to escape poverty traps (including higher prices for the same goods or for fulfilling the same needs) and raising up to the middle class thanks to a mobility ladder. Effectively working democracy and macroeconomic policies have been crucial. However, they should not be taken for granted and innovative anti-poverty policies may be needed under negative macroeconomic dynamics, severe public expenditure constraints, and political failures for the poor and the middle class to organise . The paper has presented a wide number of conditions that are structurally and systematically modifying prices depending on the income of the buyer. Their specific examination in a country and for a certain case and social group could be instrumental for devising appropriate responses.