Hi Experts (: ! My question is related to profit-maximization for a monopoly. I truly need help !!

Question

Given this information for a monopoly company producing cars :

1. cost of production : 2 million ( 2000 in thousands) w/ nothing to maintain 
2. foreseeable demand : q= 900-150p ( q is the number of drivers (thousands) given the price per driver p)

What would be the profit-maximizing quantity and price?

Thank you in advance (:

Answer 1

1. Monopoly maximizes its profit when its marginal revenue equals marginal cost MR=MC
2. Since you don't have an equation for marginal revenue, you need to create one from the demand equation.
3. In order to do that, first thing is to express the demand equation in form p(q) instead of given q(p), because both MR and MC and price are given in money, not in quantity, and in order to be able to make them equal in the equilibrium.

q=900-150p

1. put 150p on the left side, and q on the right side

150p=900-q

1. divide whole equation by 150

p=6-1/150 q

1. this is now our reverse demand function
2. next thing we need to do is create MR function
3. in order to do that we need to know that in monopoly diagram, MR's slope is always 2 times bigger than slope of the demand curve
4. which means we are going to copy the reverse demand function but we will multiply its slope by 2 (slope is the number multiplying q), and instead of p we write MR

MR= 6 - 2/150 q

MR= 6- 1/75 q

1. now that we have MR function, next thing to do would be to make it equal to MC function:

MR=MC

unfortunately, I do not understand first data you provided about the cost, because cost of production with nothing to mantain means it is a total cost, but I am not sure what happens with this company's marginal cost... so this is where my help stops but if anyone is able to explain how to get MC, all you need to do is solve the equation MR=MC which will give you the result for q, and then plug it in reverse demand function which will give you the answer for p