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Two firms A and B produce goods A and B, respectively. The linear demands for the two goods are, respectively, QA=100-4PA+1.5PBQB=120-2PB+0.5PA Production costs are constant

Two firms A and B produce goods A and B, respectively. The linear demands for the two goods are, respectively, QA=100-4PA+1.5PBQB=120-2PB+0.5PA Production costs are constant but not equal: LACA=LMCA=$2LACB=LMCB=$3

  • Using calculus, derive the equations for best response curves.
  • Sketch a graph of the two best-response curves. Label both axes and response curves.
  • If firm A expects firm B to set its prices at $20, what is firm A's best response? If firm B predicts firm A will price good A at $36, what is firm B's best response?
  • What is the Nash equilibrium price and quantity for each firm?
  • How much profit does each firm earn in Nash equilibrium?
  • If firm A and firm B set prices of $22 and $35 respectively, how much profit does each firm earn? Why don't they choose these prices then?

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