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Emilio buys pizza for $\$ 10$ and soda for $\$ 2 .$ Hehas income of $\$ 100 .$ His budget constraint willexperience a parallel outward shift if which of thefollowing events occur?a. The price of pizza falls to $\$ 5,$ the price of sodafalls to $\$ 1,$ and his income falls to $\$ 50 .$b. The price of pizza rises to $\$ 20$ , the price of sodarises to $\$ 4,$ and his income remains the same.c. The price of pizza falls to $\$ 8,$ the price of sodafalls to $\$ 1,$ and his income rises to $\$ 120$ .d. The price of pizza rises to $\$ 20,$ the price of sodarises to $\$ 4,$ and his income rises to $\$ 400 .$

d

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Chapter 21

The Theory of Consumer Choice

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Hey, guys, it's Brian here. And today I'm going to help you work over this little budget constraint problem that we have over here. So yeah, first, when you will just get straight into it. When you first look at the problem on, I'll give you a set of givens ripe. So it tells us that first Amelia has an income budget of $100 you're gonna write that down? His budget is $100 that he gets from his income on it causes that Peter's cost 10 bucks friend and that cell has caused to yours. So basically, in this scenario, we're considering the different options that Emilio has with his. With his budget of $100 what combinations of pizzas and set is can you get with an income of 100 bucks on DH? That's what's going to be on the budget constraint line. So, you know, just are just start off this problem. You're going to want to start off by drawing the budget constraint line. Given this information. Hi, it's a It's a start as a basic. You know, Axl, I access and we're going to start by labeling the T axes the Y axes will label as a number of sodas, and then the excesses were able as a number of Peter's. And basically, we want a line to model all the different combinations and numbers of sodas and pizzazz that he can buy with 100 bucks. The most effective shortcut in drawing this line is by looking at the two end points. So if we're to look at the numbers so it is that he can buy each story caused two bucks and he has an income of 100 bucks. So if you were to buy only searchers, you'd be able to buy an accident of 50 sits not only did the same thing on this pizza on access if you wanted to buy our Peter's, each pizza cost 10 bucks, so we'll be able to buy 10 pizzas. And then this line over here is your budget constraint line on this budget constraint line on gives you a couple of information. The first it tells you what you can afford and what you can't afford. All the points inside this line represent combinations of sodas and pizzazz that you can't afford. So, for example, if your toe by, Let's say, you know, five cans of soda and five pizzas would have a point somewhere around here. That would be a green point that's inside your budget line on the costing you less than 100 bucks if you're able tto If you wanted a body combination, and so it is and Peter's outside this budget line, you would end up with a total of more than 100 bucks. So anything outside this line is something that you can afford. So that's the first set of information that you get from this craft on the other useful information that you get from this graph, ISS comes from the slope. So if you notice from the slime, you'll notice that the slope is five abduction negative five. But we're gonna disregard on the negative sign for a second. I'm basically what that tells you is the opportunity cost of one pizza is five seconds and the other way around. So the opportunity cost of one soda Karen would be one fits of a pizza. So on that slope on, we call that the relative prices of these two ghosts sodas and peters and yeah, and now the more important as we go later on. But first, we're gonna go right into solving this problems we want. What this problem is asking is an outward parallel shift, right? Has been outward and terrible. Yes. Excuse My messy handwriting. I haven't said of him. Thank you. Okay, so we're looking for a ship that's outward in peril. So if you were toe predict something, will you say it looks something like this, right? Something that isn't complete outward shift and something that is parallel or maintains a slope of negative factory. So that's what we're looking for. So it's you on which one of these scenarios meets that condition, right? So the first condition that they give us is when Peter's good to $5 said Pizzas are $5 sodas for $1 and then your income goes down. Teo 50 bucks and I'm just new scenario and blue. So if you were to see the maximum number of Celtic ins that he could buy in this scenario, he has 50 bucks. Each study can cost one. Buck said he'd be over by 50. Um, and I'm trying to see the maximum number of Peter's. He can buy his 50 bucks each Pizza cost five bucks. So if you were to buy only Peters. No, sir. Can't you be able to buy 10 Peters? And if you notice you're well and they're getting the same budget constraint line, which tells us the letter a can't be our option because we're looking for As we said before, we're looking for an outward shift in this line. Does not shit at all. So we can cross out a from that, and then we'll move on to be That was a I was a And then be Scenario B is when pizzas cost 20 bucks Now said has caused four bucks now and then. Your income today is the same 100 bucks. So it's modeled this tryingto get the budget constraint line for distant aria. So the maximum number of Peter's he could buy would be five. Should be somewhere around here. And then the maximum number of soda cancer P could buy would be 25 over here, so your budget constraint line would look like this. This line is a shift, and it's parallel. But the only problem we have is we're looking for an outward ships, right? Eso this. This scenario here on doesn't fulfill that outward shift requirements. So we can also cross out B because we end up with a shift that goes inside original budget control. So we know it's not a you know, it's not bee. I can't and I'm going here is okay, and then we'll get scenario C scenario C on Peter's cost. Eight bucks service cost one buck, and your budget is on. It goes up to 120 bucks. So, um yeah, OK, so let's draw the budget constraint line for dis example. Well, the green for this one, you already not. It isn't by now, probably Honey pizzas, Can you buy Deal two by 13. And how many studies can you buy Would be 127 b? Uh oh. Be appointed way appeared once this label here 1 20 So you end up with a line that looks sort of like this, and if you look here on this is a shift, it's complete shift. It shifts outwards. But the only problem we have is that Carol Requirement, right? You can see here that these two lines aren't parallel on. This graph obviously isn't accurate. Sketch But if you wanted to check whether these two lines were parallel, you would check the slope. Right? So here we said the soap was negative. Five. I'm here to slow. Would be. I'm not negative five. I said we know that these two lines have different slopes and therefore they're not Parable. So we also know that Letter C doesn't fulfill a requirement of the outward peril ship so we can process CS. And then we're left with our final on choice, which is auctioning D auction deed on Peter's cost. 20 bucks. I'm sort of cost four bucks. And meanwhile, his income and up to 400 plus walk each other. Okay, what's model? The budget constraint line for this last scenario. Same thing he convey by yes, 400 bucks each pizza cost $20. That you would be able to buy 20 pieces on each soda can cost four bucks. He has $400. He would be ableto bard 100 service 100. Sorry about that. And then if you draw the line Oh, Quintus. Yes. Ah, it's a sketch here so you can see that the Easter relative, We they look relatively parallel by nor to be mathematically accurate again. You look at the slope, right? And you will say that this slope is negative five. That this left is also negative. Fun seeing at least 200 parallel. We see that this line's shifted completely and you see that the shift is outwards. So we know that scenario D is what we're looking for. Yeah, yeah, that's the That's the example for this problem. I'm I hope that helped and see you next time.

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