Introduction

The egg is a staple food in Mexican diet, is a source of high quality protein, higher than that of milk and meat (^{Torre et al., 2012}); however, it is also considered a food high in cholesterol (^{McGee, 2007}). From the seventies the belief that dietary cholesterol caused an increase in blood colesterol was generated, so recommendations were aimed at reducing egg consumption. But the latest recommendations suggest that moderate intake of this food does not increase the risk of cardiovascular disease (^{IEH, 2009}).

Institutions such as the American Heart Association says that cholesterol from eggs does not pose an added risk for cardiovascular disease, enabling the recommendation of taking one egg a day, instead of the previous recommendation of up to three eggs a week (^{IEH, 2009}). The National Heart Foundation from Australia, notes that can be eaten up to six eggs per week as part of a healthy and balanced diet, including people with diabetes or metabolic syndrome, without this increasing the risk of cardiovascular disease (Heart Foundation, 2014).

For its part, the Spanish Society of Community Nutrition (SENC) in their food guidelines for Spanish population indicate that for a child, person of small, or medium, or inactive size, may be appropriate the consumption of three to four eggs per week while a portly, or physically active person could consume up to seven eggs per week, in the context of a varied and balanced diet (^{IEH, 2009}). Mexico is the main consumer of per capita table eggs worldwide, according to the National Union of Poultry Farmers (UNA) egg consumption per capita in 2014 reached 21.9 kg (^{UNA, 2014}), equivalent to almost a daily egg.

Egg consumption in Mexico in the last three decades (1980-2013), has shown a continuous growth rate of 2.4% (Figure 1). To continue at this rate, it is estimated that by 2030 the per capita egg consumption will reach 32.92 kg per year (about 527 eggs), approximately an egg and a half a day, more than the recommended healthy intake. So it is expected that generic egg consumption per capita will not grow at the pace it had been doing and consumption may stabilize in the coming years. Therefore, the economic strategy for the producer is to take advantage that the differentiated egg market is starting to grow.

Figure 1. National apparent consumption per capita from 1980-2030.* 

Differentiated egg. The egg is a food with high nutrient content, it contains an abundant supply of linoleic acid, minerals, almost all vitamins (except vitamin C) and two plant pigments: lutein and zeaxanthin; once it is cooked, it becomes one of the most complete foods that exist, because cooking deactivate proteins that are not beneficial to the human body (^{McGee, 2007}). A complete removal of egg from diet is a practice that has been done for some years now, but studies and research on the subject, have shown that by not consuming this food in the diet produces more harm than good (^{Carrillo, 2005}).

Countries such as Japan, United States and Canada have decreased their consumption, which according to ^{Rojas (2005)} is because to the consumers from these countries are more concerned about their health, an example of it are the problems associated with cholesterol. Hence, the egg industry has been given the task of designing new types of egg based on these trends (^{Cruz, 2012}). A few years ago started to appear in the market eggs with a higher content of certain nutrients such as the case of omega 3 (mainly EPA and DHA), some minerals, vitamins and precursors from the latter (^{IEH, 2009}).

Another type of differentiated eggs are added with vitamins and trace minerals. The main vitamins that are used to enrich them are: vitamins E, A, D3, folic acid, B12, biotin and B2; among the most used minerals to add to the egg are iron, iodine, manganese, selenium and chromium. The latter can cover between 15 and 60% of the daily needs of a person (^{Torre et al., 2012}). Enriched eggs with lutein and zeaxanthin, help to provide a higher level of carotenoids naturally and with high bioavailability, being of great importance to the organism, mainly for the sight. It has been proven that these pigments protect the eye from damage caused by ultraviolet radiation, reduce the risk of macular degeneration and cataracts. In Latin America, the egg contains about 0.2-0.3 mg of carotenoids, while an enriched egg provides between 0.6 to 0.8 mg, which means it is three times more than a multivitamin (^{Torre et al., 2012}).

There are also differentiated eggs with medical applications. "In this type of eggs, the chicken is exposed to a specific antigen (for example: Escherichia coli) and an immune system to produce antibodies is used, which will not only protect against this bacteria but it will pass the egg the chicken lies. Hhumans who consume these eggs will be protected from E. coli infections immediately; to this protection is known as passive immunity" (Rosales, 2006 cited in ^{Torre et al., 2012}).

In addition to the eggs that are enriched in the market, there are another class of eggs differentiated by the production system like: organic, pastured, free range, to mention the most common. The differentiation of the egg, is not only given from enrichment, modification of certain components or how are produced, but also have been given in terms of health and safety aspects, handling and increased shelf life, adapted to the needs of the consumer. Hence there is another market segment within the egg industry, which is increasing, and is the egg products or processed egg products market. As shown in Table 1, the table egg consumer is willing to pay a higher price for a differentiated egg, of up to three times, but for the moment this market is small but with high growth.

Market development of differentiated eggs in Mexico is recent and hardly participates with 5% of the total supply, however, is increasing (De Regil, 2008 cited by ^{Torre et al., 2012}).

Economic importance. The dynamics of domestic egg production and demand, have been growing steadily. In particular, domestic production has grown as a result of technological improvement: genetic selection, nutrition and health of the laying hens (^{Torre et al., 2012}). This development has increased productivity per hen, by going from 9.14 kg of egg in 1980 to 13.15 kg of egg in 2013. According to projections, egg production (Figure 2) shows that by 2030 production will grow a little more than double (180%) compared to 2015.

Figure 2. Dynamics of production for table egg in Mexico from 1980 - 2030.* 

The business of producing generic egg is no longer an option for small and medium producers. The real price of egg (deflated by the national index of consumer prices 2013) fell on averge from $ 33.80 kg from 1980-1982 to $ 17.11 kg from 2011-2013. A drop close to 50% per average kg. The year of lower real price was 2005 when it reached $ 11.63 kg. The recent price rise has been due to health problems, but once this temporary situation is predictable that the actual price per kg of egg generic will follow downward.

The actual gross revenue of the producer per 100 hens have decreased from 31 254.35 pesos from 1980-1982 to 22 475.41 pesos in 2011-2013, a decrease of 28%, the drop is not as marked as in price due to the productivity per hen increased in the same period by 41%. On average in 2013 a hen laid an egg every 28 h but as can be seen in Figure 3, hen productivity tends to stabilize.

Figure 3. Productivity per laying hen, 1980-2013. 

Gross revenues from small and medium producers will likely continue downward if remain in the generic market egg. The economic strategy of these producers must change and address to a differentiated egg consumer market. The trend in differentiated egg, as it is still a reduced market, is that small and medium producers produce it with preestablished conditions and big brands market it. Bachoco markets the brand Free hen, Airs from the field an organic egg farm.

Large egg producers like Bachoco, San Juan, El Calvario and Poultry Tehuacan, have their main strategy to increase its production of generic egg. The reason is that to maintain real gross income left for example 1 000 hens in 1980, in 2013 the flock had to be 2 200 hens. The laying hen inventory increased from 72 million birds in 1980-1982 to 188 million birds in 2011-2013 this an increase of 2.6 times (Figure 3).

Given the above, egg intake in Mexico is reaching the limit of healthy recommended intake, which will be reflected in a decrease in consumption of this food in certain segments of the population in the coming years, a conscious part of the influence of food is the physical well-being; for reasons of health conditions or even by age; as well as income issues; so the behavior of the demand for this food will not be given to that observed in Figure 1. Considering the benefits of this food given by its nutritional richness, its vast use in the culinary arts and cultural aspect, the demand for this product will grow, but it will only be at the rate of population growth 1.8%, according (INEGI); also, a transition ot its consumption towards a differentiated egg will be given, in other words, with functional qualities that confer the egg the characteristic of not representing a risk factor to health and if posible will provide additional benefits regardless of nutrition.

If this behavior stabilizes, generic egg consumption will affect the production and therefore profits of small and medium producers, representing a problem for the poultry sector. While the growth of output and productivity are present according to estimates, the supply of egg will grow further as demand, impacting in a reduction of egg prices nationwide, being a second factor that will further reduce the profitability of these producers. Since a portion of the Mexican population already reached the limit or exceeded egg consumption for health, consumption will begin to stabilize, and part of the population that already reached the recommended limit of consumption per capita will seek a healthy alternative to continue eating this food, so it will require differentiated egg. Hence the economic strategy to improve the profitability of small and medium egg producers, will be in differentiate the egg and market it through large producers that cater to the already saturated generic egg market (^{Brambila, 2006}).

The objective of the research is to demonstrate that per capita egg consumption in Mexico has already reached its limit of healthy consumption, so the demand for generic egg will go downward, while consumption will begin to move towards differentiated egg.

Materials and methods

The trend in per capita consumption of egg shown in Figure 1, is obtained from a simple projection of the previous growth rate, but it is expected that demand will stabilize, so consumption data for the period from 1980 to 2013 is to be fit to a difference equation of second order linear non homogeneous and moving equilibrium to estimate the per capita amount of egg to be consumed at stabilization. Use of difference equation in this study assumes that per capita egg consumption will stabilize, which should be tested. If generic egg consumption per capita stabilizes, then differentiated egg consumption opens a growing market that is the strategy for small and medium producers.

If the difference equation of second order linear non homogeneous does not tend to moving equilibrium, but on the contrary tends to increase, then the generic market has many years of growth to come. In this way, the central hypothesis of this research is that generic egg consumption tends to equilibrium, this is when stabilized. Apparent consumption per capita (CNAP) has as sources of information SIACON-SAGARPA, FAOSTAT, SIAVI and INEGI in which was obtained anual data at national level on egg production, imports and exports, as well as the number of inhabitants, for the period 1980-2013. CNAP was calculated by subtracting domestic production, export and adding imports and this result is divided by national population. The resulting value is again divided by 1 000 in order to express it in kilograms.

To estimate the function of apparent domestic consumption over time, an difference equation second order linear non homogeneous and moving equilibrium was used, described in ^{Chiang and Wainwright (2006)}. A dynamic analysis was used to determine if, given enough time, the variable apparent per capita consumption (CNAP) tends to equilibrium, therefore in this dynamic model, the trajectory in time of the variable is determined, based on a known pattern of change.

The general solution R (t) for the difference equation of second order, linear, non homogeneous and moving equilibrium, consider the sum of two components, the particular solution (Rp) and complementary solution (Rc).

Particular solution (Rp).

To determine the maximum apparent domestic consumption, the equation was broken [1]:

Where : R_t= apparent domestic consumption with two lags in time; R_t+1= apparent domestic consumption per capita with a lag in time; R_t+2= apparent domestic consumption per capita; a₁, a₂, a₃ and c= are constants; t = is a time index;

To determine the particular solution of the equation [1], the following was done:

IF R(t)= Kt, so R_t+1= K (t + 1) y R_t+2= K (t + 2)

Substituting in [1]:

Solving for K in [2]:

The particular solution of equation [1], also known as moving equilibrium is given by Kt:

Complementary solution (R_c)

The complementary solution parts from establishing the following equation:

That is, it is a reduced solution of equation [1].

In this case, R_c (t) is defined as:

R_c(t)= Ab^t, so R_t+1= Ab^t+1 R_t+2= Ab^t+2

Being as:

Ab^t+2 + a₁Ab^t+1 + a₂Ab^t= 0

Carrying out the cancellation of the term Ab^t:

This quadratic equation has two characteristic roots, each of which is an acceptable solution for Ab^t . Since equation [4] is of second order, then results in two roots b₁ and b₂.

The complementary function is expressed as:

The total function of apparent domestic consumption over time is in terms of the sum of complementary functions (R_c) and the particular solution (R_p):

If b₁ and b₂ are real numbers and in absolute terms minor to one, then by increasing t, b_i tends to zero so the total function tends to moving equilibrium. That is, the function is convergent. If higer bi is negative but less than one, then the function is oscillatory convergent. If bi are greater than one, the function is divergent form moving equilibrium.

A1 and A2 values are obtained by forming two equations based on the known values of CNAP, and time t= 0 and t= 1.

y

Finally, the corresponding values to constants a₁, a₂, a₃ and c, which are used in both particular and complementary solution, were obtained by estimatimating the following linear regression, using the Statistical Analysis System (SAS) statistical package:

Results and discussion

To determine the trajectory in time of apparent domestic consumption; that is, the values of R(t), difference equation of second order linear non homogeneous and mobile equilibrium was used, which required as an input, the previous estimate of the constants used in the particular equation (Rp) and complementary equation (Rc).

The values for the constants, product of linear regression are as follows:

Where Rt+2 is the apparent domestic consumption, Rt+1 as a delayed period in time and Rt period with two delay times.

Thus, equation [8] is expressed as follows:

R_t+2= 4.0723 + 0.5832R_t+1 - 0.0029R_t + 0.1734t

To calculate values from particular equation Rp, it parts from [1], and subtistutes the constants previously obtained, so Rp is expressed as:

To calculate the complementary solution it started from formula [5], which is in terms of b. The result for roots, b1 is 0.5781, and b2 is 0.0051.

Since b1 and b2 values are real and in absolute terms minor than 1, by increasing time, these numbers tend to zero; that is, the function tends to moving equilibrium and is convergent. This shows that the per capita consumption of generic egg tends to stabilize.

Finally it was proceed to estimate the values for CNAP in time R(t), which is the sum of the complementary solution (Rc) and particular solution (Rp):

Substituting values:

Table 3 shows the estimated per capita consumption in the differential equation used. Generic egg consumption per capita tends to stabilize and will grow at the rate that population rise. For example, the annual growth rate of egg consumption from 2010 to 2020 will be according to our estimate of 1.9% and the anual growth rate of population owth is of 1.8%.

The projected per capita egg consumption in Mexico for this study until 2020 will be 24.61 kg per person. With the above it shows that although CNAP continues to increase, the growth rate is declining so generic egg consumption is beginning to stabilize.

So far there are no previous studies on egg consumption trend in Mexico where economic analysis tools are used as in this study, so that future data confirmed the hypothesis of the research.

If per capita consumption of generic egg is going to stabilize, then the economic strategy for small and medium producers is differentiate.

Conclusions

It was shown that has been reached the limit of healthy consumption for generic egg in the country, which is about 24.6 kg per person, this is approximately 5.5 eggs per week.

Differentiated egg represents for small and medium producers the economic strategy to follow; and for consumer an alternative and healthy source of consumption. It is possible to argue that, to the extent that the level of per capita income of consumers increases, will result in increased demand for differentiated egg in detriment of demand for generic egg. The consumer is paying up to 3 times more per kg of differentiated egg, such as organic, natural, with more omega, etc. Also in the market are already differentiated eggs: ligth, vegetarian, enriched with omega-3, vitamins and minerals, organic, free range, yolks and whites liquid, dehydrated egg yolks, and liquid egg; these types of eggs have a higher price to the consumer. It is advisable to research the appropriate technologies that small and medium producers must apply to obtain a differentiated egg.