Credence Goods, Misleading Labels, and Quality Differentiation

Abstract

Due to differences in information disclosure mechanisms, consumer misinformation about the quality of many credence goods is more endemic at intermediate levels of the quality spectrum rather than at the extremes. Using an oligopoly model of vertical product differentiation, we examine how consumers’ overestimation of the quality of intermediate-quality products affects firms’ incentives to improve product quality. The firms non-cooperatively choose the quality of their product before choosing its price or quantity. Irrespective of the nature of second stage competition, Bertrand or Cournot, we find that quality overestimation by consumers increases profit of the intermediate-quality firm, and motivates it to raise its product’s quality. In response, the high-quality firm improves its product quality even further but ends up with lower profit. Overall, average quality of the vertically differentiated product improves, which raises consumer surplus. Social welfare increases when the firms compete in prices but falls when they compete in quantities.

Appendix

Equations (15)–(17) and (21)–(23) show that, under both Bertrand and Cournot competition, profit of each firm in the first stage of the game is a function of true product qualities and the misinformation parameter, i.e. $\pi _i (s_b ,s_n ,s_g ,\beta )$ with $i=g,n,b$. The FOC for profit maximization with respect to quality chosen by each firm is

$$\begin{aligned} F_i (s_b ,s_n ,s_g ,\beta )\equiv \frac{\partial \pi _i (s_b ,s_n ,s_g ,\beta )}{\partial s_i }=0 \end{aligned}$$

Totally differentiating the three FOCs and arranging the equations in matrix form, we obtain

$$\begin{aligned} \left[ {{\begin{array}{ccc} {{\partial F_b }/{\partial s_b }}&{} \quad {{\partial F_b }/{\partial s_n }}&{} \quad {{\partial F_b }/{\partial s_g }} \\ {{\partial F_n }/{\partial s_b }}&{} \quad {{\partial F_n }/{\partial s_n }}&{} \quad {{\partial F_n }/{\partial s_g }} \\ {{\partial F_g }/{\partial s_b }}&{} \quad {{\partial F_g }/{\partial s_n }}&{} \quad {{\partial F_g }/{\partial s_g }} \\ \end{array} }} \right] \left[ {{\begin{array}{c} {{ds_b }/{d\beta }} \\ {{ds_n }/{d\beta }} \\ {{ds_g }/{d\beta }} \\ \end{array} }} \right] =\left[ {{\begin{array}{c} {-{\partial F_b }/{\partial \beta }} \\ {-{\partial F_n }/{\partial \beta }} \\ {-{\partial F_g }/{\partial \beta }} \\ \end{array} }} \right] \end{aligned}$$

The above system of three equations can be solved simultaneously using Cramer’s rule to obtain the equilibrium value of $ds_i /d\beta$ as a function of $\beta$. In particular, the sign of $ds_i /d\beta$ indicates the comparative static effect of a change in $\beta$ on the equilibrium value of $s_i$. Given the complexity of equations (15)–(17) and (21)–(23), we obtain large algebraic expressions for ${\partial F_i }/{\partial \beta }, {\partial F_i }/{\partial s_j }$ and $\partial F_i /\partial s_i$, which are not reported in the paper. Instead, we report their values in Table 3 for two alternative values of $\beta$, i.e. $\beta =1$ (misinformation is absent) and $\beta =0.9$ (misinformation is significant). Table 3 shows that the magnitude and, in certain cases, the sign of these partial derivatives depend on (i) the nature of market competition, i.e. Bertrand or Cournot, and (ii) the prevailing level of misinformation. Note that the SOC for profit maximization by firm i requires that ${\partial F_i }/{\partial s_i }<0$.