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Economics: Consumer's Optimal Combination of Goods


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About this Lesson

  • Type: Video Tutorial
  • Length: 11:27
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 122 MB
  • Posted: 03/29/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: Consumer Choice & Household Behavior (8 lessons, $13.86)
Economics: Consumer Optimization (3 lessons, $4.95)

In this economics tutorial, we will talk about the consumer's optimal combination of goods, how it is determined and why it is important. Taught by Professor Tomlinson, this video lesson was selected from a broader, comprehensive course, Economics. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/economics. The full course covers economic thinking, markets, consumer choice, household behavior, production, costs, perfect competition, market models, resource markets, market failures, market outcomes, macroeconomics, macroeconomic measurements, economic fluctuations, unemployment, inflation, the aggregate expenditures model, banking, spending, saving, investing, aggregate demand and aggregate supply model, monetary policy, fiscal policy, productivity and growth, and international examples.

Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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What would you do if you had Chris' preferences and $12.00 worth of income? How would you allocate your limited income over all the possibilities available to you? Would you buy more toys, more snacks, a lot of one or the other, or a balanced combination? How do economists figure out what consumers are going to do, given their preferences and given the constraints of income and price? We're going put the indifference curves that represent preferences together with the budget constraint, which represents opportunities to show you how economists think about consumer optimization.
Consumer optimization is the behavior of households trying to maximize satisfaction subject to the constraints of income and prices. So let's take a look now at the graph that we've developed. First, we have this dark line, which you'll recall represents the budget constraint. That is, it represents all the combinations of toys and snacks that the consumer can buy given the limited income and the price of the two goods. My axes aren't labeled here, so it doesn't look like I have meaningful graph. Someone is going to have to give me a label. Let's see. Ah. There's a snack, so we'll label the vertical axis with snacks, and here's a toy, so we'll label the horizontal axis with toys. Make sure that your axes are always labeled; otherwise your graphs are meaningless.
Now, here we have the representation of the consumer's feasibility set. That is, the opportunities that the consumer has given income and prices. So, if you spend all of your income on snacks at a price of $1.00 per snack and an income of $12.00, you can buy 12 snacks. If you spend all of your income on toys at a price of $3.00 per toy, you can buy four toys. And the slope of this budget constraint represents the relative price of toys and snacks, which is the price of toys at $3.00 apiece divided by the price of snacks at $1.00 apiece for a number of three. Three is the relative price of toys and snacks and it's the slope of this green line. No. I guess it's a blue line. It's the slope of this line.
Notice one more thing. This line is downward sloping, which means that its number is negative. The trend slope of this line is the negative of the relative prices, but let's ignore the negative sign for just a minute and focus on the intuition. How do you think about relative prices? How do you think about the slope of the budget constraint? This number three says this, "If you will give up one toy, if you give up one toy, you're going to have enough extra income to buy three snacks." Three is the relative price of toys measured in terms of snacks.
Now, if this blue line represents your possibilities, what are you going to do? Well, economists imagine that consumers do one and only one thing. That is, they seek the combination of goods that maximizes satisfaction. Let's find that combination. Look at all of these red indifference curves that I've drawn in here for Chris. All of these red indifference curves represent combinations of goods and services that are equally desirable. Here's a low level of satisfaction, this level of satisfaction on this indifference curve to the northeast represents an improvement and you can do even better by going way, way up here to the far northeast. The further to the northeast you go, the better off you are, because more is better in this model.
Now, I could go in and label these indifference curves. It looks like I've labeled this one U[0], which represents our baseline level of satisfaction and an improvement we might call it U[1], which means this curve represents more satisfaction. And I might label this curve, underneath here, I might call it U[-1] because it's worse. See the numbers don't really matter, as long as the numbers increase as satisfaction increases. Which point is going to be the most satisfying to Chris? The answer is simple. Chris is going to choose that point on his budget constraint that lies on the highest obtainable indifference curve. Chris is going to find that point that gets him to the highest level of satisfaction and that is the point that he will choose.
In this picture, the highest indifference curve that Chris can reach is the one that I've labeled U[0], and the combination of toys and snacks that maximizes Chris' satisfaction is going to be two, four, six snacks and two toys. With six snacks and two toys, how much money is Chris spending? Well, let's see. Six times $1.00 apiece is $6.00 on snacks and two toys times $3.00 apiece is $6.00 on toys. Six and six makes a total of twelve and that, of course, is Chris' income, which is why this point is on the budget constraint. The total spending is equal to $12.00, the amount of money Chris has to spend.
So, to find the point that gives Chris the most satisfaction, find the budget constraint and then look for the indifference curve, the highest indifference curve that that budget constraint touches. Now, there's something to notice about how to identify that highest attainable indifference curve. Notice that the budget constraint is tangent to that indifference curve. That is, the budget constraint touches it in one and only one place. Any other budget constraint, any other indifference curve--Well, let me make sure I say this clearly. Any other indifference curve that touches this budget constraint will touch it in two places. Only at this highest attainable indifference curve do we have a single point of tangency.
Let's look at some other possibilities. Suppose we look at this lower indifference curve. Notice this lower indifference curve touches Chris' budget constraint up here and it touches it again, down here. The thing to notice about these two points of interception is that at both of these points the indifference curve has a slope that's different from the slope of the budget constraint. That is it's not a tangency, it's an interception. It's a point where the budget constraint and the indifference curves have different slopes. The indifference curve cuts into and goes through the budget constraint.
Here's a little bit of intuition to let you know why this can't be the best point for Chris. Think about this. At every point on the budget constraint, the slope is three. That means Chris always has the opportunity to trade one toy for three snacks. Down here, at this particular point, the slope of the indifference curve is flatter. That is, the marginal rate of substitution is less than three. That is, Chris would be willing to give up a toy for less than three snacks, maybe just for two snacks. Ah, think about what that means. Chris is willing to give up a toy for only two snacks, but the market will give him three snacks. What's Chris going to do? Obviously, he's going to trade with the market. Obviously, he's going to give up his one toy and take his three snacks.
Two snacks would make him indifferent. Three makes him better off. That's an improvement on his situation. So, Chris starts moving up his budget constraint, trading toys for snacks until he finally gets to the point at which his desire to trade is equal to his ability to trade. That is, at this point, where the slope of the indifference curve, the marginal rate of substitution is also three, Chris is willing to trade one toy for three snacks and that's exactly what the market will allow. At that point, Chris can no longer improve his situation by trading away his toys. He stops. He has reached an optimum.
Look at this point up here. At this point, the marginal rate of substitution is very high, higher than three. That is, that Chris would be willing to give up more than three snacks to get an extra toy. Aha. But the market will only charge him three snacks. He's willing to give up four. So what's he going to do? He'll give up the three snacks and take an extra toy and he's better off. He's better off because he's willing to give up four snacks and he only had to give up three. That is, he pockets an extra snack and he moves down the budget constraint. Chris makes himself better off. He continues to trade until finally the marginal rate of substitution is equal to the relative prices in the market.
So, there you have it. The conditions of consumer optimum, the conditions of maximizing satisfaction is that the marginal rate of substitution is equal to the relative prices of the goods in the market. At that point, an indifference curve is tangent to the budget constraint and that's the highest level of satisfaction that Chris can afford.
Let's do a quick summary here. The budget constraint represents your opportunities and its slope is the relative price in the market. The indifference curves represent your preference and their slope is the rate at which you will trade off the goods, one for the other. The consumer gets the most satisfaction by finding the highest attainable indifference curve. That's going to occur at the point where the budget constraint is tangent to or touches the indifference curve at one place. The interesting thing about that point is that's the place where the relative prices are equal to the marginal rate of substitution, the slope of the indifference curve. That's the point at which the rate at which the consumer is willing to trade is equal to the rate at which the market will allow him to trade. Now, let's mess with that budget constraint and see how the optimum point moves around as prices change. This will get us a demand curve.
Consumer Choice and Household Behavior
Consumer Optimization
Locating the Consumer's Optimal Combination of Goods Page [2 of 2]

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