부산대학교 도서관

Differentiated oligopolies under Cournot (quantity) and Bertrand (price) competitions are analyzed in the framework of a one sector general equilibrium model. There are $n$ firms, $i=1,\dots,n$, each deciding supply $q_i$ of brand $i$ under the same cost function $cq_i+f$, where $c$ and $f$ are marginal and fixed costs are measured in units of labor; and $L$ consumers who have an identical additive utility function $\sum_{i=1}^n u(x_i)$ over the brands, each supplying one unit of labor. Given $n$, the authors derive equilibrium mark-ups under 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 the equilibrium consumption level of a brand determined by the equilibrium conditions $Lx_i=q_i$, $i=1,\dots,n$, 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-Pratt relative measure of risk aversion, is interpreted here as Relative Love for Variety (RLV) that measures the consumers' preferences for variety. Interestingly, as $f/L$ tends to zero and the number of firms $n$ tends to infinity, both mark-ups converge to $r_u(0)$; thus, the limit economy is competitive if RLV is zero, or monopolistically competitive if it is bounded away from zero. Free entry equilibria of Cournot and Bertrand competitions are also investigated.