Introduction

The increase in food prices worldwide is due, among other factors, to the increase in the price of fuels necessary for productive activity and the strong economic growth of countries with strong demand for food such as China and India. These countries have about 37% of the world population and presented an annual economic growth rate between 7 and 12% in the last two decades (^{Gandhi and Zhou, 2014}). This has been reflected in an increase in the demand for basic products and an increase in their prices above the usual (^{Jenkis, 2011}). Other factors that influence the price of food are weather phenomena, the use of food as inputs for biofuels, the increase in demand for meat by emerging countries and exchange movements (^{Bekkers et al., 2017}).

The agri-food sector has undergone important changes (^{Vinnari and Tapio, 2008}). In developed countries whose income and well-being have grown, meat consumption represents a smaller share of household spending and the population’s tendency is to consume organic and organic food (^{Poelmas and Rousseau, 2017}). In developing countries, the impoverishment of an important part of the population limits their access to food, including meats (^{Berges and Casellas, 2007}). High food prices affect low-income consumers in these countries (^{Bekkers et al., 2017}).

In Mexico, the income of the population has been affected by the precariousness of wages and the shortage of well-paid jobs. In the period from 1980 to 2016, the minimum wage showed a real decrease of 65%. This situation acquires more importance when observing that 60% of the PEA earns less than 3 minimum wages (^{INEGI, 2015}). As a result, in 2016 there were 53.4 million people (43.6% of the total population) in poverty and 9.3 million people in extreme poverty. In addition, about 62 million inhabitants had an income below the welfare line and 24.6 million had a lack of access to food (^{CONEVAL, 2018}).

The commercial opening has also influenced the meat market in Mexico. The beef cattle ranch was completely liberated upon the entry into force of the North American Free Trade Agreement (NAFTA) between Mexico, the United States of America and Canada, under the assumption that it was a competitive activity. However, in some regions such as the north of the country, livestock activity lacked infrastructure for production and marketing. The use of traditional technology generated low yields and high production costs compared to imported meat from the United States of America whose price was lower (^{Vidaurrazaga and Cortez, 2000}). On the demand side, per capita consumption went from 23 kg in 1970 to 34 kg in 1990 and to 63 kg in 2012 (^{SAGARPA, 2012}).

The decrease in real income in Mexico should cause a decrease in the demand for meat, mainly because the population in poverty does not have access to this type of food. On the other hand, the livestock production was modified with the commercial opening because the small producers did not manage to remain before the imports of cheaper meats, mainly from the United States of America. Therefore, the price of meat is modified affecting the demand. The objective of the article is to determine the effect of prices and changes in income on the demand for meats in Mexico.

To analyze the income-consumption and price-consumption relationship, an almost ideal demand system (AIDS) for meat in Mexico and, based on the parameters obtained, Marshall, Hicksian and income elasticities are obtained. The meats contemplated in this study are beef, pork, chicken, sheep and goat meat. The AIDS model data correspond to the 1980-2016 period and were obtained from the databases of the Food and Agriculture Organization of the United Nations (FAO), the Agrifood and Fisheries Information System (SIACON) of the Ministry of Agriculture, Livestock, Rural Development, Fisheries and Food (SAGARPA) and the Commercial Information System Via Internet of the Ministry of Economy.

Materials and methods

The AIDS model was proposed by ^{Deaton and Muellbauer (1980)}. In the first stage of the model, the consumer assigns his income optimally to the purchase of a group of goods and in the second stage the assigned income is distributed among the different goods (^{Hernández and Martínez, 2003}). The Marshallian demand function expressed in participations on expenditure is given by the following AIDS model.

Where: w_i= It is the participation of the ith good in the group’s expense; i, j= 1, 2, ..., n, n is the total of goods in the subgroup; t= 1, 2, ..., t, t is the total number of observations in the sample; α_i= ordered to the origin; p_jt= prices of goods in the group in period t; γ_ij= price coefficients; β_i= expense coefficients; X_t= total expenditure on the goods considered.

The participation of the ith good in the group’s expense is given by:

P_t= is a Translog price index, whose logarithm is defined by:

Where: p_i, p_j= prices of the goods in the group; α_o, α_k and γ_i = parameters to be estimated.

The homogeneity conditions are considered independent, so the model assumes the basic conditions of, additivity.

Homogeneity.

Symmetry.

The model used has the properties of a first-order approximation to any derivable demand system, with a functional form consistent with the family expenditure data as a flexible representation of any arbitrary demand system (^{Martínez and Vargas, 2004}). To express the model in terms of linear equations, in the parameters the price index given in 2 is replaced by the Stone price index that is defined in equation 3.

Because the Stone index does not satisfy the property of commensurability, the Stone index is replaced by the Tornqvist index, which is an approximation of the dividing index and is superlative for the welfare aggregation function (^{Moschini, 1995}). The Tornqvist index is defined as:

Therefore, the system of linear equations to estimate is the following:

The parameters α_i, γ_ij y β_i were estimated using the generalized least squares method (^{Hernández and Martínez, 2003}).

Results and discussion

Table 1 shows the system of linear equations estimated using the AIDS model. In each row the estimators of the Marshallian demand functions of each meat are presented. The Marshallian demand expresses the participation of each meat in the total expenditure of meat. The estimators α_i, are the ordered to the origin, the estimators ϒ_i, are the coefficients of the prices and β_i are the coefficients of the expense. Below each variable, the approximate standard error is presented and the data with an asterisk is not significant at a 5% significance level.

Table 2 and 3 show the elasticities (Marshallian and Hicksian) price of demand, cross price and expenditure. The values of the main diagonal represent the price elasticity of the demand; that is, the effect of the price of certain meat with respect to itself. The elasticities outside the main diagonal represent the cross-price elasticity of the demand the negative values indicate a complementary relationship between the meats studied, while the positive values represent a substitution relation.

Marshallian demand is obtained under the assumption that the individual maximizes his utility subject to his income; therefore, the elasticity of expenditure or income is presented only in the Marshallian elasticities table. In the eighties the real price of beef was very unstable due to high inflation rates (^{Ferrusquia, 1985}). Domestic producers did not invest in the development of the industry (^{López, 1996}; ^{Palacios, 2002}) and large supermarkets appeared that encouraged the import of bovine meat at a lower price than the national one (^{López, 1996}).

After the 1990s, the policy of reducing subsidies in Mexico (^{Chauvet, 1997}; ^{García et al., 2000}) encouraged imports and economic stability after the 1995 crisis generated a slight increase in consumption. The Marshallian price elasticity for beef is 0.34 and shows that the consumption of this meat is not very sensitive to changes in its price. The Hicksian price elasticity also showed that beef has an inelastic demand (-0.83). In the 1980s, investment in infrastructure for pig production in Mexico was very low (^{Corona, 2006}). Lack of investment encouraged the importation of pork to meet domestic demand.

Imports at low prices discouraged domestic production and slightly promoted consumption (^{García et al., 2004}). The demand for pork meat is inelastic according to the Marshallian price elasticity (-0.80). As of 1996, chicken meat is the most consumed in Mexico (^{Márquez et al., 2004}; ^{Benítez et al., 2010}). The increase in per capita consumption of chicken meat was due to the decrease in its price. The decrease in the price of chicken meat was due to the heavy investment in infrastructure for its production compared to the production of other meats (^{Corona, 2006}). The Marshallian and Hicksian elasticities obtained indicate that the demand for chicken is elastic (-1.13 and -1.17) and allow us to observe that the chicken industry has responded best to changes in the meat market (^{Eales and Unnevehr, 1988}).

Sheepmeat has a Marshallian price elasticity of 0.67 and goat meat of -0.61, which reflects a low response of consumption to changes in their prices. These meats are the least consumed in the world (^{Madruga and Bressan, 2011}) and therefore their inelastic demand is explained. In Mexico, the consumption of sheep meat is higher in the center of the country and the deficit in production is covered by imports from Australia, New Zealand, the United States of America and Chile (Soto and Delgado, 2010).

Goat meat has a high nutritional value (^{Webb et al., 2005}) because it is rich in proteins and with low levels of fat (^{Carlucci et al., 1998}); however, their participation in the consumption of red meats in the world is only 6% (^{Felix et al., 2001}). In Mexico, the share of goat meat consumption is less than 1% within the group of meat analyzed. Goat consumers prefer to consume the meat that is produced in the country (^{Rebollar et al., 2007}) because it is used in traditional dishes such as cabrito, barbecue and birria; for this reason, it is not common to market it in carcass since it is consumed fresh.

Conclusions

In the period from 1980 to 2016 the prices of bovine, porcine, ovine and caprine meat in Mexico were not very sensitive to movements in their prices. This indicates that if the commercial opening influenced on the prices of these meats, the effect was not so severe in the demand. On the other hand, chicken consumption is very sensitive to changes in its price; therefore, the improvements in technology and the commercial opening that cheapened prices were decisive for chicken to become the most consumed meat in the country.

Cross-price elasticities show that the decline in pork consumption was not due to the price of beef because they have a very weak substitution effect. The price of chicken meat is the one that has a greater substitution effect on pork consumption. In the analyzed period, the price of bovine meat practically does not affect the consumption of chicken and pork and the prices of chicken and pork also do not affect the consumption of beef. The foregoing suggests that the price of chicken meat has been decisive in the movement of demand for meat in Mexico; mainly in the decline in the consumption of pork.

These cross-price elasticities also show the low importance of sheep and goat meat in the diet of mexicans, since the prices of these meats do not affect the consumption of chicken, cattle and pigs. Sheep and goat meat are not part of the basic diet of Mexicans, but it is very consumed in special events and days; in this market these meats do have a substitution effect.

The comparison of expenditure elasticities indicates that under a scenario of economic growth and the income of the country’s population, the most benefited sector will be chicken production. An improvement in the level of income would increase the consumption of meat in general and the variations in prices only cause a substitution effect between them. The imports of cheaper meats are not reflected in the consumption, the favoring of the meat industry in the country is determined by the improvement of the living conditions of the population; mainly from the income level.