Question

Big State U charges in-state and out-of-state students different tuition rates. In-state students pay $2,000 a term and respond according to the following demand equation:

Q₁ = 25.000 - 3T i

Where Qi is in-state student enrollment and Ti is in-state tuition. Out-of-state students pay $4,500 a term and their demand is:

Qo = 45000 - 8To

WHere Qo is out-of-state enrollment and To is out-of-state tuition.

a) Calculate the number of each type of student which will enroll and the total enrollment at Big State. Calculate price elasticity for each type of student.

b) Assume the marginal cost for students is $3,000 per student. Is Big State charging an optimal tuition rate for in-state students? Explain.  

c) Assume the school wishes to institute these tuition changes. What might be the response of students? What about state taxpayers?

Answer 1

(a)

For In-state students, when Ti = $2,000:

Qi = 25,000 - (3 x 2,000) = 25,000 - 6,000 = 19,000

For Out-of-state students, when To = $4,500:

Qo = 45,000 - (8 x 4,500) = 45,000 - 36,000 = 9,000

Total enrolment = Qi + Qo = 19,000 + 9,000 = 28,000

For In-state,

Elasticity of demand = (dQi/dTi) x (Ti/Qi) = - 3 x (2,000/19,000) = - 0.32

For Out-of-state,

Elasticity of demand = (dQo/dTo) x (To/Qo) = - 8 x (4,500/9,000) = - 4

(b) Lerner Index (LI) = -1 / Elasticity of demand = (P - MC) / P where P: optimal price

For In-state,

LI = -1 / -0.32 = 3.125

3.125 = (P - 3,000) / P

3.125P = P - 3,000

2.125P = 3,000

P = $1,412

Since actual tuition is less than $1,412, Big State is not charging an optimal tuition rate.

(c) Absolute value of elasticity of demand is lower for In-state than for Out-of-state students (0.32 < 4). Therefore, Big State can increase revenue by increasing the price for In-State students and decreasing the price for Out-of-state students. State tax-payers will benefit from these changes if tax rate is not increased to fund the lower tuition for Out-of-state students.