Question

3. The Mineola Corporation hires a consultant to estimate
the relationship between its profits and its output The consultant reports
that the relationship is

π = -10 – 6Q + 55Q2 – 2Q3 + 025Q4

a The consultant says that the firm should set Q equal to 1
to maximize profit Is it true that dπ/dQ = 0 when Q=1? Is π
at a maximum when Q = 1?

b Mineola’s executive vice president says that the firm’s
profit is a maximum when Q=2 Is this true?

c If you are the chief executive officer of the Mineola
Corporation, would you accept the consultant’s estimate of the relationship
between profit and output as correct?

Answer 1

= - 10 - 6Q+ 55Q2 - 2Q3 + 0.25 Q4

The first order condition for profit maximization is d/ dQ= 0 and the second order condition is d²/dQ² <0

d/dQ = -6 +110Q -6 Q² +Q³ .....(1)

a) from (1) when Q= 1 d/dQ = -6 + 110 -6 + 1 = 99. Thus d/dQ is not equal to 0 when Q=1. THus is not maximum when Q=1.

b) WHen Q=2 from (1) we get d/dQ = - 6+ 110 x 2 - 6x 4 + 8 = 182. Thus profit is not maximum at Q=2.

c) No, the estimation is not correct because the first order condition for profit maximazation cannot be satisfied so maximum profit cannot be determined