# Cournot’s duopoly

Consider the following Cournot’s duopoly, where two identical ﬁrms compete by setting quan-tities. Suppose the Market demand is P = 80 − 2Q and ﬁrm’s cost function is TC = 20qi. (a) Determine ﬁrm’s equilibrium quantity, proﬁt and the market equilibrium price. Explain. (b) Now suppose that ﬁrm 1 can set the quantity ﬁrst. Find each ﬁrm’s equilibrium quantity, proﬁt and equilibrium price. Explain. (c) Let’s get back to the Cournot’s model. Suppose ﬁrms decide to form a cartel. In the static (one-period) case, will they be able to sustain the cartel? Explain using the appropriate pay-oﬀ matrix. (d) How will your answer to part (c) change if you consider the inﬁnitely-repeated game? Show all your work! (Hint: you will need to ﬁnd the range of values for the discount factor)

P(1)

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