Statistics Solutions

(Solution Library) (An intercustomer price discrimination problem) Assume that a monopolist faces two groups of consumers. The first group has a demand

Question: (An intercustomer price discrimination problem) Assume that a monopolist faces two groups of consumers. The first group has a demand function

\[{{P}_{1}}=160-8{{Q}_{1}}\]

The second group has the demand function

\[{{P}_{2}}=80-\frac{1}{2}{{Q}_{2}}\]

The monopolist has the total cost function

\[TC\left( Q \right)=\frac{1}{2}{{Q}^{2}}+4Q\]

where \(Q={{Q}_{1}}+{{Q}_{2}}\).

  1. Determine total revenue from Group i, as it depends on output sold to Group i, i = 1, 2.
  2. Given your answers in (a), determine total revenue that the monopolist derives from both groups.
  3. Given your answer in (b) and TC(Q), determine how much output the profit maximizing monopolist will sell to Group i, i = 1, 2. What prices will the monopolist charge the groups? What will the monopolist's profit be?

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