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
(10)
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.
18
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