Statistics Solutions

(Steps Shown) Consider a market in which 2 firms (1 and 2) sell differentiated goods, with the following demand curves: Q_1=100-4P_1+2.5P_2 , Q_2=75-3P_2+2.5P_1

Question: Consider a market in which 2 firms (1 and 2) sell differentiated goods, with the following demand curves:

\[\begin{aligned} & {{Q}_{1}}=100-4{{P}_{1}}+2.5{{P}_{2}} \\ & {{Q}_{2}}=75-3{{P}_{2}}+2.5{{P}_{1}} \\ \end{aligned}\]

Firm 1 has a marginal cost of $2\unit, and firm 2 has a marginal cost of $3\unit.

  1. Find the Bertrand equilibrium price of each good.
  2. If the two firms were to collude, by how much would total profits increase?

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