So, this marginal cost curve is missing the part that first goes down, and

then increases.

But in some sense we can disregard that part, because we know the firm is

never going to produce at the point that is below the average variable cost.

So again, here's a numerical example, downward sloping demand curve,

downward sloping marginal revenue curve, upward sloping marginal cost curve,

so let's go ahead and solve for the monopolist quantity and price.

Finding the profit maximizing output is

setting marginal revenue equal to marginal costs.

In this case, it's 150- 2Q = Q,

or solving for Q we get that the monopolist output is equal to 50.

So suppose this firm is making jeans their monopoly output is where marginal costs

equals marginal revenue, and the firm should go ahead and produce 50 units.

And what is the price?

We have to take this quantity and plug it back into the demand curve,

so that the pm=150-50.

It's equal to $100 per unit.

Graphically what we're doing is we're taking this quantity, plugging it back

into the demand curve, and we get that the price is equal to $100.

This is the profit maximizing output and price.

We can go ahead and calculate profits if we want.

We know that profits are equal to revenue minus total

cost of revenue is 50 times 100 of 5000.

And what our costs?

We're given the total cost curve here, we have the fixed cost of a 1000,

and we have the variable cost which are .5 times a quantity of 50 squared.

And we could go ahead and calculate this if we wish.