Budget line발음듣기
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Budget line
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It's a derivative idea of what you've seen and often in an introductory algebra course where A, you've gotten a certain amount of money and you can spend it on a certain combination of goods.발음듣기
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Lets say your income, your income in a month is Y and lets say that you spend all of your money.발음듣기
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To show how overly simplified we can make a model we are going to only assume that you can spend on two different goods and that's so that we can actually plot all the combinations on a two dimensional surface like the screen over here.발음듣기
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Obviously, most people buy many more or they at least are choosing between many, many more than two goods.발음듣기
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But let's say you can choose between 2 goods and let's just take goods that we've been doing using in recent videos.발음듣기
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Well, there's going to be the amount that you spend on chocolate will be the price of chocolate times the quantity of chocolate you buy which is the number of bars.발음듣기
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And then the amount you spent on fruit will be the price of fruit per pound times the quantity of fruit.발음듣기
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For example, if Y = $20 a month and the price, actually we'll plot this in a second, the price of chocolate is equal to $1 per bar and the price of fruit is equal to $2 per pound.발음듣기
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You know what the Ps are and the Y and then you could actually graph one of these quantities relative to the other.발음듣기
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Why don't we put the quantity of chocolate on this axis over here and let's put the quantity of fruit on this axis over here.발음듣기
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First, if we wanted to graph it I like to put it, since I've put quantity of chocolate on the vertical axis here, I'd like to solve this equation for quantity of chocolate as a function of quantity fruit and it should make it pretty straight forward to graph.발음듣기
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We have our income, our income Y = price of chocolate times the quantity of chocolate plus the price of fruit times the quantity of fruit.발음듣기
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Let me get rid of this this yellow part right over here and the best way to do that is to subtract it from both sides.발음듣기
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Let's subtract the price of fruit times the quantity of fruit and I could substitute the numbers in first and that might actually make it a little bit easier to understand but I like to keep it general first.발음듣기
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You see, you don't have to just use with these numbers you could just see the general result here.발음듣기
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I'm going to subtract it from the left hand side and the right hand side and the whole point is to get rid of it from the right hand side.발음듣기
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This cancels out, the left hand side becomes your income minus the price of fruit times the quantity of fruit.발음듣기
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This is going to be equal to your right hand side which is just the price of chocolate times the quantity of chocolate.발음듣기
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Now if we want to solve for the quantity of chocolate we just divide both sides by the price of chocolate and then you get it, and I'll flip the sides.발음듣기
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You get the quantity of chocolates, is going to be equal to your income, your income divided by the price of chocolate minus the price of fruit times the quantity of fruit all of that over the price of chocolate.발음듣기
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We can actually substitute these numbers in here and then we can actually plot what essentially this budget line will look like.발음듣기
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This term right over here, $20 per month divided by $1 per bar which would actually give you 20 bars per month if you work out the units.발음듣기
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This is actually an interesting term, your income, your income in dollars divided by the price of an actual good or service.발음듣기
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The reason why it's called real income is it's actually pegging what your earnings to what you can buy.발음듣기
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It's pegging it to a certain real goods, it's not tied to some abstract quantity like money which always has a changing buying power.발음듣기
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What you could buy for $20 in 2010 is very different than what you could buy for $20 in 1940.발음듣기
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Here, when you divide your income, divide it a by a price of some good it's really telling you your income in terms of that good.발음듣기
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You could view your income as $20 per month or you could view your income if you wanted your income in chocolate bars.발음듣기
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They would be equivalent to you assuming that you could sell the chocolate bars for the same price you could buy it and that's somewhat of an assumption.발음듣기
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If you wanted to do the units, it would be 20 bars per month and you could do a little bit of dimensional analysis to come up with that.발음듣기
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The price of fruit is going to be $2 and I actually want to look at the units because that's interesting.발음듣기
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You have a dollar and the numerator of the numerator and a dollar, the numerator of the denominator, those will cancel out.발음듣기
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You could actually view this as, this is going to be the same thing just to look at the units.발음듣기
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This is going to be, this is the same thing as the numerator times the inverse times the reciprocal of the denominator right over here.발음듣기
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What we've actually done over here, this term right over here, it gives us bars of chocolate per pound of fruit.발음듣기
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You could view this as the relative price, this right over here is the relative price of fruit in this example.발음듣기
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It's telling you the opportunity cost, it's telling you how much fruit cost in terms of chocolate bars.발음듣기
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One way you could say is if you buy no chocolate, if the quantity of chocolate is 0, what is going to be the quantity of fruit?발음듣기
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Then you could solve this or you could just say, "Look, if I have $20 a month then I'm going to spend it all on fruit.발음듣기
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Let's say this right over here is 10, this is 5, so this is also on our budget line and every point in between is going to be on our budget line.발음듣기
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Another way you could have done this and this comes straight out of kind of your typical algebra 1 course.발음듣기
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You could say, in this case, if you view this as the Y axis, you say your Y interceptor, you say, "My chocolate quantity interceptor is 20 and then my slop is negative 2. My slope is negative 2."발음듣기
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You see this slope as we go forward, if we buy one more pound quantity of fruit we're giving up 2 bars of chocolate.발음듣기
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One statement I did just make, I said every point on this line is a possibility and I can only say that if we assume that both of these goods are divisible goods which means we can buy arbitrarily small amounts of it, that we could buy 10th of a bar of chocolate on average especially.발음듣기
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If they weren't divisible, they're indivisible then only the whole quantities would be the possibility points.발음듣기
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We'll just assume they're divisible, especially even if the store only sells indivisible bars of chocolate.발음듣기
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If you buy one bar of chocolate every 4 months, on average you're buying .25 bars of chocolate per month.발음듣기
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Remember, we had a curve that really showed all of the if we were producing 2 goods, what combinations of goods we could produce.발음듣기
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