How Do You Calculate the Profit-Maximizing Price for a Monopolist?

[jose_m]

Homework Statement

For a monopolist's product, the demand equation is:

p = 42 - 4q

and the average-cost function is

c = 2 + (80/q)

Find the profit-maximizing price.

Homework Equations

When i started to solve the problem, i deduced from what i needed to find that I needed to make up a function, plugging in the above functions into profit = (price-cost)quantity.
To what extent I'm correct I'm not sure.

The Attempt at a Solution

I tried plugging it in like this: profit = ((42-4q-2-(80/q)) all that multiplied by q. I don't seem to know if i multiply that whole equation just by q, or by finding a formula for q from those other functions they already gave me. I tried it and it gave me q= 80/(c-2) but then, do i have to substitute c in that formula.

I really don't know where to go from here. would appreciate any help given please.

 

[HallsofIvy]

At maximimum profit, demand= cost. I would have thought that was one of the frst thing you would have learned!

 

[jose_m]

go it solved! thanks for that little fact i did miss. that equals to 4q^2-40q+80, which its derivative is 8q-40, and its critical value is 5, with a maximum of 5. thanks. :D

 

[EnumaElish]

Since this is a monopoly problem, you should be looking to equate marginal cost (MC) to marginal revenue (MR).

Total cost is:

C = Average Cost times q = cq = 2q + 80

MC = C' = 2.

Total revenue is:
R = pq = 42q - 4q^2.

MR = R' = 42 - 8q

MC = MR ===> 2 = 42 - 8q ===> 8q = 40 ===> q = 5, so your answer is correct.