– Okay. Now let’s go ahead and think about what

a monopolist actually does. So this is going to be

a series of lectures, and I’m going to cover

how a monopolist maximizes profits. And before we really

get into this, we’re going to need to go ahead and get two pieces

of information. One is we need

to use demand data to determine total revenue

at different levels of quantity and the marginal revenue

of different levels of Q. So I’m going to go ahead and do a little example

here for you guys. So what do we mean by all that? Up to now, we have often

looked at the demand curve as a function of the price. We’ve often looked at quantity

demanded as a function of price. Now we’re going to go

the other way around and we’re going to look at price

as a function of quantity. Then we’re going

to use that information to determine total revenue, and then we’re going

to use that information to determine marginal revenue. So let’s suppose

that if we have our monopolist and they decide they want

to sell one unit, they can charge $11 for it. Then if they produce one unit,

their total revenue is $11. And as they went

from zero to one, their revenue went

from zero to 11. So the marginal revenue

of that first unit is one. And let’s suppose

that as they go to two units, they have to cut their price to 10 bucks to be able

to sell the additional unit. So if they produce two units, they’re going to have $20

of total revenue, two times ten. And the marginal revenue

here then is the change in revenue over the change

in the number of units. So marginal

revenue equals change in total revenue

over change in quantity, which in this case is nine. And then if we

have three units produced and that makes us

have to cut the price to $9, then now our

total revenue is 27. And we can see that the marginal

revenue is seven. And one more here,

if producing four means that we have to cut our price

to eight to be able to solve them all, then the marginal revenue

of this fourth one is $5. And you can see that in all

cases, actually, the marginal revenue is less

than the price, and that sometimes

gets a little bit tricky for people

to understand why that is. And the reason is not only

did we sell the second one for $10, we also cut the price

on the first one down to $10. So that’s why we have

the marginal revenue even lower. Likewise, when we go to three, not only did we sell the third

one for $9 instead of $10, we also cut price

on the previous two. So that’s why our

marginal revenue is $9 minus $2 gets us to $7 and so on

and so forth down here. You can see that if we

kept on going this way, we would eventually

get into a situation where we would

have negative marginal revenue because eventually the amount

that we would gain on price from selling one more unit

would be less than the loss, the lower amount that we would

get for the previous units. So as we’re going

to maximize our profit, we need to find out what our total revenue is

for all of our different levels of Q. Once we’ve got that, we’re going to go ahead and match that with

some marginal cost information. So I’m going to go ahead

and set up another example here. Now that you already understand

the concept of marginal revenue, I can go a little

bit faster here. Let’s suppose

that when they sell zero units, that’s consistent

with setting a price of $6. And obviously you get zero total

revenue if you sell zero units. Marginal revenue

doesn’t make sense here because there’s

no previous level to compare to. Total costs of zero units

would be our fixed costs. And let’s suppose

our fixed costs are $4. Marginal cost doesn’t

make any sense here because there’s no previous

level of costs to compare it to. If we have quantity of one, let’s suppose that if we want

to sell one unit, we have to cut our price to $5. That gives us

a total revenue of $5. Marginal revenue is how much

we changed our revenue, and we changed it by $5. And let’s suppose that producing this first unit caused us

to incur $2.50 of costs. So marginal cost was $2.50. And you can see that we

made ourselves better off by producing this first unit

because it added $5 to revenue and it only added

$2.50 to costs. So our marginal profit

on that is $5 minus $2.50 gives us $2.50

of marginal profit. If selling two units means

that we have to cut our price to $4, then our total revenue

of two units is $8. The marginal revenue

of this second unit is $3. And let’s suppose that this one has a lower

marginal cost than the first one because we have some increasing

returns for awhile. Let’s suppose that we know

that it has a $1.50 of marginal costs. Notice I can go ahead

and solve this around. Before I did this one

minus this one gets you there. And so total costs of one

minus total costs of zero gets me the marginal cost

of the first unit. We can also turn that around and go total cost of one

plus marginal cost of the second gets us

to total cost of the second. So I think that is $8. $6.50 plus $1.50 is $8. And this firm is now

breaking even. Just to make things

a little less boring, I’m going to go ahead and make this demand curve start

to change its slope. So to sell that third unit, I have to cut my price

but not by a full dollar here. And so now my total

revenue is three times $3.50 or $10.50 and the marginal

revenue here is $2.50. And let’s suppose this one has

a marginal cost of $1 so that we have total

cost of $9. And notice this third

unit was still profitable to produce because it

added $2.50 to our revenue and $1 to our costs. And now we’re going to go ahead

and say that $3 if we want to sell four units,

$12 of revenue. We have a marginal

revenue here of $1.50. And let’s say we now are going

to have marginal costs of $2 for this fourth unit so that our

total costs go to $11. And you can see

now that this fourth unit was not very profitable for us. It only brought

in $1.50 of revenue, but it had a marginal

cost of $2, so its marginal profit was $.50. So here is

our profit maximizing quantity. Again, just

like with perfect competition, to maximize profits,

we want to produce all the units that have marginal revenue

greater than marginal cost. So the first

unit passes that test. The second unit, $8 is more than $1.50. Yeah,

that passes the test. The third unit, $2.50 is more

than $1 so it passes the test. Third and fourth unit does not

pass the test. So that’s how we’re going

to maximize profits– produce all the units of Q that have marginal revenue

greater than marginal costs, just like with perfect

competition.

Thank you. that helped a lot!