I have a demand function of Q=100-2p. Marginal Cost is 0. How do I find the price to charge?

Question

I have a demand function of Q=100-2p. Marginal Cost is 0. How do I find the price to charge?

Answer 1

MC=MR. We need to find out what MR is.

TR=p x q. (As the answer above me stated, MR is the derivative of TR in terms of Q, so we need to solve this in terms of q.

p x 100 - 2p = 100p - 2p²

MR = dTR/dQ

= 100 - 4p

4p=100

p=25

Price that should be charged is 25.

Answer 2

MR=MC

TR=p*Q

But we first need to get this in terms of Q, because marginal revenue is the derivative of TR in terms of Q.

2p=100-Q

p=50-Q/2

p*Q=50Q-Q^2/2

MR=dTR/dQ

     =50-Q

MC=0

50-Q=0

Q=50

50=100-2p

2p=50

p=25