Monopoly
Monopolist Optimizing Price (part 1)- Total Revenue. Starting to think about how a monopolist would rationally optimize profits
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- 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
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