A political economy model of market intervention

Abstract

We argue that political competition based on income redistribution à la Lindbeck and Weibull (Public Choice 52:273–297, 1987) may cause distortive regulation in a competitive sector. For this purpose, we propose a model in which imposing a production quota allows the extraction of rents that are then used for vote-buying purposes. Our model permits us to analyze the response of regulatory policy to political factors, such as the size of a group of informed voters and the accuracy of their information about the incumbent. We also show that the extent of voter influence on policy outcomes is shaped by the state of market demand. In particular, if demand becomes weaker, market intervention increases in a magnitude that depends positively on the electoral weight of informed voters.

Appendix

Proof of Proposition 3.2

Since both candidates are identical, the problem to be solved is symmetric. Therefore, we prove the proposition only for candidate I. The same steps should be followed for candidate O. Observe that in any equilibrium, the constraint $\sum _{i=1}^{n}\delta_{i}^{I}\leq1$ must hold with equality since function EU ^I(.) is strictly increasing in $\delta_{i}^{I}$. Then, the problem to be solved is:

$$\left\{\begin{array}{ll}\max_{ \{ \delta_{i}^{I} \} _{i=1}^{n}} & EU^{I}(\delta^{I},\delta ^{O}) \cr\noalign{\vspace{3pt}}\mbox{s.t.} &\begin{array}{l}\sum_{i=1}^{n}\delta_{i}^{I}=1, \cr\noalign{\vspace{3pt}}\delta_{i}^{I}\geq0, \forall i\in N.\end{array}\end{array}\right.$$

We can write the incumbent’s utility function as:

$$EU^{I}\bigl(\delta^{I},\delta^{O}\bigr)=CS\bigl(X^{I},\theta\bigr)\sum _{i=1}^{n}\frac{1}{r_{i}-l_{i}}+Z^{I}\sum _{i\in J}\frac{\delta_{i}^{I}}{r_{i}-l_{i}}+Z^{I}\sum _{i\in H}\frac{\delta_{i}^{I}}{r_{i}-l_{i}}+K^{O}, $$

(6.1)

where $K^{O}=\sum_{i=1}^{n}\frac {r_{i}}{r_{i}-l_{i}}-CS(X^{O},\theta )\sum_{i=1}^{n}\frac{1}{r_{i}-l_{i}}-Z^{O}\sum _{i=1}^{n}\frac{\delta_{i}^{O}}{r_{i}-l_{i}}$. Then, independently of the value of $\delta_{i}^{O}$, a maximizing strategy for the incumbent consist in setting $\{ \delta_{i}^{\ast I} \}_{i=1}^{n}$ such that $\sum_{i\in J}\delta_{i}^{\ast I}=1$ and $\sum_{i\in H}\delta_{i}^{\ast I}=0$, provided that r _j −l _j <r _h −l _h . The same strategy is optimal for the opposition. In equilibrium, the incumbent’s utility function has the following expression:

$$EU^{I}\bigl(\delta^{\ast I},\delta^{O}\bigr)=CS\bigl(X^{I},\theta\bigr) \biggl( \frac{n_{j}}{z_{j}}+\frac{n_{h}}{z_{h}}\biggr) +\frac{1}{z_{j}}Z^{I}+K^{O}. $$

(6.2)

If we subtract the term K ^O and then divide the resulting terms of the above equation by $( \frac{n_{j}}{z_{j}}+\frac{n_{h}}{z_{h}} )$, we can express the incumbent’s utility as:

$$EU^{I}\bigl(\delta^{I},\delta^{O}\bigr)=CS\bigl(X^{I},\theta\bigr)+\frac {z_{h}}{z_{h}n_{j}+z_{j}n_{h}}Z^{I}.$$

 □

Proof of Proposition 4.1

We compute the total derivative of Eq. (4.3) with respect to variables X ^∗ and θ, and reorder it conveniently to write:

$$\frac{dX^{\ast}}{d\theta}=\frac{- [ \frac{\partial CS^{\prime }(X,\theta)}{\partial\theta}+\frac{k}{n}\frac{\partial\Pi ^{\prime }(X,\theta)}{\partial\theta} ] }{CS^{\prime\prime}(X,\theta)+\frac{k}{n}\Pi^{\prime\prime}(X,\theta)}>0.$$

The term in brackets in the numerator is positive since both u′(.) and Π′(.) are strictly increasing in θ. □