Need economics help to Consider an industry consisting of two firms producing an identical product.

Economics
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Consider an industry consisting of two firms producing an identical product.  The inverse market demand equation is P = 2 – Q/2.  The total cost equations for firms 1 and 2 are TC1 = Q1 and TC2 = Q2, respectively. Suppose that the two firms are Cournot competitors.  The equilibrium level of output for firm 1 is:

Dec 20th, 2015

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The profit of Firm P1 = PQ1-Q1 =(2-(Q1+Q2)/2)Q1-Q1 = Q1-1/2 Q1^2-Q1Q2/2 

The profit of Firm P2 = PQ2-Q2 = (P-1) Q2 = (1-(Q1+Q2)/2)Q2= Q2-1/2 Q2^2-Q1Q2/2 

take partial derivative of  dP1/dQ1  and dP2/Q2  and let them = 0, we have 

Q1=Q2 = 2/3 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 20th, 2015

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