Question

We are the only Bubble Tea vendor on the IU Bloomington campus. Right now we are charging a price of $4 per bubble tea to all our customers. However, we have noticed that student inverse demand P₁(Q₁) differs from faculty/staff inverse demand P₂(Q₂), as seen by the given weekly demand curves:

Students: P₁(Q₁) = 10 – 0.01Q₁

Faculty/Staff: P₂(Q₂) = 5 – 0.01Q₂

In an effort to increase our profits we are thinking about customizing prices to the two different customer groups (3rd degree price discrimination). I am inclined to lower prices to students as they are always looking for a bargain! But please review both groups' prices and see if you spot any opportunities for enhancing profits. In your review, keep in mind that our marginal costs per bubble tea served are $1.

Answer 1

Inverse demand curve for students : P₁=10-0.01Q₁

Now, total revenue TR₁=P₁*Q₁ = 10Q₁-0.01Q₁²

Then, marginal revenue MR₁=dTR₁/dQ₁ = 10-0.02Q₁

For equilibrium, MR₁ = MC

or, 10-0.02Q₁=1

or, 0.02Q₁=9

or, Q₁=450 units

and P₁=10-(0.01*450) = $5.5

Similarly, inverse demand curve for faculty : P₂=5-0.01Q₂

Now, total revenue TR₂=P₂*Q₂ = 5Q₂-0.01Q₂²

Then, marginal revenue MR₂=dTR₂/dQ₂ = 5-0.02Q₂

For equilibrium, MR₂ = MC

or, 5-0.02Q₂=1

or, 0.02Q₂=4

or, Q₂=200 units

and P₂=5-(0.01*200) = $3

Then profit in price discrimination = P₁Q₁+P₂Q₂-{MC*(Q₁+Q₂)} = (5.5*450)+(3*200)-{1*(450+200)} = 2475+600-650 = $2425