Economics: Deriving the Demand Curve

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We've put indifference curves and budget constraints together to find the consumer's optimal choice under the constraint of the budget and prices. Last time we showed how when the prices changed, the consumer's optimal choice changes. Now we're ready to use the tool we've developed to show where the demand curve comes from. Where does the demand curve come from? It comes from consumers making optimal choices subject to their constraints.
Look at the graph that we had before. Here I've reproduced it in a smaller form. The blue line represents the budget constraint, that is, all the possible combinations of toys and snacks that a consumer can buy with limited income given the prices. The red line represents the highest attainable indifference curve, the most satisfaction that our consumer can get. And here's that optimal point. What I've done is taken the graphs we derived and put another graph beneath it. And this graph is our familiar price/quantity graph that we used for representing a demand curve. Notice on the horizontal axis I've represented the quantity of toys, just like on the axis above it. Quantity of toys is measured on the same scale on both of these axes. So a quantity that comes down to this axis can be dropped on down into the graph below it. These two graphs are measuring the same thing horizontally.
Vertically, this graph down below measures the price of toys. So originally, our original price of toys, which was $3.00 per toy, I call that P[0], the original price. At a price of $3.00 per toy, then our consumer wanted to buy two toys--two toys a week say. So here's a point on the demand curve. At a price of $3.00 per toy, the consumer chooses to buy two toys a week. Now, let's change the consumer's constraints by lowering the price of toys from $3.00 per toy down to $1.50 per toy. When we do that we have to redraw the budget constraint in the diagram above. So here I go--gonna redraw that budget constraint and I'm going to draw it very thick and beautiful so you can see it on the red. There you go. There's the new budget constraint.
Now with this new budget constraint we're going to be looking for a new indifference curve, and that's the indifference curve that's going to be the highest one we can get to given the constraint of the blue line. And as we saw before, in the case of Chris' preferences for toys and snacks, that combination is going to be at a point like this. Here's the new indifference curve--call it U[1], the highest attainable one, and here, right here at this point of tangency is the combination that Chris would choose to purchase in that situation. So when the price of toys drops from $3.00 a toy down to this new lower price of $1.50 per toy. When the price of toys falls, the quantity of toys that Chris consumes increases from two toys a week to, in our case, four toys.
So let me take those four toys a week, and with a dotted line, I'm going to go down below the axis, down into my downstairs diagram, and here's my new quantity, Q[1], or four toys a week. So let's put a new price/quantity dot right there at $1.50 per toy and four toys a week, and there you have it. Hey, once you've got two points, you can connect them, right? And that gives you a demand curve. So you can imagine if we kept doing this exercise, we'd get an endless combination of price and quantity points, and that becomes the demand curve for toys for Chris.
So I've labeled this curve D, that's demand. And this curve does all those things that you've seen demand curves do before. What's the purpose of this lesson? The purpose is to show you where a demand curve comes from. And where does it come from? It comes from consumers who have preferences, and who have constraints imposed by prices and income, doing the best they can with what they've got. As their circumstances change, that is, as prices change, the optimal choice will change. And the demand curve is a record of those optimal choices. As the price rises and falls, the optimal point will move around upstairs in this graph, and as it does, we record it downstairs in this graph, the demand curve.
The demand curve shows you what the consumer will purchase, the quantity of toys Chris will buy as the price of toys changes, holding constant everything else, holding constant income, holding constant the price of snacks, holding constant Chris' tastes and preferences. That's where the demand curve comes from, and that's why we spent that time developing the indifference curve tool and putting it with the budget constraint and learning how to do consumer optimization.
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Consumer Optimization
Deriving the Demand Curve Page [1 of 1]