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# Deriving demand curve from tweaking marginal utility per dollar

## Video transcript

A few videos ago we saw
that we could maximize total utility given our $5 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 it. Our 1st dollar, we got 100
utility points per dollar for that first chocolate bar and that was more than any than the first fruits, so that's where we spent it. Then we got more for the 2nd chocolate bar for that 1st pound of fruit, so we spend it there. Then for the 3rd pound or
for the 3rd bar of chocolate. Then it became equal to spend
for the 1st pound of fruit so then we spent the next $2
on that 1st pound of fruit because the price of fruit were $2. 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? In particular, what happens
to the quantity demanded? If you think about what we're doing it, we figured out with 1 price what was the quantity demanded, we demanded 3 bars. If we change the price and we get another quantity demanded, we're essentially starting
to plot our our demand curve and we can actually
derive our demand curve from this information right over here. Let's see how we could do that. Let's now assume that our
chocolate bars are $2. Now we're going to calculate. The marginal utility per dollar, this applies to both of these columns. This is for what it was $1 per bar, this is now when it's $2 per bar. Well, for that first bar,
I'm still getting 100 points of marginal utility, but now it's $2. So 100 divided 2 is going to give me 50 marginal utility points per dollar. Then for that next bar, I get 80 marginal utility points. I'm still enjoying it but
enjoying it a little bit less but I'm paying $2 for it. I'm getting 80 divided by 2 is 40 points, you know, and I'm just
giving these arbitrary units, 40 points per dollar. Then the 3rd bar is 30 points per dollar. Then the 4th bar is 20 points per dollar. Now, how would I spend my $5? Let me do this a little bit, let me do it over here. How would I spend my $5 now? My first dollar, where
would I get the most marginal utility per dollar? Where would I get the
most bang for my buck? My very 1st dollar, I can
either buy half a bar here, I could buy half a here and I'm assuming that,
for the sake of simplicity let's assume that I get the same marginal utility per dollar
for the 1st half a bar and for the 1st bar. That is constant until
I get to one entire bar. That's also true for, and
even if I buy a fraction of the pound here. My 1st dollar, I can't use these numbers, this is when the bars
were a dollar per bar, now they're $2 per bar.
This is the reality. Now actually it makes
sense for me to, at least, for that 1st dollar I can
buy a half pound of my fruit at a marginal utility per dollar of 60. My 1st dollar will go
towards .5 pounds of fruit and I'm getting a marginal
utility per dollar of 60. Where is my 2nd dollar going to go? Well, I can still get another half pound at a marginal utility of 60. Remember, we have to
ignore these right here for the sake of this argument or for the sake of this
scenario right now. I could still get another half pound for marginal utility per dollar of 60, so now I buy another half pound of fruit and my marginal utility per dollar is 60. Now, where is my 3rd dollar, my 3rd dollar going to be spent? Well, I could spend it now at a rate of a dollar per half bar, or $2 per bar for chocolate or a dollar per half bar, $2
per bar for fruit over here. I'm actually neutral. I could spend it. Let me just, for the sake of fun, say list on half a bar of chocolate and my marginal utility per dollar is 50. Then my 4th 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 not do that? I'll buy another half chocolate bar, so now I have a whole chocolate bar. Once again, I'm able
to continue buying that at 50 utility units per dollar. Then my 5th dollar over here,
what would I do with that? Well, I don't want to buy
any more chocolate bars because my marginal utility per dollar of the chocolate bar because I've exhausted what
I can buy at this utility, this utility per dollar. My marginal utility per
dollar has gone down now, but now I could still buy fruit at that same 50. Now, with that dollar, since
the fruit is $2 per pound, I can buy another half pound of fruit at a marginal utility
per dollar rate of 50. Now I buy another half pound of fruit at a marginal utility per dollar of 50. You can calculate the total
marginal utility I got, this is the marginal utility per dollar and this is a dollar spent at that marginal utility per dollar. My total utility I should say, the marginal utility is the increment, but my total utility now is 60 + 60 is 120 plus 50 + 50 + 50. So it's 120 + 150 = 270 total utility. Even more interesting here, let's think about the
quantity of chocolate bars that I have now bought
once the price is gone up. I have now bought exactly 1 chocolate bar. You could say my 3rd and 4th dollars were spent on 1 bar right over here, I bought 1 bar. Let's think about it, all else equal. Remember, ceteris paribus. 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 equal. What happened just when we changed the price of chocolate bars? Let me write it down. Just think about chocolate. If we just think about chocolate bars. Let me write price and quantity. When the price was $1
the quantity demanded was 3 bars. That was the 1st video we
saw on marginal utility. We demanded 3 bars. Now when the price has gone up to $2, the quantity demanded is exactly 1 bar. We could do everything in between, we could see what happens
if the price was a dollar 50 or if the price was 50 cents, if we actually lower the price. We would see 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, assuming you have enough rows here and we might not have it, if you lower the price. Assuming you have the marginal utility at different quantities for the two goods, you can figure out exactly
how much chocolates someone would buy given
different changes in price. We at least have 2 points
for the demand curve now. If we assume that this is
price and this is quantity right over here, when the price was $1, the
quantity demanded was 3, and when the price is $2,
the quantity demanded is 1. There, we have 2 points
for our demand curve. Our demand curve might
look something like that. If it was linear, it would go straight. It would go something straight like that. But we at least have 2 points on the curve and we could keep trying
different prices out using these information to figure out the exact shape of that curve.