Emilio buys pizza for 10 and soda for 2 . He has income of 100 . His budget constraint will e

Emilio buys pizza for 10 and soda for 2 . He has income of...

Key Concepts

Budget Constraint

A budget constraint represents all the combinations of goods and services that a consumer can afford given their income and the prices of the goods. It is typically expressed as an equation and visually depicted as a line whose intercepts indicate the maximum quantity of one good that can be purchased if no units of the other good are bought.

Parallel Shift of the Budget Line

A parallel shift in the budget line occurs when there is a change in the consumer's income while the prices of the goods remain constant. This type of shift moves the entire line outward or inward without altering its slope, reflecting a change in purchasing power but not in the relative prices of the goods.

Income Changes

Changes in income directly affect the position of the budget constraint. An increase in income shifts the constraint outward, allowing for a higher consumption of both goods, while a decrease shifts it inward. This concept is key to understanding how budgetary limits adjust without affecting the rate at which one good can be substituted for another.

Effect of Price Changes on the Budget Line

Price changes modify the slope of the budget line rather than shifting it parallelly. When the price of one good changes, it alters the consumer's opportunity set by changing the rate of trade-off between goods, resulting in a rotation of the budget line. This helps distinguish the separate impacts of changes in income versus changes in prices.

Transcript

00:01 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 i'll give you a set of givens right so it tells us that first emilio has an income budget of a hundred dollars so you're gonna write that down his budget is a hundred dollars that he gets from his income it tells us that pizzas cost ten bucks for him and that's so this costs $2.

00:39 So basically in this scenario, we're considering the different options that emilio has with his budget of $100.

00:47 What combinations of pizzas and setas can he get with an income of $100? that's what's going to be on the budget constraint line.

00:57 So in order to start off this problem, you're going to want to start off by drawing the budget constraint line, given this information.

01:07 How you do that, it starts out as a basic, you know, x and y axis.

01:14 And we're going to start by labeling the two axes.

01:17 So the y axes will label as the number of sodas.

01:21 And then the x axis will label as a number of pizzas.

01:26 And basically, we want a line to model all the different combinations of the numbers of sodas and pizzas that he can buy with $100.

01:34 Bucks.

01:35 The most effective shortcut in drawing this line is by looking at the two endpoints.

01:41 So if we're to look at the number of sodas that he can buy, each soda costs two bucks and he has an income of a hundred bucks.

01:48 So if you were to buy only sodas, he would be able to buy a maximum of 50 sodas.

01:55 And then we're going to do the same thing on this pizza axis.

01:59 So if you wanted to buy all pizzas, each pizza costs 10 bucks.

02:03 So he'll be able to buy 10 pizzas.

02:06 And then this line over here is your budget constraint line.

02:14 This budget constraint line gives you a couple of information.

02:19 The first, it tells you what you can't afford and what you can't afford.

02:23 All the points inside this line represent combinations of sodas and pizzas that you can't afford.

02:29 So for example, if you were to buy, let's say, you know, five cans of soda and five pizzas, you would have a point somewhere around here.

02:39 That would be a green point that's inside your budget line and it'll end up costing you less than 100 bucks.

02:46 If you're able to, if you wanted to buy a combination of sodas and pizzas outside this budget line, you would end up with a total of more than 100 bucks.

02:55 So anything outside this line is something that you can't afford.

03:00 So that's the first set of information that you get from this graph.

03:03 The other useful information that you get from this graph is comes from the slope.

03:08 Notice from the slime you'll notice that the slope is five it's actually negative five but we're going to disregard on the negative sign for a second um basically what that tells you is the opportunity cost of one pizza is five soda cans and the other way around so the opportunity cost of one soda can would be one fits of a pizza so um that slope um we call that the relative prices of these two goods sodas and pizzas and um yeah and that'll be more important um as we go later on.

03:41 But first, we're going to go right into solving this problem.

03:43 So we want, what this problem is asking, is an outward parallel shift, right? it has to be outward and parallel.

03:56 Yes, excuse my messy handwriting.

03:59 I haven't set up in a mouse pad yet.

04:01 Ok, so we are looking for a shift that's outward and parallel.

04:04 So if you were to predict something, we would say it looks something like this, right? something that is a complete outward shift.

04:12 Shift and something that is parallel or maintains a slope of negative 5 right so that's what we're looking for so let's see which one of these scenarios meets that condition right so the first condition that they give us is um when pizzas go to five dollars so pizzas are five dollars um sodas are one dollar and then your income goes down to 50 bucks i'm gonna outline this new scenario in blue.

04:53 So if you were to see the maximum number of soda cans that he could buy in this scenario, he has 50 bucks.

05:01 Each soda can cost one box, so he'd be able to buy 50.

05:06 If you're trying to see the maximum number of pizzas he can buy, he has 50 bucks, each pizza costs five bucks.

05:13 So if he were to buy only pizzas, no soda cans, you'd be able to buy 10 pizzas.

05:18 And if you notice here, we'll end up getting the same budget constraint line, which tells us that letter a can't be our option because we're looking for, as we said before, we're looking for an outward shift and this line does not shift at all.

05:33 So we can cross out a from that and then we'll move on to b.

05:40 So that was a, that was a, and then b, scenario b is when pizzas cost 20 bucks now.

05:55 So it has cost four bucks now.

05:57 And then your income stays the same at $100...

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