Chapter 3 The Model
3.4 The Quota Regime
∂
∂ ∧
ta D ta
q SW
τ (16) Consider the relationship between optimal tariff and constrained domestic capacity when the domestic capacity constraint is binding,
3 0 1 ˆ
ˆ*
<
−
∂ =
∂
ta
qD
τ (17)
Eq. (17) shows that if the constrained domestic capacity is relieved, the optimal tariff will decrease.
Proposition 2: In the tariff regime,
(1) From the perspective of social welfare optimization, the government will levy lower tariff when the domestic capacity constraint is binding than that of non-binding;
(2) If the tariff is relative high, tariff reduction may improve social welfare. When the domestic capacity is constrained, the effect of tariff reduction will decrease as the level of capacity increases;
(3) If the constrained domestic capacity is relieved, the optimal tariff will decrease.
3.4 The Quota Regime
Suppose the government imposes a fix imported amount (quota), qFquo, on foreign agriculture products. Since the situation of both domestic capacity constraint and quota are non-binding is equivalent to free trade, the results is the same as Eq. (4). There are three other possibilities in the domestic market: (1) domestic capacity constraint is binding, quota is non-binding, (2) domestic capacity constraint is non-binding, quota is binding, and (3) both domestic capacity constraint and quota are binding.
3.4.1 Domestic capacity constraint is binding, quota is non-binding
Assume that the maximum domestic capacity is qˆDquo, 0≤qˆDquo≤α/3. At Stage
23
2DandF engage in quasi-Stackelberg competition under the condition of domestic capacity constraint is binding and import quota is non-binding. The objective functions of D and F are
Solve Eq. (18), obtained4
4
At Stage 1, the social welfare is
8 If the binding domestic capacity is changed, the relevant effects are shown as
4 0
3.4.2 Domestic capacity constraint is non-binding, quota is binding
Assume that the government imposes the imported product a maximum quantity limit, say qFquo, 0≤qFquo≤α/3. At Stage 2, D and F engage in quasi-Stackelberg competition under the condition of domestic capacity constraint is non-binding and import quota is binding. The objective functions of D and F are
Solve Eq. (22), obtained5
4 Refer to footnote 3.
2
At Stage 1, the social welfare is
2 2 If the binding quota is changed, the relevant effects are shown as
4 0 the social welfare will increase when binding constrained domestic capacity is relieved or is further limited the binding quota.
Proposition 3: In the quota regime, the social welfare will increase when
(1) the binding constrained domestic capacity is relieved as quota is non-binding;
(2) the binding quota is further limited as domestic capacity constraint is non-binding.
3.4.3 Both capacity and quota are binding
Suppose the domestic producer has a maximum capacity limit , and the government imposes the imported product a maximum quantity limit
quo maximization under the condition of both domestic capacity constraint and import quota are binding. The objective functions of D and F are
25
Since both of the domestic capacity constraint and imported quota are binding, and
quo
qˆD qFquo are mutual independent variables, but D and F are still affected by the other competitor’s output because the other competitor’s output will influence the market price ~pquo =α−qˆDquo−qFquo. If the binding factors are changed, the market price may change
At Stage 1, the social welfare is
2 If the domestic capacity constraint is relieved or the government releases extra quota to foreign importer under the condition of both of the domestic capacity constraint and imported quota are binding, the social welfare will be improved, shown as Eq. (29).
0
Compare the contribution to social welfare of the two binding variables,
ˆ 0
Eqs. (29) and (30) can be concluded as Proposition 4.
Proposition 4: In the quota regime, if the domestic capacity constraint and quota are both binding,
(1) both of the relieving domestic capacity and releasing more quota will increase social welfare;
(2) relieving domestic capacity can contribute more to social welfare than that of releasing more quota.
3.4.4 Comparative static analysis with respect to binding quota
Comparative static analysis with respect to qFquo while domestic capacity constraint is non-binding and binding.6
1. Domestic capacity constraint is non-binding
From Eqs. (23) and (24), the comparative static analysis with respect to qFquo is derived as
2. Domestic capacity constraint is binding
Because binding,qˆDquo and qFquo are mutual independent variables, a changingqFquo can only affect market price p~quo and then affect π~ , Dquo π~ and social welfare. From Eqs. (26) Fquo and (28), the comparative static analysis with respect to qFquo is derived as
0
qF in the case of domestic capacity constraint is non-binding; Whereas, in the case of the domestic capacity constraint is binding, from Eq. (32), ∂SW~ quo/∂qFquo =qFquo >0. Because the range of quota is 0≤qFquo≤α/3, the optimal quota is the same, qFquo*=α/3. Proposition 5: In the quota regime, the optimal quota is α/3 in both the cases of domestic capacity constraint are non-binding and binding, the same as free trade regime.
6 If the import quota qFquo is non-binding, the foreign importer will decide its optimal quantity according to
27
3.4.5 Compare the difference between quota regime cases and free trade regime 1. market price
3 0
2. domestic profit
9 0
3. foreign profit
9 0
4. social welfare
6 0
Observe Eqs. (33)~(36), the results can be concluded as Proposition 6.
Proposition 6: In the quota regime, comparing with free trade regime,
) , ( I O
(1) the market price in all cases is greater than or equals to free trade regime;
(2) the profit of the binding parties is less than or equals to free trade regime, while the profit of the non-binding parties is greater than or equals to free trade regime;
(3) the social welfare in all cases is less than or equals to free trade regime except in the case of domestic capacity constraint is non-binding and quota is binding.
In Proposition 6 (3), in the case of domestic capacity constraint is non-binding and quota is binding, the domestic producer will produce more output and then accrue more profit than those of free trade regime (i. e. part of foreign products are shifted to domestic producer).
Naturally, the social welfare in the case of domestic capacity constraint is non-binding and quota is binding will be greater than or equal to the social welfare in the free trade regime.