Question: Consider an oligopoly in which the inverse demand function is

\[p\left( \sum\limits_{i=1}^{n}{{{x}_{i}}} \right)=a-b\sum\limits_{i=1}^{n}{{{x}_{i}}},\,\,a,b>0\]

and each firm’s cost \(c\left( {{x}_{i}} \right)=c{{x}_{i}}\), \(0<c<a\). First, given n, determine the Cournot-Nash equilibrium output, profit, deviation of price from marginal cost and deadweight loss. Then evaluate the limits of all those as n tends towards infinity. Comment on the significance of your results.