The Effects of Reforming the Chinese Dual-Track Price System

Differentiating (12) and combining it with the Slutsky equation (3) for each type
of household yields

dp = αxχm _:

dp ∆

dp      -α(p — p)x1_m

dx         ∆

where

∆ = αS +(1— α)S — x_m(x^s — αx)) — (1 — α)x (x_m — x_m) — x^s_p.   (15)

If x¹ ≤ x² and x^s — αx) ≥ 0, then, given that S¹ < 0 and S² < 0, we have ∆ < 0.

mm

Since both types of household face the same market price p, the condition
x¹_m ≤ x²_m holds for many common specifications of preferences. Thus, homothetic
and quasi-homothetic preferences with linear Engel curves have x¹_m = x²_m. Fur-
thermore, much of DTP has been of necessities - for example, many foods and
housing. To the households employed in the non-state sector, without the direct
allocation from the plan-track, those goods may be considered more as luxuries
compared to the households with government subsidy, who pay less for those goods
in money terms. Therefore, we view x¹_m <x²_m as a reasonable assumption, reflect-
ing a concave Engel curve. αx) is the total ration allocated by the central planning
system, which is part of the total supply of X . This gives our next proposition.

21

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