find marginal cost and invesrse demand curve

Question

A monopolist faces a cost function equal to 

C(Q) = 10Q + 2

and a demand function of 

Q^D(P) = 250 -P

what is the monopolist's marginal cost curve?

what is the inverse demand curve that monopolist faces?

Answer 1

Marginal cost (MC) is just the partial derivative with respect to q of the total cost function, which is given as:

C(Q) = 10Q + 2

so

MC = 10

Inverse demand function is found by rearranging the demand function so its P = whatever.

So after rearranging the function, the inverse demand function is:

P = 250 - Q

You didn't ask, but to find MR, just take the partial derivative of the total revenue function: which is TR = P * Q

So, TR = 250Q -Q²

and MR = 250 - 2Q