Question

The annual inverse demand for a year of studies at UK is P(q) = 12,000 - .15q. The marginal cost is $3,000

a. What is the profit maximizing tuition rate and how many student enroll

b. For poorer families, the inverse demand is P(q) = 8,000 - 5q. Is it profitable to offer "need based" scholarships to poorer families? (Determine new P and Q and think in tems of 3rd degree price discrimination)

Answer 1

We have been given the following information

Inverse demand function = P(q) = 12,000 – 0.15q

P = price, and q = output

Marginal cost (MC) = $3,000

Equilibrium is achieved where the marginal revenue (MR) is equal to the MC

Total Revenue (TR) = P×q

TR = 12,000q – 0.15q²

MR = ?TR/?q = 12,000 – 0.3q

MR = MC

12,000 – 0.3q = 3,000

0.3q = 9,000

Equilibrium output (q) = 30,000

P(q) = 12,000 – 0.15q

P = 12,000 – 0.15(30,000)

Equilibrium price (P) = $7500

Now, it is given that inverse demand function for poor families is P(q) = 8,000 – 5q

Marginal cost (MC) = $3,000

Equilibrium is achieved where the marginal revenue (MR) is equal to the MC

Total Revenue (TR) = P×q

TR = 8,000q – 5q²

MR = ?TR/?q = 8,000 – 10q

MR = MC

8,000 – 10q = 3,000

10q = 5,000

Equilibrium output (q) = 500

P(q) = 8,000 – 5q

P = 8,000 – 5(500)

Equilibrium price (P) = $5,500

Yes, it is profitable to offer “need based” scholarship to poorer families.