부산대학교 도서관

Differentiated oligopolies under Cournot (quantity) and Bertrand(price) competitions are analyzed in the framework of a one sectorgeneral equilibrium model. There are $n$ firms, $i=1,\dots,n$, eachdeciding supply $q_i$ of brand $i$ under the same cost function$cq_i+f$, where $c$ and $f$ are marginal and fixed costs are measuredin units of labor; and $L$ consumers who have an identical additiveutility function $\sum_{i=1}^n u(x_i)$ over the brands, each supplyingone unit of labor. Given $n$, the authors derive equilibrium mark-upsunder Cournot and Bertrand competitions,$m^C(n)=\frac{1}{n}+\frac{n-1}{n}r_u(x)$ and$m^B(n)=\frac{n}{n-1+r_u(x)}r_u(x)$, respectively, where$r_u(x)=-\frac{x u''(x)}{u'(x)}$ and $x=x^*_1=\dots=x^*_n$ is theequilibrium consumption level of a brand determined by the equilibriumconditions $Lx_i=q_i$, $i=1,\dots,n$, and $c\sum_{i=1}^nq_i+nf=L$, as$x=1/(cn)-f/(cL)$. The term $r_u(x)$, which is identical to Arrow-Prattrelative measure of risk aversion, is interpreted here as Relative Lovefor Variety (RLV) that measures the consumers' preferences for variety.Interestingly, as $f/L$ tends to zero and the number of firms $n$ tendsto infinity, both mark-ups converge to $r_u(0)$; thus, the limiteconomy is competitive if RLV is zero, or monopolistically competitiveif it is bounded away from zero. Free entry equilibria of Cournot andBertrand competitions are also investigated.