Assume that a monopolist faces two groups of consumers. The first group demand f

Question

Assume that a monopolist faces two groups of consumers. The first group demand function is: P1=160-8Q1. The second group demand function is: P2=80-1/2Q2. The monopolist has the total cost function TC(Q)=1/2Q^2+4Q, where Q=Q1+Q2. A) Determine total revenue from group i, as it depends on output sold to group i, i=1,2 B) Given answer in A, determine total revenue that monopolist derives from both groups. C) 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 monopolist profit be?

Explanation / Answer

Assume that a profit maximizing monopolist faces an inverse demand function given by p(.) where p'(y) < 0, and a total cost function c(.) given by c(y), where c'(y) > 0.Prove that the imposition of a lump sum tax T > 0 does not affect the profit maximizing price and output of the monopolist. Mathematically.So, your profit function that you maximize over y is:Profit=p(.)-c(.)And then to max profit you differentiate with respectto y:d(profit)/dy=p'(y) -c'(y)This is the First Order Condit

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