leo4687
leo4687
12.03.2021 • 
Business

Suppose a nonlinear price discriminating monopolist faces an inverse demand​ curve: P = 175 - Q​
and can set three prices depending on the quantity a consumer purchases. The​ firm's profit​ is: ​
pi = P1 Q1 + P2 (Q2 - Q1) + P3 (Q3 - Q2) - mQ3
where p1 is the high price charged on the first units Q1 ​(first block) and p2 is a lower price charged on the next (Q1 - Q2) units and is the lowest price charged on the remaining (Q3 - Q2) units. Q3 is the total number of units actually​ purchased, and m ​= ​$50 is the​ firm's constant marginal and average cost. Using​ calculus, determine the​ profit-maximizing values for p1, p2​, and p3​, and the​ firm's profits.

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