Academic journal article Atlantic Economic Journal

# Market Power and Output Stability under Demand Uncertainty

Academic journal article Atlantic Economic Journal

# Market Power and Output Stability under Demand Uncertainty

## Article excerpt

Market Power and Output Stability under Demand Uncertainty

It has been shown by Shaffer [Economics Letters, 1983] that market power has a destabilizing effect on output adjustments under multiplicative shocks to demand such that the market shares of large firms tend to behave in a pro-cyclical fashion. Quite contrary to Shaffer's findings, this note proves that market power tends instead to have a stabilizing impact on output stability, confirming the traditional industrial organization throughts.

Consider an industry facing random shocks to market demand. The output of the ith firm is [x.sub.i] and the total industry output is X = [ZIGMA][x.sub.i.] The stochastic market demand is defined as p = [alpha]p(X), where [alpha] is a positive random variable (with mean value of alpha) reflecting a multiplicatively stochastic shock to market demand, and P' (X) [is less than] O. The total cost function of the ith firm is c=c([x.sub.i]), where c' [is greater than] O and c" [is greater than] O.

The expected profit-maximizing output of the ith firm (denoted as [x.sub.i.sup.*]) then must satisfy the necessary condition: alpha p(X) (1 + [t.sub.i]/[eta] = c' ([x.sub.i.sup.*]), where [eta][=(dX/dp)(p/X)[is less than] O] is the price elasticity of demand and [t.sub.i][= (dX/d[x.sub.i.sup.*]) ([x.sub.i.sup.*]/X) [is greater than] 0] is the conjectural variation elasticity of the ith firm. Note that (1 (Mathematical Expression Omitted) Next, assume as in Shaffer that [eta] and [t. …

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