If a company can charge the same price to customers from gro

If a company can charge the same price to customers from group A and group B (no price discrimination), what price should it charge, how many units will it sell to each group, and what will profit be prior to considering fixed costs?

Info: Solving for profit maximization and optimal pricing

Marginal cost is constant and is $100 per customer.

The demand equations for each group is:

Group A: Q_a=1000-2P_a

Group B: Q_b=800-P_b

Solution

For A: Qa=1000-2Pa

or, Pa=500-Qa/2

For B:Qb=800-Pb

or, Pb=800-Qb

We know from the question Pb=Pa and at equilibrium Pa=Pb=MC=$100

So, 100=500-Qa/2

or, Qa=800

and Qb=800-100=700