The name is absent

changes. If we define C [sH (λ)] as the social cost of lobbying, this is clearly increasing
in the lobbying activity.

As an example, let us look at lobbying for export subsidies in the model with
Cournot competition. Under free entry and perfectly substitute goods, assuming that
marginal costs are increasing enough and defining σ = c⁰⁰ (z)z/c⁰ (z) as the elasticity
of marginal cost, the politico-economic equilibrium specific subsidy can be derived as:

1 + λ + λσ(1 — ε)∕ε

1 - λ - λσ

which is clearly increasing and even convex in the weight that politicians give to the
profits of the exporting firm λ. Moreover, the equilibrium subsidy is unambiguously
increasing in σ but, contrary to the optimal subsidy, decreasing in ε for λ or σ large
enough.

Finally, the lobbying activity by the exporting firm determines λ, and this frame-
work provides a simple way to understand the benefits of lobbying for this firm. If the
cost of the lobbying activity to obtain a weight λ in the objective function of politicians
is L(λ), which is assumed increasing and convex, the investment in lobbying will select:
λ to maximize Π^H — L(λ), whose first order condition is(SI + ∏H) sH (λ)= L⁰(λ).
Using the first order condition above we can derive a more informative expression for
the equilibrium lobbying:

~

L0(λ)

C ⁰[sh (λ)]sH (λ)

whose right hand side contains the ratio between the marginal cost of lobbying for
the exporting firm, and the product of the marginal cost of subsidization with the
derivative of the policy with respect to λ, which is just the social marginal cost of
lobbying. The bottom line is that even if there is a strategic incentive to export
promotion, lobbying activity induces excessive export promotion.²⁵ If this distortion
is strong, a commitment to free trade may be optimal for domestic welfare.²⁶

Appendix C: Supporting demand and reducing costs

Many different policies can affect the profits of exporting firms. Imagine some
policy which increases demand for the domestic product and makes it more rigid
relative to the demand for foreign firms. Under quantity competition, the profit of the
domestic firm would be:

∏^H (z, βH,s)=zp (z, βH,s) — c(z)

²⁵However, notice that, if other groups are lobbying the equilibrium may imply a
policy closer to the optimal one, since its costs are born by the all society.

²⁶ One could also study issues of international policy coordination in this framework
(see Alesina, Angeloni and Etro, 2005, and Etro, 2006, for a recent related work). I
will not pursue this here.

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