Deriving demand curve from tweaking marginal utility per dollar | Khan Academy

published on July 17, 2020

A few videos ago we saw that we could maximize total utility for our fot given our five dollar spending by calculating the marginal utility per dollar for each incremental dollar we could spend on each of these Goods and then just for each dollar maximizing its over first

Dollar we got a hundred utility points per dollar for that first chocolate bar and that was more than any than the first fruit so that's where we spent it and then we got more for the second chocolate bar than we would have even

For that first pound of fruit so we spent it there then for the third pound for the third bar of chocolate and then it became equal to spend for the for the first pound of fruit so then we spent the next two dollars on that first pound

Of fruit because the price of fruit were two dollars what I want to do in this video is explore what happens when I change the price of the chocolate bars what happens to our marginal utility per dollar over here and what in particular

What happens to the quantity demanded and if you think about where we're at what we're doing is we figured out with one price what was the quantity demanded we demanded three bars if we change the price and we get another quantity

Demanded we're essentially starting to plot out our demand curve and we can actually derive our demand curve from this information right over here so let's see how we could do that so let's now assume let's now assume that our

Chocolate bars are two dollars so now we're going to calculate so this marginal the marginal utility per dollar this applies to both of these columns this is for when it was $100 per bar this is now when it's two dollars per

Bar well for that first bar I'm still getting a hundred points of marginal utility but now it's two dollars so one hundred divided by two 100 divided by two is going to give me 50 marginal utility points per dollar then for that

Next bar I'm going to I get eighty marginal utility points I'm still enjoying it but enjoying it a little bit less but I'm paying two dollars for it so I'm getting eighty divided by two is forty points when you know and I'm just

Giving these arbitrary units forty points per dollar then the third bar is thirty points per dollar then the fourth bar the fourth bar is twenty points per dollar now how would I spend my $5 so let me do

This a little bit let me do it over here so how would I spend my $5 now so my first dollar where would I get the most marginal utility per dollar where would I get the most bang for my buck so my very first dollar I can either buy half

A bar here I could buy half a bar here and I'm assuming that for the sake of for the sake of simplicity let's assume that I get the same marginal utility per dollar for the first half a bar and for the first bar that is kind of constant

Until I get to one entire bar and that's also true for and even if I buy a fraction of the pound here so my first dollar I can't use these numbers this is when the bars roll a dollar per bar now they're two dollars

Per bar this is the reality so now actually it makes sense for me to at least for that first dollar I can buy a half pound of my fruit at a marginal utility per dollar of 60 so I will buy my first dollar will go towards 05

Pounds 05 pounds of fruit of fruit and I'm getting a marginal utility per dollar of 60 now whereas my second dollar going to go my second dollar is going to go well I can still get another half pound out at a marginal utility of

60 I can't remember we have to ignore this right here for the sake of this argument or for the sake of this scenario right now so I can still get another half pound for marginal utility per dollar of 60 so now I buy another I

Buy another half pound of fruit and I my marginal utility per dollar is 60 now where is where is my third dollar my third dollar going to be spent well I could spend it now on I could spend it now at a rate of $100 per 1/2 bar or $2

Per bar for chocolate or $1 per 1/2 bar two dollars per bar for fruit over here so I'm actually neutral so I could spend it let me just for the sake of fun say let's submit it on 1/2

Bar of chocolate half a bar of chocolate and my marginal utility per dollar is fifty is fifty then my fourth dollar my fourth dollar once again I could do a couple of different things here I could buy another half bar because I

Can buy up to a whole bar at this marginal utility per dollar up to a whole bar so why do that so I'll buy another half chocolate bar so now I have a whole chocolate bar and once again I'm able to continue buying that at

fifty-fifty utility units per dollar and then my fifth dollar my fifth dollar over here what would I do with that well I don't want to buy I don't want to buy any more chocolate bars because my

Marginal utility per dollar of the chocolate bar because I've exhausted kind of what I can buy this utility my this utility per dollar so my marginal utility per dollar has gone down now but now I can still buy fruit at that same

50 so now with that dollar since the fruit is $200 per pound I can buy another half pound of fruit for four at a marginal utility per dollar rate of 50 so now I buy another another half pound of fruit at a marginal utility per

Dollar of 50 and you can calculate the whole the entire the the total of marginal utility I got this is a marginal utility per dollar and this is and this is a dollar spent at that marginal utility per dollar so my total

Mard my total utility I should say the marginal utility is the increment but my total utility now is 60 plus 60 is 120 plus 50 plus 50 plus 50 so it's one 120 plus 150 is equal to 270 total utility total utility but even more interesting

Here let's think about the quantity of chocolate bars that I have now bought once the price has gone up I have now bought exactly one chocolate bar so you could say my third and fourth dollars were spent on one bar right over here I

Bought one bar so let's think about it all else equal remember ceteris paribus so we haven't changed the price of fruit we haven't changed consumer preferences which would have changed your marginal utility

Numbers right over here all else equals what happened just when we change the price of chocolate bars and let me write it down so if we just just think about chocolate so if we just think about chocolate bars

So let me write price and quantity when the price was $1 when the price was $1 the quantity demanded the quantity demanded was 50 sighs the quantity demanded was three bars that was the first video we saw on marginal utility

We demanded three bars now when the price now when the price is has gone up to $2 the quantity demanded is exactly one bar is exactly one bar and we could do it everything in between we could we could see what happens if the price was

A dollar fifty or if the price was fifty cents if we actually lowered the price we would see how the how the and there might actually be a situation where you would have to have higher quantities here especially when you lower the price

But by doing that you can you can just using the assuming you have enough rows here and we might not have it if you lower the price but assuming you have the marginal utility at different quantities for the two Goods you can

Figure out exactly how much chocolate someone would buy given different changes in price so we at least have two points for the demand curve now so if we assume that this is price and this is quantity right over here when the price

Was $1 the quantity demanded was three and when the price is $2 the quantity demanded the quantity demanded is one so there we have two points we have two points for our demand curve so our demand curve might look something might

Look something like that but this is all the if it was linear it would go straight it would go something straight like that but we at least have two points on the curve and we could keep trying different prices out using this

Information to figure out the exact to figure out the exact shape of that curve

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