Dual Track Reforms: With and Without Losers

Figure 4: Price control and involuntary participation/exclusion

liberalization is also efficiency-enhancing. A similar argument can be made with respect to
the case when P^e < P and D^f(P ) > Se(P ). We conclude:

Proposition 3 Suppose that the government sets the price with infra-marginal agents par-
ticipating in the exchange involuntarily. Then anticipated dual track liberalization is Pareto
improving if and only if one of the following holds:

a. P^e > P and Se⁰(P ) ≥ D^f(P)

b. P^e < P and D^f0(P ) ≥ Se(P)

Proof. The argument is identical to the proof of Proposition 2 once we redefine D as D,
and S as Se.                                                                 QED.

Considering Figure 4, if Se⁰(P) < D^f(P), the transaction in the first period will decrease
when the liberalization is anticipated. Consequently, some additional users will be rationed
out in the first period and hence made worse off. They will be made worse off in the
second period as compared to the status quo because they have to pay the free-market
price P^e > P if they choose to transact. This means that a Pareto improvement cannot be
achieved. However, the liberalization could remain efficiency enhancing, since the efficiency
gains from removing involuntary participation can be arbitrarily large.

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