result, sellers are more willing to engage in a transaction in the first period, while buyers
tend to demand less and this helps to alleviate, rather than exacerbate, the shortage created
by price fixing. The analysis for the case in which P < Pe and there is excessive supply in
the first period is analogous, and the next proposition summarizes our discussion:
Proposition 2 Suppose that the status quo policy is domestic price fixing, combined with an
import quota. Let P be the domestic target price fixed by the government. Then, domestic
cum trade liberalization is efficiency enhancing and Pareto improving if and only if one of
the following two conditions holds:
Pe > P and S0(P) ≥ D(P) (2)
Pe < P and D0(P) ≥ S(P) (3)
Proof. We first establish the sufficiency for condition (3) using Figure 3 as an illustration.
Since Pe < P, demand decreases and supply increases because of arbitrage, and in particular
D0(P) < D(P). Furthermore, given that the demand is larger than the supply, i.e. D0(P) ≥
S(P ), the supply must be binding without liberalization, i.e. D(P) > S(P ). Therefore
Q1d=min{S0(P),D0(P)} ≥ min{S (P), D(P)} =Q
Since the price does not change and the expansion of output is voluntary for both buyers
and sellers at the margin, all agents must be weakly better off. We now turn to the necessary
condition. Suppose that Pe < P , but D0(P ) < S(P ). Then Q1d < Q1 and hence some buyers
will be rationed out as a result of such arbitrage. The same logic applies to condition (2).
QED.
Proposition 2 states that dual track liberalization is both efficiency enhancing and Pareto
improving either when there is excessive supply in the first period but dual track liberalization
leads to a price increase, or when there is excessive demand in the first period but dual track
liberalization leads to a price reduction. Notice that the two scenarios are possible only
because the initial policy distorts not only the price but also the quantity.
As suggested earlier, the scenario analyzed above is a specific version of involuntary ex-
clusion/particiation. More generally, we denote by involuntary exclusion those situations in
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