Define abbreviations and acronyms the first time they are used in the text, even after they have been defined in the abstract. Abbreviations such as IEEE, SI, MKS, CGS, sc, dc, and rms do not have to be defined. Do not use abbreviations in the title or heads unless they are unavoidable.

Due to weakly separable utility over broad groups of goods, usually we allocate broad group of goods over total expenditure at first; then allocate group expenditure over individual commodities. The extended linear expenditure system (ELES) is based on the basis of the linear expenditure system [2].

The ELES model expression is as follows:

Here, is the annual expenditure of a household spending on goods or services of i-th; and Y is the income of household. According to the model, the could be calculated, is the marginal propensity to consume (MPC).

In economics, the marginal propensity to consume (MPC) is the concept that the increase in personal consumer spending (consumption) occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is called as propensity to consume.

Mathematically, the definition of MPC function is expressed in the following: MPC = ΔC/ΔY, ΔC-the change in consumption; ΔY-the change in disposable income that produced the consumption. Usually, we use the OLS to estimate the MPC like b in function (1).

Deaton and Muellbauer [3] have developed the linear approximate almost ideal demand system (LA/AIDS), which was used to estimate price and income elasticities. The AIDS model only illustrates the axioms of choice, but does reflect preferences and other social and economic factors.

The AIDS demand function used in this study is in the following:

where the w_i is the expenditure share of the ith food or food group, X is living expenditure and Zs are social and demographic variables (preference, household size, coefficient of family burden, income source, region, and so on.), x is the total expenditure, P_j are prices of food group items, and lnP* is a Stone price index. α_i, β_i, γ_ij, α is are parameters to be estimated.

Stone Price Index, that is:

The model must meet the following restrictions:

In practice, the LA-AIDS model is used more frequently than the non-linear AIDS model [4]. The estimates from an LA-AIDS model would approach the estimates for AIDS except for an intercept term.

Expenditure elasticities and Marshallian (compensated) elasticities were com- puted from the estimated parameters of the LA-AIDS model using the close approximation of the exact formulas are given in Equations (3)?(4).

Expenditure elasticities:

Marshallian (uncomensated) price elasticities:

while i = j, δ = 1, or δ = 0.

There are eight commodity groups for the stage of the demand system: food, clothing, housing, family equipment, transportation, education, health care, and other commodities.

From ELES model, the results for the first-stage commodity groups are presented in Table 1. All parameters are significant at the 1% level. Here we just focus on marginal propensity to consume, neglecting the expenditure elasticities and price elastic.

Food: In the urban household, averagely 22% of income is used for food consumption, but for difficult group, the proportion reaches 43%; while the highest income group the proportion is only 15%; from absolute value, the difficult group has less expenditure for food.

Clothing: about 10% of income is used for clothing, and in the lowest group, its proportion is 10%, the proportion for other groups ranges from 6% - 8%.

Housing: comparing with the average level, the difficult group spends 12% income for housing, as is the double times to average level; except the lowest group, its housing proportion is 10%, and the others range 5% to 7%.

Health: the average proportion of health care expenditure is 4%, but difficult group account for 9% from income share.

There is no more different in the consumption tendency of family equipment, transportation, education, and others between different income groups.

Generally, for the lowest group, especially difficult group, lower group have higher share in food, clothing, health and housing expenditure.

The diagonal number in each group of Table 2 indicates the own-price elasticities. The own-price elasticities are negative sign, as show that food demand structure is related to the market price; and the group for low income is more sensitive than other groups, for almost all own-price elasticities are higher than other two groups.

From the cross-price elasticities within the food group have positive signs, implying that major food items have substitute relationship; and the negative cross-price elasticities means the complement relationship.

The second stage consists of six commodities within the food group: grain, meat (pork, lamb, beef, chicken, etc.), egg, aquatic, milk and other food items.

Considering the sample number in the model, the samples are separated into 3 kinds: low group, middle group and high group.

The estimates of expenditure elasticities for commodities in the food group indicate that most of commodities are necessary goods. Grains have the lowest expenditure elasticities, but they are still in the normal good range. The expenditure elasticites for meat is the luxury good to low group, but aquatic, milk and others are luxury goods for all groups.

Source: the authors calculate through models.

Source: the authors calculate through models.