This study relies on a linear programming model to estimate welfare ratios in19th century Lima. By using a linear programming model, the food basketguarantees the intake of basic nutrients at the minimum cost. The subsistencecost includes the cost of food and other basic needs. The estimates show thatlow-skilled workers in Lima were able to cover their basic needs in 1800-1875.The results also show that living standards of low-skilled workers declinedduring the Guano Era. Living standards in Lima, however, compared favorably toseveral cities in Europe.

In the last years, several studies have focused on the standards of living in LatinAmerica. Information on real wages and height suggests that living standards in manyparts of Spanish America compared favorably to Europe in late colonial times (Dobado-González and García-Montero, 2014). Inthe 19th century, real wages improved in some Latin American economies and remainedor declined in others.1 There wereimportant differences in living standards within Latin America; Argentina, forinstance, had higher living standards than other cities in the region.2

Peru in the 19th century constitutes an interesting study case of living standards.Peru was one of the main commercial and economic centers in the Americas in colonialtimes. After Independence, Peru remained an important economy in the region. In thefirst decades of the 19th century, political instability affected the economy. Theeconomic situation of Peru changed in the mid-19th century. In the 1850s and 1860s,Peru experienced a commercial boom due to the exportation of guano. The Guano Erawas in fact one of the periods of fastest export growth in Latin America. Theexpansion of foreign trade led to the expansion of the economy in several regions ofPeru, especially on the coast.

Could Limenians cover their basic needs in the 19th century? How did living standardsevolve during this period? Did low-income families experience an improvement inliving standards during the Guano Era?

Some studies suggest that low-income families in Lima did not increase their livingstandards during the Guano Era. For instance, Twrdekand Manzel (2010) indicate that height (proxy for nutrition) did notchange during this period in spite of the economic bonanza. Other studies suggestthat low-skilled workers could cover their basic needs, but experienced a decline inliving standards during the Guano Era (Arroyo-Abad,2014; Zegarra, 2020a).

Welfare ratios constitute a useful indicator to determine the capacity of families tocover their basic needs. The welfare ratio is calculated as the ratio between totalfamily income and the cost of subsistence.3 The cost of subsistence (also known as poverty line) is thecost of basic needs, such as food, clothing, fuel, housing, among others. If thewelfare ratio is higher than 1.0, families are able to cover their basic needs.

Two methods can be employed to estimate the subsistence food basket and welfareratios. One of those methods consists of using historical diets to determine thecomposition of the subsistence basket. In this case, welfare ratios are consistentwith consumption habits. A potential weakness of relying on historical diets is thathabits could vary across people and over time; so choosing a particular diet may bearbitrary and may introduce biases in the estimation of welfare ratios. Analternative methodology to estimate welfare ratios consists of using a linearprogramming model. Linear programming can be used to estimate the least-cost foodbasket that guarantees a minimum intake of important nutrients. Linear programminghas been recently used for the estimation of welfare ratios in several economies(Allen, 2017; Zegarra, 2021). This method is useful to determinetheoretically the food basket that a family must consume in order to ingest basicnutrients at the lowest possible cost. A potential weakness of the method is thatfamilies do not necessarily count with complete information on prices and nutrientsand do not rely on a mathematical tool for the selection of their diets.4

Two studies have estimated welfare ratios for 19th century Lima. Like most historicalestimations of welfare ratios, Arroyo-Abad(2014) relied on historical diets to estimate welfare ratios. In anotherstudy, I relied on a linear programming model to estimate the cost of food, butassumed that the composition of the food basket was not very different from 1860sdiets (Zegarra, 2020a). Importantly, bothstudies assume that people should ingest at least minimum quantities of calories andproteins. A balanced-nutrition diet, however, should also include other nutrients,such as fat, iron and vitamins.

In this study, I estimate welfare ratios for low-skilled workers in 19th century Limausing an alternative methodology. I use a linear programming model and assume thatthe food basket should guarantee the intake of calories, proteins, fat, iron andsome basic vitamins at the lowest possible cost. I do not assume that the foodbasket should be close to historical diets. I add expenses on fuel, clothing,housing and other basic goods in order to calculate the cost of subsistence. I thenestimate the welfare ratios of low-skilled workers as the ratio between the familyincome and the cost of subsistence. The results of the linear programming model showthat the least-cost food basket was composed of a large quantity of chickpeas, inaddition to potatoes and mutton.

The estimates show that the welfare ratio in Lima was usually above 1.0. Low-skilledworkers earned enough to cover the basic needs of their families. However, livingstandards declined during the Guano Era. Living standards were then negativelycorrelated with economic growth, at a time of increasing terms of trade andimmigration of chinese workers. This result is consistent with the findings forother countries in Latin America: the evidence for the region suggests that ifeconomic growth is associated with an increase in terms of trade and massiveimmigration, real wages may decline. Nevertheless, in spite of the decline in realwages during the Guano Era, low-skilled workers in Lima in the mid-19th century werenot poorer than some of their Western European counterparts. Although livingstandards in Lima were below those in London, the welfare ratio in Lima was similarto the ratios in Amsterdam, Paris and Strasbourg in the 19th century.

Peru has always been an economy in rich natural resources. The country has abundantmining resources in the highlands and rich valleys on the coast. Historically, Peruhas exported natural resources. In colonial times, most of Peruvian exports wereminerals and agricultural products. Among minerals, Peru’s main export wassilver. The country also exported agricultural products, such as sugar and bark.After Independence, Peruvian exports were also natural resources. From the late1840s, Peru exported guano, entering into the Guano Era. In the 1870s, nitratesincreased in importance. Sugar and cotton were also important exports in the 19thcentury.

The importance of the Peruvian export sector varied across regions. In the northernhighlands, most of the southern highlands and in the jungle, mining had a limitedscope and most agriculture was not destined to exportation. Exports came primarilyfrom the coast and the central highlands.

By the mid-19th century, Lima had around 100 000 inhabitants. Lima was the largestcity of Peru, a country of 2 000 000 inhabitants. Limenians conducted a variety ofactivities. In 1858, low skilled workers represented around 40% of the labor force(Zegarra, 2020a); among them, servants,launderers, cooks, laborers and mailmen were relatively important. In addition,artisans accounted for 25% of the labor force of Lima and merchants for 15%. TheState employed around 12% of the labor force of Lima, including military personaland bureaucracy. Some people worked in nearby chakras, but they represented a minorproportion of the labor force of Lima (only 1%).

The Peruvian economy experienced important changes during the 19th century. In the1820s, Independence wars affected the export sector. Exports of minerals fellbetween 1795 and 1830. Civil wars hit the country following Independence. Civil warswere frequent in 1825-1845 (Tantaleán, 2011).The Presidency changed 18 times between 1830 and 1845. Evasion, low levels ofeconomic activity and civil unrest contributed to the limited capacity of the Stateto collect taxes.

The political and economic situation of the country dramatically changed from themid-1840s. Civil wars were less frequent and governments were more stable. Inaddition, Peru started the exportation of guano from the late 1840s (Hunt, 2012). The export sector increasedrapidly in the following years. In particular, the value of exports increased from 9000 000 dollars in 1850 to 31 000 000 in 1860 and 50 000 000 in 1870 (Zegarra, 2018). Economic activity in Limaexpanded. The credit market of Lima increased during the Guano Era (Camprubí, 1957): credit remained below 500 000dollars in 1835-1845, but then increased to nearly 2 000 000 dollars in 1855 (Zegarra, 2016).

Peruvians consumed a variety of foods in the 19th century. Some people consumed muchmeat and bread, whereas others consumed large quantities of maize, legumes andtubers.

In Lima, bread, meat, maize and tubers were widely consumed. In 1839, the annualconsumption of an average Limenian included around 115 kg of bread, 67 kg of meat,55 kg of maize, 43 kg of tubers (potatoes, sweet potatoes and yucas), among otheritems (see table 1). In the late 1860s, theannual diet of artisans in Lima was composed of almost 170 kg of meat, more than 100kg of bread, 63 kg of rice, 42 kg of beans, in addition to lard, sugar and otheritems. Soldiers consumed similar quantities of meat, bread and beans as artisans,but far more tubers, more noodles and less rice. Convicts also consumed largequantities of meat and bread; in addition, they consumed far more potatoes thanartisans and soldiers.5

The consumption of meat in Lima was relatively large for international standards. Forinstance, in modern Europe, a respectable diet of laborers included around 26 kg ofmeat per year (Allen, 2001). The highconsumption of meat in Lima could be explained by a relatively low price of meat.Meat was indeed relatively cheap in Lima compared to London. In 1800-1850, onekilogram of beef in Lima cost around 2.5 times a kilogram of maize, the cheapestsource of calories. In London, in the same period, one kilogram of beef cost aroundfive times a kilogram of oats or barley, the cheapest sources of calories.Certainly, relative prices are not the only possible factor behind the largeconsumption of meat: one could also argue that living standards in Lima wererelatively high.

In the highlands, the diet was different. It seems Indigenous people in Peru rarelyconsumed meat. Hill (1860), for example,indicated that people in Cuzco (in the Southern highlands of Peru) rarely ate meatmore than once a week; and, on the rest of the week, their diets were primarilycomposed of maize and barley.6 Inthe late 1860s, laborers in the highlands consumed meat, but their diets werelargely composed of maize. Potatoes, legumes and bread were also important items intheir diets.

Diets varied according to economic level and social status. As expected, low-incomefamilies consumed smaller quantities of meat and other expensive sources of caloriesthan medium-or high-income families. All over the coast, coolies did not consume asmuch meat as artisans;7 instead,they consumed more rice and legumes. Slaves consumed large quantities of potatoes.Laborers in the highlands also consumed large quantities of potatoes and maize.

Did Peruvians and, in particular, Limenians consumed enough nutrients for a healthylife? To answer this question, I rely on the nutrients’ requirements for ahealthy life and the chemical composition of foodstuffs. People require calories andproteins for survival. In addition, people require fat, iron and vitamins for abalanced nutrition. Requirements of nutrients depend on age, height, weight and typeof occupation. Calorie requirements partly depend on weight. I assume a weight of 55kg for adult men and 50 kg for adult women.8 I also assume a daily energy requirement of 2.2bmr for men and 1.8 bmr for women, which implies heavy workfor men and moderate work for women. A man of 18-30 years of age would then need 3300 kcal calories per day, and a woman in the same age range would need 2 200 kcalcalories per day.9 Following Allen (2017), I rely on Indian dietaryrequirements of proteins, fat, iron and vitamins (Rao, 2009). Since Indian dietary requirements are calculated assuming aweight of 60 kg for men (only slightly more than the weight of Limenians), thoserequirements may be close to the nutrition needs of 19th century Limenians.Therefore, in addition to 3 300 kcal calories, a male adult would require 60 g ofproteins, 38 g of fat, 17 mg of iron, 1.7 mg of thiamine, 21 mg NE of niacin, 1 µgof vitamin B12, 200 µg of folate and 40 mg of vitamin C per day.

Information on the chemical composition of foodstuffs comes from severalsources.10 I adjust theinformation from the composition tables to obtain the actual consumption ofnutrients per purchased kilogram of food. In particular, I take into account thatsome portions of the foods were discarded. Indian dietary requirements take intoaccount the loss of nutrients during cooking (Allen,2017; Rao, 2009).

Let us analyze whether Limenians obtained enough nutrients for a healthy life. In thelate 1830s, Limenians did not consume enough calories. On average, a male adultconsumed 2 700 kcal calories per day. This amount was below the daily requirement of3 300 kcal calories for hard work. In the late 1860s, some consumed enough calories.Artisans, for instance, obtained 15% more calories than needed. Soldiers andconvicts also covered their requirements of calories. Coolies, slaves and laborersin the highlands, however, consumed fewer calories than required. For some people,other nutrients were not ingested in sufficient quantities. For instance, slaves didnot consume vitamin B12, because of the lack of meat in slaves’ diets (as reportedby contemporary accounts). Some diets were also deficient on vitamin C.

Therefore, our calculations suggest that diets varied across locations andoccupations and that not all Peruvians satisfied their nutrition needs.Nevertheless, one must be cautious about these calculations. The information ondiets is scattered. I do not count with detailed information about the diets ofLimenians. For 1839, I estimated the average consumption of foods in Lima. For thatyear, however, it is not possible to determine how diets varied across Limenians.There is information on the diversity of diets in Peru for some occupations for1869, but not for other years.

In the following sections, I opt for a different method to determine whetherLimenians were able to cover their basic needs. In particular, I estimate welfareratios.

In the last two decades, a large number of studies have estimated welfare ratios inorder to determine the capacity of workers to cover the basic needs of theirfamilies. The welfare ratio is calculated as the ratio of total family incomedivided by the cost of subsistence, where the cost of subsistence includes the costof food and other basic expenses. If the welfare ratio is greater than 1.0, then thefamily income is higher than the cost of subsistence. If the welfare ratio is lessthan 1.0, then the family income is lower than the cost of subsistence.

To estimate the cost of food, one needs to assume the composition of the foodbasket at subsistence levels. Most studies usually rely on historical diets inorder to estimate the cost of food of low-income families. Historical dietsconstitute valuable information on consumption patterns. Relying on historicaldiets to estimate the cost of subsistence, however, may be problematic. Onepotential problem is that historical accounts usually do not provide informationon all types of diets, but only on an average diet. Using an average diet for along period may overshadow the differences in diets over time and so bias theresults. On the other hand, when comparing living standards across countries, itis not clear which food baskets should be used. Using the same basket for allcountries may not account for the differences in relative prices and habits.Assuming different diets, however, also involves challenges: it would be hard todetermine whether the different baskets are comparable.11

In addition, one must be careful about the content of nutrients in historicaldiets. If the consumption habits in the past did not grant the intake of allnecessary nutrients for a healthy life, then one must necessarily adjust thosediets. Diets with excessive nutrients may be also problematic: diets withexcessive calories may be relatively expensive. By using an over-expensive foodbasket, one may reach the incorrect conclusion that wages were not high enoughto cover the basic nutrition needs of low-income families.

Foodstuffs vary on the composition of nutrients. Some items provide manycalories. Others provide many proteins and vitamins. Foodstuffs also vary onprice. For instance, meat was far more expensive than maize and tubers in 19thcentury Lima. Considering the differences in prices and in the chemicalcomposition of foodstuffs, it is not clear which basket would be the cheapestform of ingesting all necessary nutrients. Should the subsistence basket includemaize and meats? Should it also include legumes and potatoes?

Linear programming can be very useful to estimate the composition of thesubsistence food basket. By using a linear programming model, one can determinethe quantities of foodstuffs that minimize the cost of food subject torestrictions on nutrients’ intakes.

I use a linear programming model to determine the least-cost food basket of Limain the 19th century. I assume that Limenians could consume the following items:wheat bread, maize, rice, noodles, quinoa, common beans, chickpeas, butterbeans, potatoes, beef, mutton, chicken, lard and sugar.12 I only rely on these goods because of theavailability of price information. Limenians could have also consumed othergoods, but information on prices of other goods is scattered.

The linear programming model can be expressed as follows:

subject to

where $\documentclass {article} \usepackage{wasysym} \usepackage[substack]{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage[mathscr]{eucal} \usepackage{mathrsfs} \usepackage{pmc} \usepackage[Euler]{upgreek} \pagestyle{empty} \oddsidemargin -1.0in \begin{document} $\sum_{j=1}^{N}p_{j}q_{j}$ \end{document}$ is the total cost of the food basket, N isthe number of items in the food basket,pj is the price of goodj per kilogram, andqj is the consumed quantityof good j in kilograms. I impose Krestrictions on nutrients. In those restrictions,αjk is the quantity of nutrientk in a kilogram of product j(k = 1, 2, .., K),FkLis the minimum quantity of nutrient k for a healthynutrition.

Following Allen (2017), I calculated therequirements of nutrients for an average person. To do so, I relied on thedistribution of the population for Lima from the Census of 1876. Requirements ofcalories come from Food and AgriculturalOrganization of the United Nations (1985); requirements of othernutrients come from Rao (2009). Then anaverage person in 19th century Lima would need at least 2,538 kcal calories, 52g of proteins, 33 g of fat, 19 mg of iron, 1.3 mg of thiamine, 16 mg NE ofniacin, 0.7 µg of vitamin B12, 183 µg of folate and 41 mg of vitamin C perday.

Linear programming is not exempted from criticism. The optimal basket may notreflect consumption habits, and habits may be hard to change. In addition,families do not necessarily count with complete information on prices andnutrients. Families also do not rely on a mathematical tool such as a linearprogramming model when selecting their diets. For low-income families, however,relative prices may play a key role (Allen,2017).

Rather than stating that a linear programming model is superior to usinghistorical diets, I argue that both methodologies are complementary. Each methodhas advantages and disadvantages. When using historical diets, welfare ratiosare useful to determine the capacity of families to cover their actualconsumption habits. When using linear programming, welfare ratios are useful todetermine whether the incomes of families could have granted their basic needs,including having a balanced-nutrition diet.

I rely on the linear programming model to estimate the composition of the foodbasket. I assume pj is equal to themedian prices in 1800-1873 for each product in Lima. I take into account therequirements of calories, proteins, fat, iron, thiamine, niacin, vitamin B12,folate and vitamin C. I call the optimal basket the "balanced-nutrition basket"or simply bn basket.

Table 2 reports the balanced-nutritionbasket for an average person. The basket is composed of 239 kilograms ofchickpeas, 15 kg of potatoes and 17 kg of mutton per year. The basket satisfiesall restrictions. The binding constraints are those for calories, vitamin B12and vitamin C. Chickpeas have a large participation in the food basket. Thisresult is not surprising: at median prices of 1800-1873, one gram of silver onchickpeas yielded 2 248 kcal calories, much more than one gram of silver onother foodstuffs. Chickpeas also provided more proteins, iron, thiamine andfolate per gram of silver than other foodstuffs. Meanwhile, the selection ofmutton can be explained by the provision of vitamin B12: one gram of silver onmutton provided 3.8 μg of vitamin B12, whereas one gram of silver on beefprovided 2.6 μg of vitamin B12.

Figure 1 depicts the evolution of the costof the balanced-nutrition food basket per day. The daily food cost for theaverage person was around one gram of silver in the 1800s. It then increasedduring Independence wars, surpassing 1.9 grams of silver in the late 1810s.After Independence, the daily cost of food declined to 1.2 grams of silver inthe early 1830s. It remained around one gram of silver in the late 1840s andearly 1850s. During the Guano Era, however, the food cost increased. In theearly 1870s, the daily cost of food was around two grams of silver per day.

I calculated a single food basket for the entire period of 1800-1873 using medianprices for this period. Food baskets, however, could have changed in response tochanges in prices over time. Are there differences in the food cost whenallowing food baskets to change over time? To answer this question, I estimatethe food basket for each decade, using the median prices of each decade.13 Our estimates show thatchanges in the food basket do not affect the food cost significantly (see figure1). The main differences in the cost of food between the fixed basket and thechanging baskets refer to the late 1810s, late 1830s and early 1840s. Even then,however, the differences in the food cost were not large.

Let us compare the balanced-nutrition food basket (bn basket) and thebaskets from Gootenberg (1990), Arroyo-Abad (2014) and Zegarra (2020a), which partly rely on historical diets (seetable 3). Those studies report foodbaskets for a male adult; for comparison purposes, I converted those baskets tobaskets for an average person. Gootenberg(1990) relies on historical diets to estimate a price index for Lima.Gootenberg’s food basket was not a subsistence basket but was supposed toreflect the consumption habits of artisans. The basket for an average person iscomposed of more than 80 kg of bread and around 130 kg of meat per year. Thisbasket is also composed of dozens of kilograms of rice and beans per year. Thebasket was very expensive: at median prices of 1800-1873, it would cost around3.2 grams of silver per day, equivalent to 2.5 times the cost of the bnbasket. Other studies assume that the food basket was similar to 19thcentury consumption habits (Arroyo-Abad,2014; Zegarra, 2020a). Thosebaskets were more expensive than the bn basket, but cheaper thanGootenberg’s basket.14

Welfare ratios are useful to determine whether families are able to cover their basicneeds. The welfare ratio is calculated as the ratio of total family income dividedby the cost of subsistence, where the cost of subsistence includes the cost of foodand other basic goods and services. I rely on the balanced-nutrition basket tocompute the food cost. I call our welfare ratios "balanced-nutrition welfare ratios"or, simply, bn welfare ratios. If the welfare ratio is greater than 1.0,then the family income is higher than the cost of subsistence. If the welfare ratiois less than 1.0, then the family income is lower than the cost of subsistence.

The subsistence cost includes the cost of food, as well as the cost of fuel,clothing, housing, and other basic items. I rely on the fixed basket (estimated withthe median prices of 1800-1873) to calculate the cost of food. I add the cost offuel, clothing, soap, candles, oil and housing. To estimate the requirement of fuel,I rely on the relation between the quantity of wood and the quantity of food in thebudget of artisans in the late 1860s, as reported by Pardo (1870). I then assume that an average person required 1.79 M BTUof fuel per year.15 In addition, Iassume that an average person required 3 meters of cotton, 1.3 kg of candles, 1.3 kgof soap, and 1.3 liters of oil per year.16 I assume that a family is composed of four members, so thesubsistence cost of a family is four times the cost of an average person. In thecase of Lima, considering that children and adolescents represented almost half ofthe population, the assumption of four members (two adults and two children) in afamily is reasonable.17 Inaddition, I assume that a family rented a room in a callejón. Acallejón (in plural, callejones) was abuilding composed of an alley and several rooms, inhabited by poor families.

Information on salaries of low-skilled workers comes from primary and secondarysources.18 Wages refer tolaborers, doormen, mailmen and servants.19 The appendixdescribes the data sources. For doormen, mailmen and servants, information refers toannual salaries. Information on laborers’ salaries is available from the1800s. For doormen and servants, information on salaries is available from the late1820s; for mailmen, wages are available from the late 1830s. For laborers,information refers to payments for a day of work or jornales. Iassume that laborers could work between 250 and 365 days per year. Several studieshave assumed that laborers worked 250 days per year (Allen, 2001). Other studies, however, have questioned this assumption(Stephenson, 2018). For Lima, I do notcount with information on the number of working days per year. However, since annualincomes of servants were around 250 times the jornal (payment for aday of work) of laborers in most of the period and annual incomes of doormen andmailmen were around 365 times, it is reasonable to assume that the number of workingdays of laborers ranged between 250 and 365.

A possible weakness of the data is that wages refer to government workers. Salariesin the private sector could be different from government salaries. The governmentmay take time to adjust salaries to market conditions. Scattered evidence, however,suggests that, at least in the long term, government salaries reflected marketconditions. For instance, contemporary observers indicate that laborers earnedaround one peso per day in the late 1860s. The data also shows that laborers earnedaround one peso per day in 1867-68.

Figure 2 depicts the evolution of dailynominal wages in grams of silver. For doormen, mailmen and servants, the daily wagewas calculated as the annual labor income divided by 365. For laborers, I calculatedthe daily wage as D times the jornal (payment fora day of work), where D = {250/365, 1}. In the 1800s, 1810s and1820s, laborers earned between 10 and 15 grams of silver per day. Daily wages oflaborers then increased to 11.6-17 grams of silver in the late 1830s, but laterdeclined to 8.6-12.6 grams of silver in the early 1850s. In the following decades,daily wages of laborers increased, becoming 17-24 grams of silver in the early1870s. Meanwhile, daily salaries of doormen declined from 17 grams of silver in the1830s to 15 grams of silver in the early 1840s, but then increased in the followingdecades. In the early 1870s, daily wages of doormen were 22 grams of silver. Wagesof mailmen were similar to those of doormen in the 1850s, 1860s and 1870s. In thecase of servants, daily wages were around 6.5 grams of silver in the 1830s. Salariesthen remained around 10 grams of silver per day in the 1840s and 1850s, butincreased in the 1860s and 1870s. In the early 1870s, daily salaries of servantswere around 14.5 grams of silver.

Welfare ratios are calculated as the total earnings of a family divided by the costof subsistence. I assume that only one male adult worked per family and that workersdid not receive in-kind compensation for their work.20Figure 3 depicts the evolution of thebn welfare ratios (balanced-nutrition welfare ratios). Laborers had awelfare ratio of 1.4-2.1 in the 1800s. The ratio then declined in the 1810s and1820s. In the early 1820s, the ratio ranged between 1.0 and 1.5. The welfare ratiothen increased to 1.6-2.3 in the early 1830s. During the Guano Era, the welfareratio declined to 1.2-1.8 in the early 1850s and 0.9-1.5 in the late 1860s. In thecase of doormen, the welfare ratio was around 1.9 in the early 1830s, then increasedto 2.8 in the early 1850s and later declined to 1.5 in the 1860s and 1.6 in the1870s. Living standards of mailmen were similar to those of doormen. In the case ofservants, the welfare ratio was relatively low. It was below 1.0 in the 1830s,increased to 1.6 in the late 1840s, but then declined in the 1850s and 1860s. In thelate 1860s, the welfare ratio of servants was around 1.0.

In order to estimate welfare ratios, this study uses a linear programming model thatguarantees the intake of basic nutrients. Alternative food baskets could yielddifferent welfare ratios. I then estimate welfare ratios using historical diets. Inparticular, I use the food baskets from Gootenberg(1990), Arroyo-Abad (2014) andZegarra (2020a). I adjusted the foodbaskets, so they reflect the consumption of an average person. I rely on ourinformation on prices and wages and on our assumptions on family size, number ofpeople who worked and number of working days.21Figure 4 depicts the series for laborers,assuming that laborers worked 250 days per year. All series point out at similartrends: an increase in the 1830s and a significant drop in the 1850s and 1860s.Nominal salaries did not change much during the Guano Era in spite of the increasinginflation. Since nominal wages did not increase as rapidly as prices, real wagesdeclined.

Nevertheless, there are important differences in the magnitudes of the welfare ratiosbetween this study and other studies. The bn welfare ratios are usuallyhigher than the ratios estimated using historical diets. When using the basket fromGootenberg, for example, the welfare ratio is less than 1.0, far less than thebn welfare ratios. Using the baskets of Arroyo-Abad (2014) and Zegarra(2020a), the welfare ratio would be below the bn ratios most ofthe time. A comparison of the bn ratios with those for Gootenberg clearlyillustrates the differences between linear programming and historical diets. Asindicated previously, the basket from Gootenberg refers to the typical diet ofartisans. The estimates of bn welfare ratios suggest that the labor incomeof a low-skilled worker allowed him to cover the basic nutrients of his family. Incontrast, the results for the Gootenberg’s basket show that the same labor incomedid not allow the worker to afford the consumption habits of an artisan’sfamily. To afford those consumption habits, low-income families would need anotherperson (such as the wife) to work for a salary.

The bn estimates suggest that living standards did not improve during theGuano Era. Other estimations of welfare ratios also suggest that the livingstandards of low-income families did not increase during this period ofmacroeconomic bonanza (Arroyo-Abad, 2014;Gootenberg, 1990; Zegarra, 2020a). In addition, the evidence on the height oflow-income Limenians supports the hypothesis that living standards did not improveduring the Guano Era. In particular, Twrdek andManzel (2010) collected information on the height of convicts in Lima andfound that height did not increase during the Guano Era. Since those convictsbelonged to the low-income segments of society, the evidence suggests thatlow-income families did not improve their nutrition during the Guano Era in spite ofthe macroeconomic bonanza.

How can one explain the decline of the living standards of low-income families inLima during the Guano Era, a period of economic bonanza?

The Guano Era was a period of substantial economic growth in Lima. From a theoreticalpoint of view, it is possible that the growth of the economy led to the increase ofliving standards of all inhabitants, including low-income families. For instance,laborers and servants could have faced a higher demand for their services, whichwould increase real wages.

Real wages, however, declined. One possible explanation for the decline of realsalaries during the Guano Era is that there were nominal rigidities. Under nominalrigidities, nominal salaries do not increase as rapidly as prices and so real wagesdecline in the presence of inflation. If the expansion of the economy led to theincrease of earnings of high-income families, the higher demand for services couldhave led to higher prices. One might expect workers to require higher nominal wagesto face higher prices. If nominal wages did not change rapidly, real wages wouldhave declined. Nominal rigidities are usually associated with the existence ofcontracts or institutional restrictions. Nominal rigidities may explain a short-termdecline in real wages during inflationary periods. However, it is hard to make atheoretical argument for a negative relationship between inflation and real wages inthe long term.

The increase of terms of trade could also explain at least partly the decline of realwages in Lima during the Guano Era. Standard trade theory states that terms of trademay be correlated with the wage/rental ratio. In particular, the Heckscher-Ohlinmodel states that an increase in terms of trade may lead to a decline in thewage/rent ratio in land abundant economies and an increase in the ratio in laborabundant economies. For economies that export raw materials, a period of economicbonanza, associated with an increase in terms of trade, could be associated with thedecline in the wage/rental ratio. Terms of trade increased in Peru during the GuanoEra. The increase in terms of trade may have increased the demand for productionfactors in export sectors, in particular, in the sectors producing guano, nitrate,sugar and cotton. Since those sectors were intensive in land and capital, theincrease in terms of trade may have increased the overall demand for capital andland and may have reduced the overall demand for labor. The reduction in the demandfor labor in turn would have reduced real wages.

Immigration of workers could also explain the decline in real wages in Lima. Peruexperienced a massive immigration of Chinese coolies in 1849-74, especially in thelate 1860s. By 1876, around 50 000 Chinese citizens lived in the coast of Peru,representing around 4% of the total population. Since most Chinese immigrants wereunskilled workers, immigration could have increased the supply of low-skilled laborand so could have reduced real wages.

Therefore, in the short run the decline in real wages during the Guano Era could bepartly explained by higher inflation. In the long term, however, one would expectreal wages to depend on changes in the demand for labor and supply of labor. Theincrease in terms of trade and immigration of Chinese workers could explain thelong-term decline in real wages of unskilled workers during the Guano Era.

An international comparison of welfare ratios is useful to determine the differencesin living standards across cities and the possible determinants of livingstandards.

No study has used linear programming to estimate welfare ratios for other LatinAmerican cities. I then cannot determine whether welfare ratios in Lima wererelatively high or low for Latin American standards. However, a comparison ofthe trends of welfare ratios across cities can provide useful insights. Inparticular, such comparison may provide some insights about the relationshipbetween real wages and economic growth.

The evidence for 19th century Lima indicates that economic growth is notnecessarily associated with an increase in living standards. Does the evidencefor other Latin American economies point out in the same direction?

In the 19th century, economic growth in some Latin American countries wasassociated with increasing terms of trade, massive immigration and expansion ofthe frontier. As stated by the Heckscher-Ohlin model, increasing terms of tradein Latin America (a land-abundant region) and massive immigration would lead toa reduction in the wage/rental ratio (Arroyo-Abad, 2013; Williamson,1999). The increasing terms of trade would lead to a lower demand forlabor. In addition, immigration may have led to a greater supply of labor. Realwages could have declined due to the lower demand for labor and the greatersupply of labor. However, the expansion of the frontier could reduce orcounteract the effect of terms of trade and immigration on real wages. Thesewere certainly not the only factors affecting real wages in 19th century LatinAmerica. In some countries, civil wars also affected capital stock, the laborsupply, productivity and therefore real wages.

In Argentina, the economy expanded from 1840. As the economy grew, real wagesgrew in Buenos Aires in 1825-1849 (Gelman andSantilli, 2018). Real wages in Buenos Aires continued increasing inthe 1880-1900 (Cuesta, 2012). The growthof the economy occurred at a time of increasing terms of trade. According toArroyo-Abad (2013), terms of trade andfactor endowments affected the wage-rental ratio. Terms of trade could havereduced real wages; but the expansion of the frontier and the consequentincrease in land stock counteracted the negative effect of increase terms oftrade on real wages in the 19th century. In the early 20th century, real wagesremained stagnant. In the 1900s and 1910s, the increase in terms of trade andimmigration probably contributed to the stagnation of real wages (Williamson, 1999).

In Brazil, real wages increased in the 19th century. For instance, real wages inthe Southeast of Brazil increased by almost 200% in 1830-1900. The growth of theeconomy may have led to the increase in the living standards of the poor in the19th century. In the early 20th century, however, the situation changed. Realwages declined by 30% between 1905-1909 and 1920-1924. The increase in terms oftrade and massive immigration probably contributed to the decline in real wages(Williamson, 1999).

In the case of Mexico, real wages declined in 1760-1810 and remained relativelystagnant in 1810-1860 (Challú andGómez-Galvarriato, 2015). In the late 19th century, real wagesincreased. The pacification of the country, the integration of Mexico with theinternational economy and the introduction of new technologies probablycontributed to the increase of real wages (Challú and Gómez-Galvarriato, 2015). Decreasing terms of trade andthe expansion of the frontier probably also contributed to the increase in realwages in the late 19th century (Arroyo-Abad,2013).22

The evolution of real wages in 19th century Lima is consistent with the findingsfor other Latin American economies for the late 19th and early 20th centuries.The expansion of the economy in the region in this period did not necessarilylead to the improvement of living standards. The expansion of the frontier couldhave contributed to the increase in living standards. However, if the expansionof the economy was associated with increasing terms of trade and massiveimmigration, real wages could have declined.

Previous studies have compared living standards of Latin America and Europe. Someportray an unfavorable depiction of living standards in Latin America(relatively low living standards); others provide a favorable portrayal. Somestudies show that welfare ratios in Latin America were below those in London inthe 18th and 19th centuries.23London, however, may not be representative of Europe: some studies indicate thatLondoners had far higher welfare ratios than other Europeans (Allen, 2001).24 In addition, some estimates suggest that in the18th century Spanish America had higher welfare ratios than Leipzig (Arroyo-Abad, Davies and van Zanden, 2012),and that in the 19th century Buenos Aires and Mexico had higher welfare ratiosthan Milan and around the same ratios as Amsterdam and Leipzig.

One problem with those welfare-ratio estimates is that they have been estimatedusing historical diets. One might wonder whether historical diets are comparableacross countries. If they are not, then one should not rely on those ratios todetermine the differences in living standards between Latin America andEurope.

Until now, no study has made a comparison of welfare ratios of Latin America andEurope using linear programming. Recently, I used linear programming to estimatewelfare ratios in six European cities (Zegarra,2021). For four of those cities (London, Amsterdam, Paris andStrasbourg), I estimated welfare ratios for the 19th century. For other twocities (Munich and Leipzig), there is only information for the 17th and 18thcenturies.

In comparison to those London, Amsterdam, Paris and Strasbourg, the welfare ratioof laborers in Lima in the 19th century was not low (see figure 5). Actually,laborers in Lima had similar welfare ratios as laborers in the four Europeancities, including London, in the 1800s. The capacity of working families in Limato cover their basic needs was similar to those cities in Europe. From the1810s, the welfare ratio in London followed an upward trend. Since the welfareratio in Lima did not maintain an upward long-term trend during this period, inthe 1860s London had a far higher welfare ratio than in Lima. Therefore, overthe 19th century, there occurred a divergence in living standards between Limaand London. Nevertheless, living standards in London were not the same as inother cities. Welfare ratios in Amsterdam, Paris and Strasbourg did not followan upward long-term trend in 1800-1870. As a result, living standards in Limawere similar to those cities during this period.

Therefore, our results provide a favorable depiction of living standards in Lima.Living standards were not relatively low in 1800-1870, at least not incomparison with important European cities. One would need further research forother Latin American cities to determine whether in general living standards inLatin America compared favorably to Europe in the 19th century.

Two methodologies can be employed to determine the food basket and estimate welfareratios. Most studies have relied on historical diets to determine the food basket.This study relies on a linear programming model to determine the least cost basketthat granted a balanced-nutrition diet to Limenians. According to the results ofthis study, the balanced-nutrition welfare ratio in Lima was usually above 1.0, sofamilies were able to cover their basic needs.

The results show that the welfare ratio in Lima declined during the Guano Era. Thisfinding is consistent with other studies that also indicate that the livingstandards of the poor declined during the Guano Era, in spite of the macroeconomicbonanza (Arroyo-Abad, 2014; Gootenberg, 1990; Twrdek and Manzel, 2010; Zegarra, 2020a). The results for Lima support the hypothesis that livingstandards do not necessarily increase in response to economic growth. Similarly, inother Latin American countries, real wages did not necessarily increase in responseto the growth of the economy in the late 19th and early 20th centuries. In Peru, aland abundant economy, the increase in terms of trade may have contributed to thedecline in real wages. The immigration of Chinese coolies and domestic inflation mayhave also contributed to the decline in the living standards of the poor.

Nevertheless, in spite of the decline in real wages during the Guano Era, livingstandards in Lima were not relatively low for international standards. Lima hadaround the same welfare ratios as Amsterdam, Paris and Strasbourg in the mid-19thcentury. Although London had higher living standards than Lima, Limenians enjoyedsimilar living standards as working families in important European cities.

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