Question:
Russ buys 5 sirloins per week. True or false: If the price of sirloin rises by $5 apiece, and if Russ’ preferences and income remain constant, he will have $25 a week less to spend on other things.
Solution:
One of the first things I emphasize in my micro principles course is that the behavioral patterns we observe in the real world are shaped by prices. When prices change, so does behavior.
This idea comes straight from consumer theory. In standard models, people maximize utility by consuming each good up to the point where the marginal value of one more unit equals its market price. When the price of a good rises—as in the example we’re considering here—the marginal value at the optimum must also rise. In this case, the marginal value at the new optimum must be $5 higher to match the new price of sirloin.
Because marginal value falls as Russ consumes more sirloin, he can restore the equality between marginal value and price—the condition for his optimum—only by consuming less. Without more information about his income or preferences, we can’t say exactly how much less, but we do know that he will buy fewer sirloins than before.
Thus, the statement in the original question is false: Russ will reduce his consumption of sirloin when its price rises, so it doesn’t necessarily follow that he has $25 less to spend on other things.
Once More, With Math
We can also see this result by examining Russ’s budget constraint. Suppose Russ uses his income, M, to purchase sirloin, S, and a composite good we’ll call “all other goods,” Y. His budget constraint is therefore
M=PSS+PYY
Here, PS and PY denote the price of sirloin and the price of all other goods, respectively.
The question tells us that the price of sirloin rises by $5, so his new budget constraint is
M=(PS+5)S+PYY
Since Russ’s income, M, and the price of other goods, PY, remain constant, the maximum amount of “all other goods” he could buy if he purchased no sirloin remains the same at M/PY. In that sense, the maximum quantity of all other goods he can consume hasn’t changed.
However, the slope of his budget line has changed: sirloin has become relatively more expensive, so the budget line pivots inward around that intercept. This change in relative prices reduces Russ’s feasible combinations of sirloin and other goods, prompting him to move to a new optimum with less sirloin and more of other goods.
In this sense, Russ’s real income has fallen even though his nominal income remains the same. But because he reoptimizes—reallocating his spending between sirloin and other goods when the price changes—it does not follow that he has $25 less each week to spend on other goods.
READER COMMENTS
Fazal Majid
Oct 16 2025 at 9:56am
rick shapiro
Oct 16 2025 at 10:14am
In a real Giffen situation, his spending power doesn’t decrease by more because he is spending less on lobster. In any case, This can’t be a Giffen situation because chuck steak is cheaper; and he will find that it is much better (provided that he hasn’t neglected dental hygiene).
Jon Murphy
Oct 16 2025 at 11:04am
If you change the problem fundamentally and violate the Law of Demand, yes the answer will change. But there’s no reason to do this.
Craig
Oct 16 2025 at 12:19pm
Craig buys coffee all day every day any day. True or false: If the price of coffee rises by 50% (it HAS gone up of late actually) and if Craig’s preferences and income remain constant, he will have $X a week less to spend on other things.”
Here of course I have an advantage, I know my preferences and I’m drinking my coffee and if it ever becomes unavailable defecting to Colombia. So I know that if coffee were to cost me an additional $25 per week I’m still going to drink that coffee. Its just not a material amount of money and so I’ll cut back on something else without really even realizing what I’m cutting back on, but at that price difference I’m definitely on an inelastic portion of my personal demand curve.
We don’t know Russ’ preferences except that they actually remain unchanged. The only thing we do know is that Russ apparently does eat sirloin five times per week, so he must really like it otherwise he probably wouldn’t do that, one inference is that at that point the $5 increase may be immaterial to him. We have no idea though.
David Seltzer
Oct 16 2025 at 1:30pm
Bryan, nicely informative. You mention budget constraint M. I assume either lagrangian λ, = the ratio of marginal utility to price, (maximizing utility s. t. M). Or λ = the ratio of expenditure E to fixed utility. (minimize E s. t. fixed utility and M). Either way, in their elegance, they are mathematically equal. As you state, we don’t know Russ’s preferences, I suspect it’s because we don’t know his utility or indifference functions and therefore his MRS. Both Marshallian and Hicksian functions assume known utility functions. As a result his utility can only be weakly inferred. All one sees are Russ’s choices. It is difficult to know what his alternatives are and where they are on his indifference curve. As prices are supremely important it makes sense to speak of known trade-offs in terms of opportunity costs. Opportunity costs are known to Russ and can only be inferred by an observer,
Andrew Swift
Oct 17 2025 at 6:22am
Without information about elasticity there is no “right” answer.
It would be good to at least state explicitly the assumptions made about elasticity.
Perhaps Russ’ steak consumption is largely determined by non-financial effects — he would eat more but his doctor has warned him not to, or his wife doen’t like steak etc.
Jon Murphy
Oct 17 2025 at 9:21am
That objection is discussed in the answer.
Irrelevant. See the math.
nobody.really
Oct 17 2025 at 10:47am
Would you be so kind as to quote that discussion? I’m somehow missing it.
For all I know, Russ’s faith commands him to eat sirloin 5x/wk. Would a $25/wk fee be enough to compel him to abandon his faith? (Yeah, people may abaondon their faith for smaller reasons than that, though arguments that the Muslim tax on non-Muslims prompted conversions are disputed.)
Jon Murphy
Oct 17 2025 at 2:28pm
nobody.really
Oct 17 2025 at 4:12pm
How do I know that Russ’s marginal value for consuming steak declines? For all I know, Russ HATES eating steak, but does so to fulfill a religious commitment. Or a work-out regimen. Or a bet. Or an oath. Without more information about his preferences, we can’t say exactly how much less he would consume–if ANY.
Rob Rawlings
Oct 17 2025 at 5:25pm
‘Without more information about his income or preferences, we can’t say exactly how much less, but we do know that he will buy fewer sirloins than before’
Its easy to think of scenarios consistent with marginal utility theory where he will not buy less sirloin just because its prices rises – so that is an incorrect statement.
Knut P. Heen
Oct 21 2025 at 8:26am
Don’t tell Russ what to do. What Russ does is an empirical question.
It is entirely possible that someone has a preference for eating five steaks a week for a large range of steak prices. It is possible to be a stubborn. The Econ101 model (Cobb-Douglas utility) does not allow for such preferences, but that is a limitation of the model rather than anything else.
Avram Levitter
Nov 2 2025 at 4:48am
Russ doesn’t necessarily change his economic behaviors at all; instead he decides that in the upcoming election, he might value a candidate whose platform promises to reduce the cost of sirloin more than he did previously. Maybe if the promised reduction brings it back to the initial price, he’d even be willing to spend up to $5200 (the increase in price of 5 sirloins a week over four years) in campaign contributions.
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