Question

A monopoly firm is faced with the following demand function p=13_0.5Q the marginal cost function for the firm is given by 3+4Q and the total fixed cost is four

Determine

(a) The profit maximizing output

(b) The level of supernormal output if any

(C) the output level at the break even point

Answer 1

$P= 13-0.5Q$

TR=P.Q

$TR= 13Q-0.5Q^2$

MR=13-Q

MC=3Q+4Q

TC=3Q+2Q$^2$

1) For profit Maximization,

MR=MC

$13-Q=3+4Q$

5Q=10

Q= 2

P=13-0.5(2)= 12

2) Supernormal output

Supernormal print occurs when average revenue is greater than Average total cost

AR=$\frac{13Q-0.5Q^2}Q= 13-0.5Q$

=13-0.5(2)= 12

Ac= $\frac{3Q+2Q^2}{Q}= 3+2Q$

=3+2(2)=7

AR is greater than AC by 12-7= 5

3) Break even output

TR=TC

$3Q+2Q^2=13Q-0.5Q^2$

$2.5Q^2-10Q=0$

$Q(2.5Q-10)=0$

Q=0 0r

2.5Q=10

Q= $\frac{10}{2.5}= 4$