Answer to Question #289942 in Microeconomics for Jonte

Question #289942

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

1
Expert's answer
2022-01-24T10:48:08-0500

P=130.5QP= 13-0.5Q

TR=P.Q

TR=13Q0.5Q2TR= 13Q-0.5Q^2

MR=13-Q

MC=3Q+4Q

TC=3Q+2Q2^2


1) For profit Maximization,

MR=MC

13Q=3+4Q13-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=13Q0.5Q2Q=130.5Q\frac{13Q-0.5Q^2}Q= 13-0.5Q

=13-0.5(2)= 12

Ac= 3Q+2Q2Q=3+2Q\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+2Q2=13Q0.5Q23Q+2Q^2=13Q-0.5Q^2

2.5Q210Q=02.5Q^2-10Q=0

Q(2.5Q10)=0Q(2.5Q-10)=0

Q=0 0r

2.5Q=10

Q= 102.5=4\frac{10}{2.5}= 4



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