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Monday, March 10, 2003

Mark's ISM-Section 1.3- Utility theory-Climbing Mount Joytron. What I’m going to look at next is what economists call indifference curves. We can think of this as a topographical map of Mount Joytron. We’ve got good X going across and Good Y going up, although you can also view this in terms of good X and all other goods. Each of the contour lines is a combination of Good X and everything else that creates the same amount of joytrons. The further to the “northeast” you go, the higher the joytron count and the happier you get.

The curves are bowl-shaped (convex) because in order to keep you at the same level of happiness, you’ll have to give up some other goods in order to get more of X. Also, since we’ll get fewer and fewer joytrons for each additional unit of X, we’re willing to pay less and less to get another unit of X, thus making the curve flatter the further we go east. Unfortunately, we can’t have everything, so we’ll introduce the concept of a budget constraint. Let’s say we have a $1,000 budget and X costs $5. If we blow our entire budget on X, we can get 200 units of X. Thus, we’ll draw a line between 200 units of X and $1000; we’ll set up shop somewhere on that line.

How then do we decide how much X to buy? You get as high up Mount Joytron as you can, to where your contour line just touches (“is tangent to” in mathese) that budget line. You can look at the joytron tradeoff between X and Y by looking at the slope of a tangent line at a given point. The slope will be - (marginal joytrons per X/ marginal joytrons per Y). The slope of the budget constraint will be –(price of X / price of Y). At the point where the budget line and the tangent line have the same slope, we’ll have the marginal joytrons per dollar (MJ/$) of X be equal to the marginal joytrons per dollar of Y. At that point, you get the same bang for the buck for both X and Y.

At our equilibrium point, we’ll have
MJ per unit of X/MJ per unit of Y =$ per unit of X/ $ per unit of Y
Doing a little algebra will give us
MJ per unit of X/$ per unit of X= MJ per unit of Y/$ per unit of Y MJ/$x=MJ/$y
If you set up shop at a point northwest of your equalibrium point A (let's say point B on the graph), you'll get more bang for the buck for X than Y and want to swap for X, for the MJ/$x>MJ/$y. If you set up shop southeast of point A (let's say point C) you'll get more bang for the buck for Y and want to swap X for Y, since MJ/$x<MJ/$y. Translation into everyday language: people will look to get the most bang for the buck for the things they buy and that the joy-per-dollar they get out of one more good X should be about equal to the joy-per-dollar they get out of good Y (or Z or A or B or C). If something game them a better bang for the buck, they probably already purchased it. Coming Soon-Section 1.4-Movin' Those Budget Lines-Income and Substitution Effects.

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