Big State U charges in-state and out-of-state student’s different tuition rates.
ID: 1254466 • Letter: B
Question
Big State U charges in-state and out-of-state student’s different tuition rates. In-state students pay $2,000 a term and respond according to the following demand equation:Qi = 25,000 – 3Ti
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 = 45,000 – 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 instate students? Explain.
c. Assume the school wishes to institute these tuition changes. What might be the response of students? What about state taxpayers?
Explanation / Answer
A) To find Qi and Qo, use substitution. Qi=25,000-3Ti Ti = 2000 Qi=25000-3*2000 Qi = 19000 Qo=45,000-8To To = 4500 Qo = 45000 - 8*4500 Qo = 9000 Price elasticity uses the following formula. E = s*(T/Q), where s is the slope (dQ/dP), T is the price (which is tuition in this case), and Q is enrollment. Ei = si*(Ti/Qi) Ei = -3*(2000/19000) Ei = -0.315789474 Eo = so*(To/Qo) Eo = -8*(4500/9000) Eo = -4 B. Profit is V. Vi = (Ti-MC)*Qi Vi = (2000-3000)*19000 Vi = -19000000 So, already we know that the university is not charging the optimal tuition because profit is negative. Negative profit is never optimal because the university could earn a zero profit just not enrolling instate students. For fun, let's calculate what the optimal instate tuition would be. Vi = (Ti-MC)*Qi Vi = (Ti-2000)*(25000 - 3Ti) Take the derivative of Vi with respect to Ti and set equal to zero. (Ti-2000)*(-3) + (25000 - 3Ti) = 0 -3*Ti + 6000 + 25000 - 3*Ti = 0 6*Ti = 31000 Ti = 31000/6 Ti = $5166.67 So, the optimal instate tuition would be more than double what it currently is. C. What changes? The problem does not explain what the changes would be. Currently, the in-state students are getting subsidized education. That is, their tuition does not cover all of the costs and the remaining costs must be covered by out-of-state students or taxpayers. So, if the change is that they would get a greater subsidy, then students would favor it and taxpayers would oppose it. And if the change is that they would get a lower subsidy or (at the extreme) that the university would profit maximize, then students would oppose the change and tax payers would favor it. The question does not describe a change.
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