The Effects of Reforming the Chinese Dual-Track Price System

track ration x, while a type-2 household is allocated no ration at all. We also allow
for different endowments of Y being held by the two types.

The representative type-1 household faces the problem

max U (x¹, y¹)
x¹,y¹

subject to px¹ + y¹ ≤ y¹ + (p — p)x ≡ m¹,              (9)

where y¹ is its endowment of Y. Unlike in (1), the budget line is not kinked.
Because resale is possible, household 1 can be thought of as always selling its
entire plan-track allocation to gain the implicit subsidy (p — p)X, and then buying
the amount it wishes to consume. The implicit subsidy is a component of its full
income m¹ .

The problem for the representative type-2 household is

max U (x², y²)
x²,y²

subject to px² + y² ≤ y² ≡ m².

Because a type-2 household does not receive a plan-track allocation of X , its full
income m² is simply its endowment y².

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