Last week we got separate answers to the key questions a consumer faces: 'What is feasible?' and 'What is desirable?' This week, we see how consumers combine the answers to these two questions in order to make an actual choice. After seeing that (and noticing what this theory actually predicts), we also take note that our model works equally well if we don't know the outcome of our choices with certainty.
The key in combining what is feasible and what is desirable is to notice that our budget line and indifference curves can go on the same graph since they have the same axes. We know from this that individuals can only reach indifference curves that are in the feasible set (at least least a single point). Getting more would be nice but it's not in the cards. So, since the goal of the consumer is to maximize utility, the choice the consumer makes has to be the one that gives the highest utility for the given budget, which means it's going to have to be on the budget line somewhere.

Because of the other assumptions we make about how indifference curves work, we know that the best or highest indifference curve can't be one that cuts below the budget line anywhere, because that would mean our choice is no better than one that gives us less of both goods than we could get. So the choice of the consumer has to occur where the budget line and indifference curve are tangent (touch at one and only one point). This also yields the interesting result that the slope of the budget line, which is the relative prices and thus represents the trade-off between the two goods in the market, has to be equal to the slope of the indifference curve, which is the
marginal rate of substitution and represents the trade-off between the two goods in the mind of the consumer. This makes sense: if apples are $1/lb and oranges $2/lb, but in your mind you'd be willing to swap 3 apples to get an orange, you have incentive to change your behavior: buy fewer apples and more oranges. So the choice of the consumer has to look like the graph on the right.
Once we think of equilibrium this way, we can see that the price of the good, the price of related goods (or what you think the price will be in the future), and your income (or what you think your income will be in the future) will all change the quantity demanded in the ways we've been saying they will with demand curves. The demand curve is derived from the combinations of goods that the consumer views as utility maximizing for various prices, and this relationship shifts when anything else that changes the budget line shifts. Finally, of course, if your preferences (in the form of indifference curves) change, then of course your choice will too.
The last thing we covered this week is that we don't need to know for sure how much utility a choice will give us as long as we can figure out our
expected utility. This makes matters a bit more complicated, but it brings up the idea that people tend to dislike taking risks (this skiing guy notwithstanding). Most of us, if given the choice between going home as we are, or risking $50 against somebody else (winner takes home all $100, so $50 extra) on a fair coin flip, we'll just go home. Actually, even if the other guy puts an extra $5 on the table, so we could win bigger than we could lose, we'd still walk away. It's worth something to us to have the guarantee rather than taking the risk.
We actually assumed this was the case last week when we said consumers had diminishing marginal utility. This assumption means that the line representing different chances of winning a high level of utility or a low level is always below the utility function itself. Essentially, expecting to win $200 on average is never going to make us as happy as having $200 for sure. Not only that, but depending on our chances of winning big (where on the line we are), the gamble gives us the same utility as if we were guaranteed a smaller amount of money, say $175. We would actually be willing to pay up to $25 of the expected winnings in order to be guaranteed that we won't lose.
This
risk-aversion is what makes insurance companies profitable. You see, all of life involves gambles we can't really get out of--car crashes, house fires, severe illness or injury, you name it--and we are willing to accept a little bit less than we would get
on average if only we can be guaranteed the outcome. The insurance company makes an offer: if you win $400, we'll take the money and you'll only get $180 of it; but if you win nothing, we'll
still give you $180, and we'll eat the loss. Since we're risk averse, this guaranteed $180 gives us more utility than expecting $200
on average (which gave as much utility as a guaranteed $175). The insurance company knows if it does this a lot, it will bring in about $200 per person and only have to pay out $180. Steady employers can work this way, too: if you did your job freelance you might be able to make more money
on average, but your income would go up and down a lot depending on how business is doing this week. If you take a steady job, though, your employer absorbs at least some of the risk, so you're OK making a bit less.
So there you have it. Equilibrium choices, with and without risk. We'll have more to say about risky decision toward the end of the semester. The key idea will be that risk works this way assuming everyone involved is uncertain about the same things. Things get trickier when one side of the market knows something about the outcome that the other doesn't. But that's for another day.
Next week I'm giving an exam, so no lectern post. I'll have to come up with something fun instead!