Question

The annual inverse demand for a year of studies at UK is

P

(

q

) = 12,000 - 0.15

q

. The marginal cost

is $3,000.

a) What is the profit maximizing tuition rate and how many students enroll?

b) For poorer families, the inverse demand is

P

(

q

) = 8,000 - 5

q

. Is it profitable to offer "need based"

scholarships to poorer families? (Determine new P and Q and think in terms of 3

rd

degree price

discrimination)

Answer 1

Ans:

The profit maximising point would be when P=MR=MC,and writing profit equation

profit = P*Q - MC*Q

=> profit = (12000 - 0.15Q)*Q - 3000Q

differentiating wrt q, to get maximizing point

solving, 12000-0.3Q = 3000

=> Q = 30000

And P = $7500.

Ans b)

Yes, it is profitable to offer "need based" scholarship .

However, on applying 3rd degree price discrimination,

Marginal revenue for group 1 = 12000 - 0.3 Q

Marginal revenue for poor family (group2) = 8000 - 10q

MR(group1) = MC

=> q1* = 30000

so as,

MR(group2) =MC

=> 8000 - 10q2 = 3000

or, q2* = 500

substitute to get prices,

p1* = 7500.

p2* = 5500.

Here, since we have applied prce discrimination of 3rd degree so, organisation enrols 30000 students @ $7500 student and for the poorer families, it enrols 500 students @ $5500 per student. and makes profit!