What I want to do in this television is precede you to the idea of a budget line. actually, credibly is n’t a new idea. It ‘s a derived function mind of what you ‘ve seen and often in an basic algebra naturally where A, you ‘ve gotten a certain measure of money and you can spend it on a sealed combination of goods. What are all the different possibilities that you can actually buy ? That ‘s in truth what a budget line is. Let ‘s say that you have an income and I ‘ll do it both in the abstract and the concrete. I ‘ll do it variables and then I ‘ll besides do it with actual numbers. Lets say your income, your income in a month is Y and lets say that you spend all of your money. Your income is peer to your expenditures. Assuming in our little model here that you ‘re not going to be saving any money. To show how excessively simplified we can make a mannequin we are going to merely 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. obviously, most people buy many more or they at least are choosing between many, many more than two goods. But permit ‘s say you can choose between 2 goods and let ‘s good take goods that we ‘ve been doing using in late video recording. That 2 goods that you buy are either cocoa or fruit. You could buy chocolate by the bar or fruit by the pound. What are going to be your expenditures assuming you spend it all on cocoa and fruit ? Well, there ‘s going to be the total that you spend on chocolate will be the price of cocoa times the measure of cocoa you buy which is the number of bars. And then the total you spent on fruit will be the price of fruit per egyptian pound times the quantity of fruit. For example, if Y = $ 20 a calendar month and the price, actually we ‘ll plot this in a irregular, the price of cocoa is equal to $ 1 per bar and the price of fruit is adequate to $ 2 per impound. I think these were the prices I used in a per beat of fruit. then all of a sudden, you would know what this is, you would know what this is and this is. You know what the Ps are and the Y and then you could actually graph one of these quantities relative to the other. What we can do is, and let ‘s do that, we can graph the measure of 1 relative to the other. Why do n’t we put the quantity of cocoa on this axis over here and let ‘s put the quantity of fruit on this bloc over here. First, if we wanted to graph it I like to put it, since I ‘ve put quantity of chocolate on the upright axis here, I ‘d like to solve this equation for quantity of chocolate as a function of quantity yield and it should make it pretty straight forward to graph. Let ‘s try that out. First, I ‘m fair going to rewrite this without expenditures in between. We have our income, our income Y = price of cocoa times the quantity of chocolate plus the price of fruit times the quantity of fruit. immediately, I want to solve for the quantity of cocoa. Let me make that orange so we know that this is this one right over here. If I want to solve for that, the best way I could isolate it one side of this equality. Let me get rid of this this yellow part mighty over here and the best way to do that is to subtract it from both sides. Let ‘s subtract the price of yield times the measure of yield and I could substitute the numbers in foremost and that might actually make it a little bit easier to understand but I like to keep it cosmopolitan first gear. You see, you do n’t have to barely use with these numbers you could just see the general consequence hera. I ‘m going to subtract it from the leave hand side and the right hand side and the whole point is to get rid of it from the right handwriting side. This cancels out, the entrust hand side becomes your income minus the price of yield times the measure of fruit. This is going to be peer to your justly hand side which is merely the price of cocoa times the measure of cocoa. nowadays if we want to solve for the quantity of chocolate we barely divide both sides by the price of cocoa and then you get it, and I ‘ll flip the sides. You get the quantity of chocolates, is going to be peer 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 monetary value of chocolate. All over that over the price of chocolate. We can actually substitute these numbers in here and then we can actually plot what basically this budget trace will look like. In our position, 20, Y = 20, the monetary value of cocoa is equal to 1. price of chocolate is equal to 1. This condition correctly over here, $ 20 per month divided by $ 1 per legal profession which would actually give you 20 bars per calendar month if you work out the units. This term right over hera fair simplifies to 20. This is actually an interest term, your income, your income in dollars divided by the price of an actual adept or service. You could view this condition veracious over here as your real income. The cause why it ‘s called substantial income is it ‘s actually pegging what your earnings to what you can buy. It ‘s pegging it to a certain real number goods, it ‘s not tied to some abstract quantity like money which always has a changing buy power. What you could buy for $ 20 in 2010 is very unlike than what you could buy for $ 20 in 1940. here, when you divide your income, divide it a by a price of some adept it ‘s in truth telling you your income in terms of that good. You could view your income as $ 20 per month or you could view your income if you wanted your income in chocolate bars. You could say my income is, I could buy 20 cocoa bars each calendar month. So I could say, my income 20 cocoa bars per month. They would be equivalent to you assuming that you could sell the cocoa bars for the same price you could buy it and that ‘s slightly of an assumption. But you could say I have the equivalent income of 20 bars a calendar month. You could have besides done it in yield. I have the equivalent income of 20 divided by 2, 10 pounds of yield a calendar month. It ‘s trying your income to real things, not the abstract quantity like money. anyhow, this is going to be equal to, let me write it over here. My measure of chocolate is going to be equal to this term properly complete here as 20. If you wanted to do the units, it would be 20 bars per month and you could do a short moment of dimensional analysis to come up with that. You could treat the units fair like numbers and see how the cancel forbidden. 20 bars per calendar month minus the price of fruit divided by the price of chocolate. $ 2 per pound of fruit. The price of fruit is going to be $ 2 and I actually want to look at the units because that ‘s interest. Let me write it here. The price of yield is equal to $ 2 per pound. Let me write it this way. $ 2 per beat of fruit, I ‘ll show you how the units cancel out. then we ‘re dividing that by the price of chocolate. Dividing it by the price of chocolate which is equal to $ 1 per bar of cocoa. now, obviously the mathematics is fairly directly fore. We fair get 2, but the units are a little bit matter to. You have a dollar and the numerator of the numerator and a dollar, the numerator of the denominator, those will cancel out. You could actually view this as, this is going to be the like thing just to look at the units. 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. You could say $ 2 per pound times, the multiplicative inverse of 1 is barely 1, times 1 legal profession per dollar. then the dollars cancel out and you are left with 2 bars per british pound of fruit. What we ‘ve actually done over hera, this term good over here, it gives us bars of chocolate per hammer of fruit. It simplifies to 2 bars of chocolate per pound of fruit. It ‘s actually giving you the opportunity cost of a impound of fruit. It ‘s saying hey, you could buy a egyptian pound of fruit but you ‘d be giving up 2 bars of chocolate. Because the price, you could get 2 bars of chocolate for every pound of fruit. You could view this as the relative price, this correct over here is the relative price of yield in this example. It ‘s telling you the opportunity cost, it ‘s telling you how much yield price in terms of cocoa bars. Regardless, that numeral is fairly neat forward, it was good a 2. Minus 2 times the quantity of fruit. This is reasonably straight advancing to plot. If the quantity of fruit it 0, our quantity of cocoa is 20. This is going to be 20 over here. This is 20 and this is going to be 10. This is 15, this is 5. This is a point on our budget line right over there. There is multiple ways that you could think about this. One way you could say is if you buy no chocolate, if the measure of cocoa is 0, what is going to be the measure of fruit ? then you could solve this or you could precisely say, “ Look, if I have $ 20 a calendar month “ then I ‘m going to spend it all on fruit. “ I can buy 10 pounds of fruit. ” So to say that this right over here is 10. Let ‘s say this properly over here is 10, this is 5, therefore this is besides on our budget line and every sharpen in between is going to be on our budget line. Every point in between is going to be on our budget credit line. Another way you could have done this and this comes straight out of kind of your distinctive algebra 1 course. You could say, in this shell, 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. ” For every extra pound of fruit I buy I have to give up 2 pounds of cocoa. You could besides view this as the opportunity monetary value of yield. You see this slope as we go fore, if we buy one more pound quantity of fruit we ‘re giving up 2 bars of chocolate. One affirmation I did barely make, I said every detail on this agate line is a possibility and I can entirely say that if we assume that both of these goods are divisible goods which means we can buy randomly little amounts of it, that we could buy 10th of a measure of chocolate on average particularly. Or we could buy 100th of a pound of fruit. If they were n’t divisible, they ‘re indivisible then entirely the whole quantities would be the hypothesis points. We ‘ll precisely assume they ‘re divisible, particularly even if the store only sells indivisible bars of cocoa. If you buy one bar of chocolate every 4 months, on average you ‘re buying .25 bars of chocolate per month. evening that, on average, about anything, about anything here is divisible. This line right over here shows all of the combinations we can buy. All of the combinations of the divisible goods we could buy if we spend all of our money. That right over there is our budget line. That is our budget cable. That is our budget line. And any combination out here is unaffordable. We do n’t have enough money for that. Any combination polish here is low-cost. actually, we would end up with supernumerary money if we ‘re below the budget tune. This is n’t all that different than what we saw with the production possibilities frontier. Remember, we had a curvature that very showed all of the if we were producing 2 goods, what combinations of goods we could produce. Anything on that curvature for the productions possibility frontier was effective. Anything outside of it was unachievable and anything inwardly was attainable but inefficient.
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