Rural Urban Income and Consumption Gaps across Provinces of China, 1978-2008

Huge gaps exist and are widening between the rural and urban income and consumption across 32 provinces of China despite very impressive rates of growth of GDP in the last three decades. By pursuing rapid urbanisation and export oriented strategies Chinese policy makers seem to have switched away from the equality oriented linear model of optimal consumption to urban biased inequality tolerating non-linear model of consumption since 1978. Inequality problem will worsen further unless export oriented growth strategies are accompanied by domestic consumption based growth policies.


Introduction
The GDP of China grew at around 9.8 percent in the last three decades. Chow (2010) attributed these growth rates to total factor productivity (TFP), capital formation and very high elasticity of output to capital input. The growth rate of TFP was 3 percent, the ratio of investment to GDP was above 30 percent and the elasticity of output to capital was 0.6. However, the fruits of growth have not been equally distributed among people living in rural and urban areas. As shown in Table 1 population, consumption and income have grown faster in urban than in rural areas. Earlier Rui and Li (2007) and Chien-Hsun (1994) had highlighted on how the higher growth rate has brought sharp rural urban differences in income and consumption among provinces and regions of China. Limitations in the scale and scope of existing redistribution schemes has created enormous gaps between the rich and poor though the government seem to have subsidies or guarantees for food, housing, health and education for rural and urban residents in place. Capital accumulation, emphasised as the major source of economic growth in China after the formation of the Chinese Communist Party in 1949, was compromised during the Cultural Revolution and the Great leap forward. It was re-emphasised by export and urban focused growth strategy since 1978. New policies have resulted in unbalanced growth of income and consumption in rural and urban areas of china as rural areas are facing permanent negative income and consumption shocks relative to urban areas (see trends in Figures 1 and 2).

Analytical Structure
We try to explain features of consumption and income equality in China before 1978 with a linear model. Then we turn to a non-linear social welfare function to explain inequality tolerating and urban biased behaviour and attitudes of policy makers in recent years.

Linear Model of Equality
Linear model contains N 1 urban and N 2 rural households with C 1 and C 2 levels of consumptions related to corresponding income with share parameters as: Value of consumption is assumed to be the same for both types of households. National income (Y) and consumption (C) are aggregate of these two: In this scenario the central communist party believed in perfect equality among people, therefore the objective of the national government was to maximise the aggregate When consumption levels are proportionate to population between rural and urban areas the optimisation results in equality as (see derivation in the appendix): This implies perfect equality between rural and urban households. Since this objective did not produce enough growth it was abandoned after 1978. Provinces were allowed to grow at different speeds resulting in different levels of income to rural and urban residents. Social welfare function seems to have become non-linear since then.

Non-Linear Social Welfare Function with Inequality
Chinese government adopted export oriented growth strategy and abandoned its policies of equality under the cultural-revolution in 1978. Weights assigned to rural and urban economic activities changed; more preference was given to the urban sector that could promote exports. This change in attitudes of policy makers can be summarised using a nonlinear objective function subject to the resource balance condition of the economy as following: Optimal shares or the rural and urban consumption from this non-linear model are (see derivations in the appendix): Three different policy conditions could be analysed from these results.
Communism: when β α = . This is ideal situation, both rural and urban consumption receive equal weight in policy maker's objective function.

Empirical Evidence
We find empirical evidence on above theoretical propositions α and β from the time series data for the 30 different provinces of China for 1978 to 2008 available from the Chinese Statistical year book (www.stats.gov.cn) as summarised in Tables 2 and 3

Conclusion
There are huge and widening gaps between the rural and urban income and consumption across 32 provinces of China. Chinese policy makers switched to a non-linear optimisation model of consumption pursuing rapid urbanisation and export oriented growth strategy since 1978. Rural areas are becoming poorer relative to urban ones and likely to be so in coming years unless export oriented growth strategies are accompanied by domestic consumption based growth strategies as proposed in the linear optimisation model of consumption.

Appendix I
A. The first order conditions for optimisation for linear model: