Market Power Absent Merger Review: Brewing in Perú

Abstract

We examine the extent of market power in the brewing market of Perú, where the absence of preventive merger review eased consolidation into a single industrial brewer. We use a standard oligopoly model and exploit both seasonality in demand and atypically large and frequent variations in the structure and level of excise taxes to identify variations in market power. Our results provide evidence of the ineffectiveness of competition policy as uncontested mergers resulted in a degree of market power that decreased only with the entry of new firms.

Appendix: Measurement of Welfare Changes

The consumer surplus that is calculated from the Marshallian demand function is not an exact measure of welfare change (Vartia 1983, p. 160). The computation of the compensating variation (CV) is based on the Hicksian demand function but, in practice, we can only retrieve information from the Marshallian demand function. Hausman (1981) derives the exact CV for some Marshallian demand specifications with a single price change. However, this method is difficult to implement if the demand function is complex and two or more price changes occur. An alternative is to approximate welfare measures with the use of one-step approximations, which are easy to implement but the precision of the estimates is lower than those of numerical alternatives (Sun and Xie 2013).³⁵

Consequently, we use the numerical approaches that are proposed by Vartia (1983) and Breslaw and Smith (1995).³⁶ Suppose that initial income is $C^{0}$, the Marshallian demand is q(p, C), and the price changes from $p^{0}$ to $p^{1}$. Now divide the change in p into k small steps such that $k=1,\ldots ,n$. Within each partitioned step from $p_{k-1}$ to $p_{k}$, Vartia’s (1983) algorithm first finds a converging ending point $q(p_{k},C_{k})$ at ending price $p_{k}$ and it then approximates the integral of the Hicksian demand as the trapezoidal area between the two prices formed by the initial and ending points. Therefore, the algorithm generates a sequence of $C_{1} \ldots C_{n}$ so that:

$$\begin{aligned} C_{k}=\frac{1}{2}\left( q(p_{k},c_{k})+q_{k-1}\right) \cdot \Delta p_{k}+C_{k-1} \end{aligned}$$

(11)

where $\Delta p_{k}=p_{k}-p_{k-1}$. At step n, the estimator $C_{n}$ converges to the compensated income $C^{1}$ as the number of partitioned steps n increases. The CV is then simply the difference between $C^{1}$ and $C^{0}$.

Breslaw and Smith (1995) apply a Taylor expansion into the expenditure function and use the Slutzky equation to approximate the integral of the Hicksian demand. If the price change $p^{0}$ to $p^{1}$ is also divided into k small steps, this algorithm generates a sequence of $C_{1},\cdots , C_{n}$ so that:

$$\begin{aligned} C_{k}=q(p_{k-1},C_{k-1})\cdot \Delta p_{k}+\frac{1}{2}S(p,C)\cdot \Delta p_{k}^{2}+C_{k-1} \end{aligned}$$

(12)

where $S(p,C)={(\partial q_{k-1}}/{\partial p)}+{(\partial q_{k-1}}/{\partial C)}\cdot q_{k-1}$ is the Slutzky equation. All the parameters can be obtained from an estimated Marshallian demand function. The estimator $C_{n}$ converges to the compensated income $C^{1}$ as the number of steps n increases and the CV is again the difference between $C^{1}$ and $C^{0}$.