function

$P=200-Q_A-Q_n$

where $Q_A$ and $Q_n$ are the quantities sold by the respective firms and $p$ is the seiling price, Fotal cost functions for the two companies are

$T{O}_A=1,500+65Q_A+Q_A^2,T{O}_n=1,200+20Q_n+2Q_n^2$

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Assume that the firms form a cartel to act as a monopoliat and maximize total industry profits $($sum of firm A and Firm io profita$),$ in such a case, Company A will produce $$ units and sell at $$

Eimilarly, Company is will produce $$ unite and sell at $$

At the optimum output levels, Company a earns total profits of $$ and Company $6$ earns total profits of $$ Therefore, the total industery profits are $$

At the optimum output levels, the marginal cost of Company A is $$ and the marginal cost of Company $8$ is $$ firm's output will not change$),$

$\backslash$table$[[$Coumot Equilibriom$],[,\backslash$table$[[$Price$],[(4)]],\backslash$table$[[$t$],[(,$ enitis$)]],\backslash$table$[[$Drofits$],[(*)]]],[$Company A$,145,30,300],[$Company $0,149,25,075],[$total industey,,$55,4975]]$

Assume that two companies $($ A and B $)$ are duopolists who produce identical products. Demand for the products is given by the following linear demand function:

$P=200-Q_A-Q_B$

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Assume that the firms form a cartel to act as a monopolist and maximize total industry profits $($sum of Firm A and Firm B profits$).$ In such a case,

$q,T{C}_A=1,500+55Q_A+Q_A^2$

Assume that the firms form a cartel $to$ act $as$ a monopolist and maximize

Company A will produce

$T{C}_B=1,200+20Q_B+2Q_B^2$

$$ units and sell at $].$

Similarly, Company B will produce

$]$ and Company B earns total profits of $$ Therefore,

At the optimum output levels, Company A earns total profits of

$].$ the total industry profits are $[$

At the optimum output levels, the marginal cost of Company $A$ is $$ and the marginal cost of Company $B$ is $.$

The following table shows the long$-$run equilibrium if the firms act independently, as in the Cournot model $($i$.$e$.,$ each firm assumes that the other firm's output will not change$).$

$\backslash$table$[[\backslash$table$[[$Cournot Equilibrium$],[$Price$],[($$$)]]],[\backslash$table$[[$Output$],[($units$)]],\backslash$table$[[$Profits$],[($$$)]],,],[$Company A$,145,30,300],[$Company B$,145,25,675],[$Total Industry,,$55,$$$975$