Question

 2) Suppose our duopolists face the market demand: P = 100 – 0.5 Q. The cost 

function for firm 1 is TC1 = 5q1 and for the firm 2, it is TC2 = 0.5(q2)

2. (15 marks)

Using this information find equilibrium price, quantities, and profits if:

a. Duopolists were to behave as perfectly competitive firm

Answer 1

$TR=P\times Q\\=(100-0.5Q)Q\\=100Q-0.5Q^2$

$TC=TC_1+TC_2\\=5Q_1+0.5Q_2$