Openness, lobbying, and provision of infrastructure.

In the lobbying economy, special interest groups make political contributions to influence the government's decision to invest in infrastructure. We study the following scenario: Let there be two income groups in the economy--high and low. Suppose only the high-income group can lobby and earn profits from the industry for good X. In addition, the government can levy taxes only on the high-income group. This is a realistic scenario, because the tax burden is often borne by a small fraction of the population in many developing countries because of several factors, including the existence of a large informal sector, the high cost of administering an effective tax system, and concerns about distributional issues. (31) Auriol and Warlters (2005) provide a related explanation as to why only the rent-earning sector may pay taxes in developing countries. If the government can collect taxes only from the formal sector, it has an incentive to restrict entry into this sector to create rents; these rents can then be captured through taxation. Later we will consider the case in which taxes are imposed on the entire population.

To examine infrastructure investment under lobbying, we adapt the Grossman-Helpman (1994) framework, in which the government maximizes a linear objective function G, given by G = C([k.sub.i]) + [beta][PHI]([k.sub.i]), where C represents lobbying contributions and [PHI] denotes aggregate welfare. The parameter [beta] denotes the weight the government attaches to aggregate welfare. For simplicity, let us assume [beta] to be zero, meaning that the government cares only about its lobbying revenues. Bernheim and Whinston (1986) have shown that there is an equilibrium in this model in which agents behave truthfully; that is, they make contributions equal to the utility they receive from the government's actions. This implies that the contributions G that the government receives will equal the aggregate producer surplus of the lobbyists plus their share of the aggregate consumer surplus, net of their contribution to infrastructure investment. The contributions are given by

G = [[PI].sub.i]+[alpha][[PHI].sub.i] - [k.sub.i] (19)

where [alpha] denotes the fraction of the population that is in the high-income group, [[PI].sub.i] and [[PHI].sub.i] denote aggregate producer and consumer surplus, respectively, and i = 1,2 denotes the open-and closed-economy cases. In other words, contributions equal the profits accruing to the high income group, plus its share of the aggregate consumer surplus and minus its tax payments; and this sum equals the entire cost of infrastructure capital. (32)

Comparing the expression for G in Equation 19 with the objective function of the country social planner under the open and the closed economies (given by Equations 8 and 11, respectively), we observe that the return to investment will be lower under this lobbying scenario. This is because, while G takes into account the entire cost of capital, it includes only part of the consumer surplus.

The marginal return to investment (in either an open or a closed economy) is given by

dG/d[K.sub.i] = 2d[[pi].sub.i]/d[K.sub.i] + [alpha] d[[PHI].sub.i]/d[K.sub.i] - 1. (20)

When the economy is closed, under linear demand, from Equations 20 and 7, we get

dG/d[K.sub.2] = 4(a-[v.sub.2]g([K.sub.2])/9b + 4[alpha](a-[v.sub.2])g([K.sub.2])/9b - 1. (21)

Since [alpha] [less than or equal to] 1, comparing Equation 21 with Equation 18, we see that lobbying leads to underinvestment in infrastructure in the closed economy.

In the open lobbying economy, using Equations 20 and 5, the marginal return to investment is given by

dG/d[K.sub.1] = 8(a-[v.sub.1])g([K.sub.1])/9b + 2[alpha](a-[v.sub.1])g([K.sub.1])/9b - 1. (22)

Comparing Equation 22 with Equation 21, we see that the marginal return to investment and therefore the equilibrium stock of infrastructure will be higher in the open economy under lobbying as well. Also, comparing Equation 22 with the solution for the global social planner given by Equation 18, we observe that there will be overinvestment under lobbying as long as is strictly positive.

However, if [alpha], the proportion of high-income people in the population, is small, then Equations 21 and 22 show that the degree of underinvestment will be large for the closed economy and the degree of overinvestment will be small for the open economy. In other words, for small values of [alpha], the amount of equilibrium stock will be close to optimal in the openeconomy case and less than optimal in the closed-economy case. We can summarize as follows:

PROPOSITION 2. When investment is influenced by producer lobbies and taxes are levied only on the lobbying group, the stock of infrastructure is higher in the open economy relative to the closed economy. There will be underinvestment in infrastructure in the closed economy and overinvestment in the open economy relative to the globally optimal stock. This deviation from the optimal is large in the closed economy and small in the open economy if the lobby members constitute a small fraction of the population.

The implication is that, when income and lobbying power are highly concentrated, the stock of infrastructure may be close to optimal under the open regime but far below optimal under the closed regime; that is, trade rectifies the underinvestment problem associated with a high degree of income concentration. In the closed economy, the full benefits of investment do not accrue to the lobbyist. Only a fraction of the consumer surplus accrues to the high-income group that participates in the lobbying. Therefore, the stock of infrastructure is lower than optimal. The smaller the value of [alpha] (the fewer the members of the lobbying group), the larger is this deviation. When the country is open, the market-stealing effect of investment counteracts the underinvestment that occurs under the closed economy. For small values of [alpha], the two effects may almost cancel each other out and the stock of capital will be close to optimal in the open economy. As [alpha] approaches zero, the stock of capital in the open economy approaches the optimal amount while that in the closed economy moves away from the optimal amount. (33) Conversely, as [alpha] approaches unity (its maximum value), the stock of capital in the closed economy approaches the optimal amount while that of the open economy moves further away from the globally optimal amount. (34)

We now compare the above results to a lobbying economy in which taxes are levied equally on all agents while profits still accrue only to the high-income group, which alone can lobby. The contributions to the government in this case will equal

G = [[PI].sub.i] + [alpha]([[PHI].sub.i] - [K.sub.i]). (23)

Taking derivatives with respect to the stock of capital, we get

d[G.sub.i]/d[K.sub.i] [1/[alpha]] = (1/[alpha]) (2 d[[pi].sub.i]/d[K.sub.i]) + d[[PHI].sub.i]/d[K.sub.i] - 1. (24)

The right side of Equation 24 is just a modified form of d[[PSI].sub.i]/d[K.sub.i], with the weight l/[alpha] attached to the producer surplus term (check Equations 8 and 11). Since l/[alpha] [greater than or equal to] 1, the government attaches a greater weight to producer surplus under this lobbying scenario. Comparing this to the case of the country social planner (obtained by differentiating Equations 8 and 11), it is clear that the marginal return to investment in infrastructure stock will be higher under lobbying compared to the national-planner case in both the open and the closed economies. The high-income group gets a larger fraction of the benefits and shares a smaller fraction of the costs. Therefore, it will lobby the government in favor of overinvestment in infrastructure capital.

Substituting for d[[pi].sub.1]d[K.sub.i] and d[[PSI].sub.i]d[K.sub.i] in Equation 24, we get for the closed economy

dG/d[K.sub.2] 1/[alpha] = 4(a - [v.sub.2])g(K.sub.2)/9b[alpha] + 4(a - [v.sub.2])g([K.sub.2])/9b - 1. (25)

For the open economy, we have

dG/d[K.sub.1] 1/[alpha] = 8(a - [v.sub.1])g/9b[alpha] + 2(a - [v.sub.1])g/9b - 1. (26)

Comparing Equations 25 and 26 suggests that the positive terms on the right side of Equation 25 will be less than or equal to 8(a - [v.sub.1])g/9b[alpha], which is the first term on the right side of Equation 26; therefore, the right side of Equation 26 is greater than that of Equation 25 at any given level of K. Thus, the equilibrium stock will be higher in the open economy.

[FIGURE 4 OMITTED]

Comparing Equations 25 and 26 with Equation 18, we can see that the return to investment is higher compared to the optimal in both the closed and the open economies, since [alpha] [less than or equal to] 1. Therefore, there will be overinvestment in both the open and the closed economies. The gap between the equilibrium stock and the optimal stock will be greater in the open economy than in the closed economy. In this case with lobbying, openness exacerbates the problem of overinvestment. These results are summarized as follows:

PROPOSITION 3. When investment is influenced by producer lobbies, and taxes are levied on the entire population, the infrastructure stock is higher in the open economy than in the closed economy. There will be overinvestment in both the closed and the open economies. The extent of overinvestment is greater in the open economy.