Answer to Question #228067 in Macroeconomics for Emy

Question

Suppose a monopolist has TC = 100 + 10Q + 2Q2, and the demand curve it faces is p = 90
- 2Q. (5 marks)
a) the optimum quantity and the optimum price level
b) the profit/loss on these levels
c) at what price should the monopolist shut down?
d) Show the economic profit (loss) of the firm in a graphic representation

Answer 1

a)A pure monopoly maximizes its profit under the condition:

MR=MC

Let's define MC using the formula

MC=TC'=( 100 + 10Q + 2Q2)'=10+4Q

We define MR using the formulas:

TR=PQ=(90-2Q)Q=90Q-2Q^2

MR=TR'=(90Q-2Q^2)'=90-4Q

10+4Q=90-4Q

8Q=80

Q=10

P=90-4Q=90-40=50

b)

Profit/Loss=TR-TC=500-400=100

$TR=10\times50=500$

$TC=100 + 10Q + 2Q^2=100+10\times10+2\times10^2=100+100+200=400$

Profit=100

c) MR<MC

10+4Q>90-4Q

Q>10

Profit/Loss=TR-TC=0

90Q-2Q^2-(100 + 10Q + 2Q^2)=0

-100+80Q-4Q^2=0

Q^-20Q+25=0

Q=18.66 Q=1.33

P=90-4*18.66=15.36

P=90-4*1.33=84.68

d)