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Consider duopoly where demand is QD = 70 - P and two firms, firm A and firm B, compete against each other a la Cournot by simultaneously choosing quantity. The two firms have identical total cost TC(q) = 10q. Keep in mind that Q = qA + qB.
a) Find firm A's best response function to the quantity qB chosen by firm B and draw it in a diagram where you measure the quantity produced by firm A along the horizontal axis and the quantity produced by firm B along the vertical axis.
b) Find the Cournot equilibrium and illustrate it in your diagram. Keep in mind that your diagram must have a best response curve for firm A and a best response curve for firm B. Suppose firm A discovers a new process that lowers its total cost to TC'A(qA) = 4qA. Total cost at firm B stays the same.
c) At the new Cournot equilibrium, will firm A produce more or less than before? Will firm B produce more or less than before? Will total output be higher or lower than before? Clearly explain.
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