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So Let there be two firms with Output Level x1 and x2 .Inverse Demand Function $P=a-bX $ where $ X=x1+x2 $.Both firms have same MC denoted by $c$. Is the Perfectly Competitive O/t > Cournot O/t level ?

Solving: First finding the Cournot o/t levels :.

doing profit max of F1 & F2 and solving the equations and substituting in BR functions i get O/t levels as $x1=x2= \frac{a-c}{3b}$

Now finding Perfect Competitive O/t Levels :

I am stuck with P=MC and cant get ahead from here

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