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Deriving demand curve from tweaking marginal utility per dollar

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Where does a buyer's demand curve come from? A rational buyer wants to get as much "bang per buck" from their consumption as possible. In economics, that's called marginal utility per dollar spent. When the price of a good decreases, the "bang per buck" on that good increases, which incentivizes consuming more of it. In this video, we derive the individual's demand curve for a good by tweaking the marginal utility per dollar spent. Created by Sal Khan.

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  • blobby green style avatar for user Maxine Zentil
    At min, when you explain that it makes sense for you too put your first $1 into buying half a pound of fruit at marginal utility/per $ of 60. But since you are only getting half, wouldn't your marginal utility be 30? (because you are only getting half and not the full amount)
    (14 votes)
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  • male robot hal style avatar for user Aditya Joshi
    Why is it 'per dollar'? Why can't it be per half a dollar? Or per two dollars?
    (1 vote)
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    • leafers ultimate style avatar for user Shadow
      It is much easier to compute, but per half dollar or per two rollers works as well. There are instances, however, like if you were talking about billions of dollars, that you might use something such as per million.
      (2 votes)
  • leafers ultimate style avatar for user Caitlin Fischer
    At , why is it that the dollar goes to chocolate bars? It seems like it could just as easily go towards paying for fruit, and you would end up with only half of a chocolate bar being demanded, skewing the demand curve. I can't quite make sense of this.
    (9 votes)
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    • blobby green style avatar for user Michael Morris
      Either way works, since the utility for the first $1 (half-bar) of chocolate is 50 and the marginal utility for the 3rd $1 (1/2 lb) of fruit is also 50. If we purchased the 3rd 1/2 lb of fruit, the marginal utility for the fourth dollar would, again, be 50 while the utility for the first half-bar of chocolate would still be 50. Again, it wouldn't matter. If you spent dollars 3 and 4 on fruit however, you would want to spend dollar 5 on chocolate since the utility for a half-pound of chocolate would still be 50 while the marginal utility for yet another half-pound of fruit will have declined to 25. Therefore, dollars 3 4 5 can be spent on choc choc fruit, fruit fruit choc, fruit choc fruit or choc fruit choc - all will give you a total utility (from dollars 3 to 5) of 150.
      (6 votes)
  • blobby green style avatar for user Neeraj Chandrasekhar
    The entire video is based on the assumption that only 5$ is spent and we get the specific Demand curve.

    But if we change the disposable income to 7$ then the demand graph changes. This cant be the income effect as the graph does not move parallel upwards. Need some explanation on this !
    (3 votes)
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    • ohnoes default style avatar for user Tejas
      The income effect doesn't necessarily make the demand curve move upwards in a parallel fashion. It can move it upwards in any way. In fact, for some goods, increasing income can decrease the demand. But when we are only given a demand curve, we don't have enough information to say how demand will change when income is changed.
      (3 votes)
  • leafers ultimate style avatar for user John Kalafus
    Am I correct in assuming that you could also deduce how the the change in price of the chocolate bar shifted the demand of the fruit (to the right I think) being that you would now buy more fruit at $2 and figure out the new demand schedule for that as well?
    (3 votes)
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  • blobby green style avatar for user Ojasvi Bhalerao
    When you spent the 5th dollar, why did you take the MU as 50 ? Isn't it supposed to be 60 ?
    (2 votes)
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  • piceratops seed style avatar for user Emille Giddings
    I don't understand this example. Why were the quantities broken down by fraction? How am I supposed to think about an additional half a unit as having the same utility as a whole unit if an additional half unit of fruit yields less utility than an additional half unit of chocolate?
    (2 votes)
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  • male robot donald style avatar for user Keneth Walters
    at Sal says that for my second dollar I can buy 0.5lbs of fruit but It would not be that I can buy 1 lbs since I have 2 dollars and each one costs 2 dollars?
    (2 votes)
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  • blobby green style avatar for user Daniel Parker
    2 Questions:
    1. In determining the demand curve for chocolate, Sal says ceteris paribus, or holding all else equal, including the price of fruit. In fact, hasn't he changed the price of fruit from $1 per pound to $2 per pound?

    2. Although Sal says he is determining the demand curve for chocolate, isn't this really just the demand curve for chocolate relative to fruit (and given specific prices of fruit)? Is demand independent of other products/services or is it always relative to some other product/service?
    (1 vote)
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    • ohnoes default style avatar for user Tejas
      For your first question, he is saying all else equal. That is, he is keeping everything the same except the price, which he is changing. This is the same as control in a scientific experiment. Whenever you do an experiment, you have to hold all variables the same except the one that you are testing.

      For your second question, demand is always relative to some other product. In most cases, you will see demand relative to dollars, but in this case it is fruit.
      (2 votes)
  • leaf red style avatar for user dyann campbell
    the total utility was marginal utility spent on fruit but what about chocolate? isn't the total all spent?
    (1 vote)
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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.