Question

The inverse demand curve a monopoly faces is

p equals 100 minus Upper Qp=100−Q.

The​ firm's cost curve is

Upper C left parenthesis Upper Q right parenthesis equals 50 plus 5 Upper QC(Q)=50+5Q.

What is the​ profit-maximizing solution?

The​ profit-maximizing quantity is

​(Round your answer to two decimal​ places.)

The​ profit-maximizing price is

​

​(round your answer to two decimal​ places.)

Answer 1

Answer

TR=P*Q
P=100-Q
TR=(100-Q)Q

MR=dTR/dQ(First derivative of the Total revenue)

MR=100-2Q

TC=50+5Q

MC=dTC/dQ(First derivative of the Total cost)

MC=5

MC=MR is the profit-maximizing level of output

MR=MC
100-2Q=5
2Q=100-5
Q=95/2=47.5

Substituting this into the inverse demand equation P=100-Q
P=100-47.5=52.5

Thus the profit-maximizing quantity is 47.5 units and the profit-maximizing price is $52.5