Deriving demand curve from tweaking marginal utility per dollar

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Deriving demand curve from tweaking marginal utility per dollar발음듣기

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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.발음듣기

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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.발음듣기

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Then we got more for the 2nd chocolate bar for that 1st pound of fruit, so we spend it there.발음듣기

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Then for the 3rd pound or for the 3rd bar of chocolate.발음듣기

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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.발음듣기

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What I want to do in this video is explore what happens when I change the price of the chocolate bars.발음듣기

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What happens to our marginal utility per dollar over here?발음듣기

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In particular, what happens to the quantity demanded?발음듣기

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If you think about what we're doing it, we figured out with 1 price what was the quantity demanded, we demanded 3 bars.발음듣기

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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.발음듣기

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Let's see how we could do that.발음듣기

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Let's now assume that our chocolate bars are $2.발음듣기

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Now we're going to calculate. The marginal utility per dollar, this applies to both of these columns.발음듣기

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This is for what it was $1 per bar, this is now when it's $2 per bar.발음듣기

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Well, for that first bar, I'm still getting 100 points of marginal utility, but now it's $2.발음듣기

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So 100 divided 2 is going to give me 50 marginal utility points per dollar.발음듣기

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Then for that next bar, I get 80 marginal utility points.발음듣기

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I'm still enjoying it but enjoying it a little bit less but I'm paying $2 for it.발음듣기

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I'm getting 80 divided by 2 is 40 points, you know, and I'm just giving these arbitrary units, 40 points per dollar.발음듣기

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Then the 3rd bar is 30 points per dollar.발음듣기

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Then the 4th bar is 20 points per dollar.발음듣기

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Now, how would I spend my $5?발음듣기

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Let me do this a little bit, let me do it over here.발음듣기

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How would I spend my $5 now?발음듣기

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My first dollar, where would I get the most marginal utility per dollar?발음듣기

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Where would I get the most bang for my buck?발음듣기

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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.발음듣기

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That is constant until I get to one entire bar.발음듣기

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That's also true for, and even if I buy a fraction of the pound here.발음듣기

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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.발음듣기

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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.발음듣기

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My 1st dollar will go towards .5 pounds of fruit and I'm getting a marginal utility per dollar of 60.발음듣기

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Where is my 2nd dollar going to go?발음듣기

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Well, I can still get another half pound at a marginal utility of 60.발음듣기

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Remember, we have to ignore these right here for the sake of this argument or for the sake of this scenario right now.발음듣기

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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.발음듣기

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Now, where is my 3rd dollar, my 3rd dollar going to be spent?발음듣기

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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.발음듣기

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I'm actually neutral. I could spend it.발음듣기

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Let me just, for the sake of fun, say list on half a bar of chocolate and my marginal utility per dollar is 50.발음듣기

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Then my 4th dollar, once again, I could do a couple of different things here.발음듣기

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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.발음듣기

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So why not do that? I'll buy another half chocolate bar, so now I have a whole chocolate bar.발음듣기

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Once again, I'm able to continue buying that at 50 utility units per dollar.발음듣기

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Then my 5th dollar over here, what would I do with that?발음듣기

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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.발음듣기

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My marginal utility per dollar has gone down now, but now I could still buy fruit at that same 50.발음듣기

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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.발음듣기

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Now I buy another half pound of fruit at a marginal utility per dollar of 50.발음듣기

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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.발음듣기

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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.발음듣기

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So it's 120 + 150 = 270 total utility.발음듣기

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Even more interesting here, let's think about the quantity of chocolate bars that I have now bought once the price is gone up.발음듣기

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I have now bought exactly 1 chocolate bar.발음듣기

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You could say my 3rd and 4th dollars were spent on 1 bar right over here, I bought 1 bar.발음듣기

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Let's think about it, all else equal.발음듣기

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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.발음듣기

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All else equal. What happened just when we changed the price of chocolate bars?발음듣기

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Let me write it down. Just think about chocolate.발음듣기

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If we just think about chocolate bars.발음듣기

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Let me write price and quantity.발음듣기

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When the price was $1 the quantity demanded was 3 bars.발음듣기

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That was the 1st video we saw on marginal utility.발음듣기

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We demanded 3 bars. Now when the price has gone up to $2, the quantity demanded is exactly 1 bar.발음듣기

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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.발음듣기

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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.발음듣기

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But by doing that, assuming you have enough rows here and we might not have it, if you lower the price.발음듣기

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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.발음듣기

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We at least have 2 points for the demand curve now.발음듣기

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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.발음듣기

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There, we have 2 points for our demand curve.발음듣기

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Our demand curve might look something like that.발음듣기

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If it was linear, it would go straight.발음듣기

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It would go something straight like that.발음듣기

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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.발음듣기

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