Explain why in each answer.
1. Suppose a firm’s profit is given by
the equation p = -200 + 80Q – .2Q2. Which of the following is true?
a) The firm’s marginal profit is given by the equation: Mp = 80 – .2Q.
b) The firm’s profit-maximizing output is Q = 400.
c) The firm’s profit-maximizing output is Q = 200.
d) The firm’s marginal profit is given by the equation: Mp = 80 – 2Q.
e) The firm’s profit-maximizing output is Q = 800.
2. A firm’s total cost function is given by: C = 1,000 + 15Q. At an output of 200 units,
a) Total cost is $4,000 and marginal cost is $3,000.
b) Total cost is $3,000 and fixed cost is $1,000.
c) Total cost is $4,000 and marginal cost is 15.
d) Average total cost is constant.
e) Answers c and d are both correct.
3. A small liberal arts college is trying to predict enrollment for the next academic year. The vice president for business states that enrollment has tended to follow a pattern described by E = 18,000 – .5P, where E denotes total enrollment and P is yearly tuition.
a) If the school sets tuition at $20,000, how many students can it expect to enroll?
b) If the school seeks to enroll 6,000 students, what tuition should it charge?
c) If the school wants to maximize total tuition revenue, what tuition should it charge?
d) As the vice president for business, what tuition would you recommend? Why?
4. University of Notre Dame is a premier institution that draws students from all over the world to its campus. Although it is privately funded, it aspires to world-class quality and reputation, which are enhanced when out-of-state residents enroll. Data suggest that in-state enrollment can be described by the equation:
QI = 25,000 – PI,
where QI = in-state enrollment and PI = in-state tuition. Out-of-state enrollment is given
by: QN = 13,500 – .5PN.
a. If tuition for in-state students is $14,000 and for out-of-state students is $19,000, what is total enrollment and demand elasticity for each type of student?
b. Suppose that the marginal cost to the university of an additional student is $7,000. Is Major University maximizing profit at its current tuition charges? Explain.
c. Because of major funding cuts, the university is expecting to reduce its total enrollment to 11,000 students next year. The university is free to set any tuition charges it wishes. If the goal is to maximize total tuition revenue, what should in-state tuition, out-of-state tuition, and respective enrollments be?