Optimal point on budget line발음듣기
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Optimal point on budget line
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My budget (20) is going to be equal to the price of chocolate, which is 1 times the quantity of chocolate.발음듣기
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And if want to write this explicitly in terms of my quantity of chocolate, since I put that on my vertical axis, since that tends to be the more dependent axis, I can just subtract 2 times the quantity of fruit from both sides.발음듣기
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And I can flip them and get my quantity of chocolate is equal to 20 minus 2 times my quantity of fruit.발음듣기
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So, for example, let's say I'm sitting at some point on my budget line where I have - let's say I am consuming 18 bars of chocolate and one pound of fruit.발음듣기
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So let's say I'm at this point on my budget line. 18 bars of chocolate - so this is in bars - and one pound of fruit per month.발음듣기
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there's different combinations of chocolate and fruit to which we are indifferent, to which we would get the same exact total utility.발음듣기
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And so we can plot all those points, I'll do it in white, it could look something like this.발음듣기
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So, for example, I could have 18 bars of chocolate and one pound of fruit, or I could have - let's say that is four bars of chocolate and, let's see, and roughly eight pounds of fruit. I'm indifferent.발음듣기
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Well, we've already seen that anything to the top right of our indifference curve, of this white curve over here Let me label this.발음듣기
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This is our indifference curve. Everything to the top right of our indifference curve is preferable.발음듣기
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Let me color that in. So everything to the top right of our indifference curve is going to be preferable.발음듣기
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So all of these other points on our budget line, even a few points below our budget line, where we would actually save money, are preferable.발음듣기
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We can maximize our total utility at all these other points in between along our budget line.발음듣기
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So to actually maximize out total utility, what we want to do is find a point on our budget line that is just tangent, that just touches at exactly one point one of our indifference curves.발음듣기
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And so there is an indifference curve that touches exactly this budget line, or exactly touches the line at one point.발음듣기
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And because it's tangent - it touches in exactly one point - and also the slope of my indifference curve which we've learned is the marginal rate of substitution, is the exact same as the slope of our budget line right over there, which we learned earlier was the relative price.발음듣기
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In fact, every other point on our budget line is to the bottom left of this indifference curve.발음듣기
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So remember, everything below an indifference curve, all this shaded area - we should actually do it in another color.발음듣기
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Because indifference curve we are indifferent: but everything below an indifference curve - so all of this area in green - is not preferable.발음듣기
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Because that is the only point - or I guess you could say every other point on our budget line is NOT preferable to the points on the indifference curve.발음듣기
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So they are also not preferable to that point right over there, which actually is on the indifference curve.발음듣기
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New budget line. So now what would be the optimal allocation of our dollars? Or, the best combination that we would buy?발음듣기
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Assuming we had data on all of these indifference curves, we would find the indifference curve that is exactly tangent to our new budget line.발음듣기
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So let's say that this point right over here is exactly tangent to another indifference curve.발음듣기
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And so based on how the price - assume we have access to these many, many indifference curves we can now see based on how a price, with all else equal, how a change in the price of fruit changed the quantity of fruit we demanded.발음듣기
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Because now our optimal spent is this point on our new budget line, which looks like it's about, give or take, about 10 pounds of fruit.발음듣기
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So what we're actually doing - and once again we're kind of looking at the exact same ideas from different directions.발음듣기
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Before we looked at it in terms of marginal utility per dollar and we thought about how you maximize it.발음듣기
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But assuming we had access to a bunch of indifference curves, we can see how a change in price changes our budget line, and how that would change the optimal quantity we would want of a given product.발음듣기
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So if this is the price of fruit, and this is the quantity demanded of fruit, when the price is two the quantity is eight.발음듣기
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And these aren't to scale. When the price is one the quantity demanded is 10. Two, eight, quantity demanded is 10.발음듣기
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