what I want to start thinking about in this video

is giving that we do having monopoly on something in this example in this video

we're going to have a monopoly on oranges

giving that we have monopoly on oranges

and the demand curve for oranges in the market

how to we maximize our profit?

To answer that questions, we're gonna think about our total revenue for different quantities

and from that we're gonna get the marginal revenue for different quantities

and that we can compare that to our marginal cost curve

and should give us a pretty good sense of what quantity we should produce to optimize things

so let's just figure out total revenue first

so obviously if we produce nothing

if we produce zero quantity, we have nothing to sell

we know total revenue is price times quantity

your price is six, your quantity is zero

so your total revenue is going to be zero if you produce nothing

and if you produce one unit

and this over here is actually one thousand ponds per day

we'll call it unit ponds per day

if you produce one unit

then your total revenue is one unit times five dollars per pond

so that will be five times, actually, one thousand

so that will be five thousand dollars

and you can also view it as the area of this rectangle over here

you have the height is the price, and the width is the quantity

but we can that five times

whenever you produce one unit, you gonna get five thousand dollars

so this right over here is in thousands of dollars

and this right over here is in thousands of ponds

just to make sure we are consisted this right over here

let's keep going

so that was this point, when we produce one thousand ponds we get five thousand dollars

if we produce two thousand ponds

and now we are talking about our price is going to be four dollars

or we can say our price is four dollars we can sell two thousand ponds, given this demand curve

and our total revenue is going to be the area of this rectangle right over here

height is price width is quantity

four times two is eight

so if I produce two thousand ponds

then I will get a total revenue of eight thousand dollars

so this is seven and a half, eight is going to put a something right about there

and then we can keep going

if I produce, or if the price is three dollars per pond

I can sell three thousand ponds

my total revenue is this rectangle right over here

three times three is nine thousand dollars

so if I produce three thousand ponds, I can get a total revenue of nine thousand dollars

so right about there, and let's keep going

if I produce, or the price is two dollars per pond

I can sell four thousand ponds, my total revenue is two times four, which is eight thousand dollars

so if I produce four thousand ponds, I can get a total revenue of eight thousand dollars

that should be even with that one right over there, just like that

and then if I produce, or if the price is one thousand dollars

let me use a new color

the price is one dollar per pond I should say

I can sell five thousand ponds

my total revenue is gonna be one times five or five thousand dollars

so it's gonna be even with this here

so if I produce five thousand units I'm gonna get five thousand dollars of revenue

and if the price is zero, the market will demand six thousand ponds per day

it's free, but I'm not gonna generate any revenue because I'm gonna be given this away for free

so I will not be generating any revenue in the situation

our total revenue curve it looks like, if you are taking algebra you recognize this as a downward facing parabola

our total revenue looks like this

our total revenue...easier for me to draw curve with dotted line

our total revenue looks something like that

and you can even solve with algebraically that solve that this is a downward facing parabola

the formula right over here of the demand curve is y-intercept is six

so if I wanna right price as a function of quantity

we have price is equal to six minus quantity

or if you wanna right in a traditional slope intercept form, or "mx plus b" form

and if that doesn't make any sense you might wanna review some of our algebra play

that you can right as P is equal to negative Q plus six

Obviously these are the same exact thing

you have y-intercept of six and you have a negative one slope

if you increase quantity by one, you decrease price by one

or another way to think about it, if you decrease price by one, you increase quantity by one

so that's why you have a negative one slope

so this price as a function of quantity

what is total revenue? well, total revenue is equal to price times quantity

but we can write price as a function of quantity, we did it just now

now this is what it is, or we can rewrite it or we can even be written like this

we can rewrite the price part as... so this is going to be equal to negative Q plus six times quantity

and this is equal to total revenue

and if you multiply this out, you get total revenue is equal to Q times Q is negative Q squared

plus six Q

so you might recognize this, this is clearly a quadratic

since you have a negative out front before the second degree term right over here before the Q squared

it is a downward opening parabola

so it makes complete sense

now I wanna leave you there in this video

because I 'm trying to make an effort not to make my video too long

but in the next video, we're gonna think about is "what is the marginal revenue we get for each of this quantity"

just as a review

marginal revenue is equal to change in total revenue divided by change in quantity

or another way to think about it

the marginal revenue at any one of these quantities, is the slope of the line tangent to that point

and you really have to do a little bit of calculus in order to actually calculate slopes of tangent line

but we'll approximate with a little bit of algebra

but since you want to do is to figure out the slope, so we're gonna figure out the marginal revenue

when we're selling one thousand ponds, so exactly how much more total revenue do we get

if we just barely increase, if we just start selling another a million double ponds of oranges

what's going to happen?

so what we do is we're trying to figure out the slope of the tangent line at any point that you can see that

cause the change in total revenue is this

and change in quantity is that there's

so we're trying to find the instantaneus slope with that ponit

or you can think of it as the slop of the tangent line

and we will continue doing that in the next video

What is the purpose of finding the different between the optimizing price and total revenue?