Answer to Question #53342 in Microeconomics for Asif

Question

A study indicated that the average cost function for a high school is
AC=10.3-0.4Q+0.00012Q^2, where Q is the number of students in the school.
a) What size school (i.e in terms of number of students) results in minimum average cost?
b) Find equations for total and marginal cost.

Answer 1

AC=10.3-0.4Q+0.00012Q^2,
a) Such size of school (i.e in terms of number of students) results in minimum average cost, for which AC' = 0, so:
-0.4 + 0.00024Q = 0
Q = 0.4/0.00024 = 1667 students.
b) The equations for total and marginal cost can be found in such way:
TC = AC*Q = 10.3Q - 0.4Q^2 + 0.00012Q^3
MC = TC' = 10.3 - 0.8Q + 0.00036Q^2