Query:
Russ buys 5 sirloins per week. True or false: If the worth of sirloin rises by $5 apiece, and if Russ’ preferences and revenue stay fixed, he could have $25 per week much less to spend on different issues.
Resolution:
One of many first issues I emphasize in my micro ideas course is that the behavioral patterns we observe in the actual world are formed by costs. When costs change, so does conduct.
This concept comes straight from client idea. In commonplace fashions, individuals maximize utility by consuming every good as much as the purpose the place the marginal worth of another unit equals its market value. When the worth of an excellent rises—as within the instance we’re contemplating right here—the marginal worth on the optimum should additionally rise. On this case, the marginal worth on the new optimum have to be $5 greater to match the brand new value of sirloin.
As a result of marginal worth falls as Russ consumes extra sirloin, he can restore the equality between marginal worth and value—the situation for his optimum—solely by consuming much less. With out extra details about his revenue or preferences, we will’t say precisely how a lot much less, however we do know that he’ll purchase fewer sirloins than earlier than.
Thus, the assertion within the authentic query is fake: Russ will cut back his consumption of sirloin when its value rises, so it doesn’t essentially observe that he has $25 much less to spend on different issues.
As soon as Extra, With Math
We are able to additionally see this consequence by analyzing Russ’s funds constraint. Suppose Russ makes use of his revenue, M, to buy sirloin, S, and a composite good we’ll name “all different items,” Y. His funds constraint is due to this fact
M=PSS+PYY
Right here, PS and PY denote the worth of sirloin and the worth of all different items, respectively.
The query tells us that the worth of sirloin rises by $5, so his new funds constraint is
M=(PS+5)S+PYY
Since Russ’s revenue, M, and the worth of different items, PY, stay fixed, the utmost quantity of “all different items” he might purchase if he bought no sirloin stays the identical at M/PY. In that sense, the utmost amount of all different items he can devour hasn’t modified.
Nonetheless, the slope of his funds line has modified: sirloin has change into comparatively dearer, so the funds line pivots inward round that intercept. This transformation in relative costs reduces Russ’s possible combos of sirloin and different items, prompting him to maneuver to a brand new optimum with much less sirloin and extra of different items.
On this sense, Russ’s actual revenue has fallen despite the fact that his nominal revenue stays the identical. However as a result of he reoptimizes—reallocating his spending between sirloin and different items when the worth adjustments—it doesn’t observe that he has $25 much less every week to spend on different items.