Question

A firm’s profit is given by the following function, which maps output q ≥ 0 onto profit (revenue minus cost). π(q) = 11q − (q 2 + 2q + 10) = −q 2 + 9q − 10, The firm is constrained by a quota such that output q cannot be greater than a value Q. (a) What is the domain of this profit function? 1 of 2 ECON10071/20071 - 2020/21 (b) Given this, what is (global) profit maximising output when (i) Q = 6, and when (ii) Q = 2.

Answer 1

a.

$Q=\varepsilon(0.Q)$

b.

i.$if Q=6:\pi(0)=-10,\pi(6)=8,\pi(4.5)=10.5$

global maximizer of profit q=4.5

ii.

if Q=2,producing q=4.5 is not allowed