Question

In the short term, a MONOPOLY is capable of differentiating, for the same market, two different demand behaviors: (6)

 Q1 = 24 - 0.20P1

 Q2 = 10 - 0.05P2

If the company faces a cost function CTC = 35 + 40Q

i. What price will the company charge if it applies price discrimination? It shows, for each of the previous situations, that the price established by the MONOPOLY allows you to MAXIMIZE PROFITS

ii. Calculate the value of TOTAL BENEFIT

Answer 1

Price Discrimination
Q₁ = 24-0.20P₁                Q₂= 10-0.05P₂
P₁ = 120-5Q₁                     P₂ = 200-20Q₂

Given CTC = 35+40Q, thus MC = $40

i) With price discrimination (P₁ is not equal to P₂)
P₁ = 120-5Q₁                    
MR₁= 120-10Q₁
For profit maximization MR₁ = MC
120-10 Q₁ = 40
   required Q₁= 8 thus the optimum level of production for market 1 is 8 unit
required P₁ = (120-(5*8)) = $80

P₂ = 200-20 Q₂
MR₂= 200-40 Q₂
For profit maximization MR₂ = MC
200-40 Q₂=40
required Q₂= 4 thus the optimum level of production for market 2 is 4 unit
required P₂= (200-(20*4))= $120

ii) total quantity = Q₁ + Q₂ = 8+4= 12 units

So profit with price discrimination = TR₁ + TR₂ – TC
     = (80*8) + (120*4) – {35+(40*12)} =$ 605

Hence, total benefit with price discrimination is $605