Question

1 Your firm has two groups of customers that may be distinguished by their slightly different demand characteristics. Demand for type 1 customers: P=500-5q Demand for type 2 customers: P-250-25q, The cost of producing a unit of your firm's product is 100(q+q) A If it is feasible to charge different prices to the two types of customers, what prices should you charge? You are required to show what you are maximizing and how you get to your conclusion. If it is not feasible to charge different prices to the different groups of customers, what price should you charge? You are required to show what you are maximizing and how you get to B. your conclusion

Answer 1

A) Demand for type 1 customers P₁=500-.5q₁

Total revenue TR₁=P₁q₁=500q₁-.5q₁²

and marginal revenue MR₁=dTR₁/dq₁ = 500-q₁

Demand for type 2 customers P₂=250-.25q₂

Total revenue TR₂=P₂q₂=250q₂-.25q₂²

and marginal revenue MR₂=dTR₂/dq₂ = 250-0.5q₂

Cost C=100(q₁+q₂)

MC = 100

Now, for maximization of profit, MR₁=MR₂=MC

or, 500-q₁=100

or, q₁=400

and P₁=500-(.5*400)=$300

Again, 250-.5q₂=100

or, q₂=150/0.5 = 300

and P₂=250-(.25*300)=$175

B) With a single type of customers q=q₁+q₂

or, q=1/0.5(500-P)+1/0.25(250-P) (here P₁₌P₂=P)

or, q = 1000-2P+1000-4P

or, q = 2000-6P

or, P=1/6(2000-q)

or, P=2000/6-q/6

Total revenue TR=Pq=(2000q/6)-(q²/6)

and marginal revenue MR=dTR/dq = 2000/6 - q/3

Now, for maximizing profit, MR=MC

or, 2000/6 - q/3 =100

or, 2000-2q = 600

or, 2q=1400

or, q=700

and P=2000/6-700/6 = 1300/6 = $216.67

C) A monopolist cannot price discriminate if it is unable to divide customers into different sub-markets or if does not want reselling to occur.