Question

Let the demand curve be Q = 1,000 - 2P

Let the total cost curve be TC = 100 + 0.5Q^2

What is the price charged by the monopolist?

A) $100

B) $250

C) $375

D) $500  

This is all the info I have, so good luck. I don't have an equation for you.

Answer 1

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Answer c) 375 $

The Equilibrium levle of quantity and price  for a monopolist is at the point when MR = MC .

Demand curve is Average revenue curve .
AR = Price

Q=1000-2P
P= (1000-Q)/2
AR = (1000-Q)/2

TR = AR*Q = (1000 Q-Q²)/2
MR curve can be derived by differentating TR equation
MR = d/dQ of (1000 Q-Q²)/2
MR = 1/2 ( 1000-2Q)
= 500- Q

TC = 100 +0.5 Q ²
MC = d/dQ ( 100+0.5 Q²)
= 1Q

At MR = MC,
500-Q = Q
500 = 2Q
Q = 250 units


P= (1000-Q)/2
At Q = 250 units,
P = (1000-250)/2
= 750/2
= 375 $