[Editor’s note: We’re bringing back price theory with our series on Price Theory problems with Professor Bryan Cutsinger. You can view the previous problem and Cutsinger’s solution here and here. Share your proposed solutions in the Comments. Professor Cutsinger will be present in the comments for the next two weeks, and we’ll again post his proposed solution shortly thereafter. May the graphs be ever in your favor, and long live price theory!]
Question:
Consider a consumer who user her money income to purchase only two goods: X and Y. Suppose the prices of these goods double as does this consumer’s money income. Evaluate: There will be no change in the quantities of X and Y she purchases.
Share your questions and proposed solutions in the Comments!
READER COMMENTS
Mike
Nov 13 2024 at 12:40pm
At first blush, the consumer has no choice but to continue purchasing X and Y, and the relative price of these goods hasn’t changed so she should continue to purchase the same quantity of each. However, there is some ambiguity in the question.
Does the phrase “a consumer who uses her money income to purchase only two goods: X and Y” mean:
The consumer uses all of her income to purchase some combination of X and Y; or
If the consumer purchases something, it must be some combination of X and Y.
In other words, does the consumer have the option to save money? If so, the problem is much more complicated because numerous factors may influence whether she saves money, such as her discount rate and her expectation about whether the prices of X and Y is going to fall back down or continue to rise.
Bryan Cutsinger
Nov 17 2024 at 8:20pm
Mike,
Great point! My intent was for you to assume this person buys ONLY two goods, X and Y. In my answer, I’ll explore these issues you bring up.
-Bryan
Craig
Nov 13 2024 at 3:05pm
On one level its just changing the nominal price tag of course. I would say in real life there could be marginal tax considerations, but post inflation there’s also the concept that post tax/post mortgage disposable income might rise faster if the mortgage is fixed, but then of course they are now buying three more than two things!
Bryan Cutsinger
Nov 17 2024 at 8:14pm
Craig,
Great point about the interaction of higher income and taxes. In the U.S., wage income taxes are indexed to inflation, so this interaction effect should be minimal. Capital gains and interest income are not, however, so, depending on the source of this person’s income, she may choose different amounts of X and Y.
-Bryan
Kurt Schuler
Nov 13 2024 at 8:45pm
A number of countries have replaced their old currencies with new ones at two for one. For instance, Jamaica introduced the Jamaican dollar, equal to half a Jamaican pound, in 1969. (The idea was to replace the old nondecimal pounds-shilling-pence unit with a decimal unit fairly close in value to the U.S. dollar.) I am not aware of that or similar changes elsewhere causing any changes in consumer demands, because all wages and prices simply doubled in nominal amounts. So, that could be one way that the case works.
You fail to specify in your question a ceteris paribus clause, though. So, unlike the Jamaican case, other things could be happening in the background that will affect your consumer’s preferences. Suppose that X and Y are groceries and bus fare. Suppose further that because of other changes in the economy a grocery store opens right around the corner and the consumer no longer needs to ride the bus to go get groceries. The bus fare hasn’t changed and food prices haven’t changed but the consumer will take the bus less.
Bryan Cutsinger
Nov 17 2024 at 8:12pm
Kurt,
Fair point about all else not being equal. The question does assume constant preferences. In your example, I think of the proximity of the new grocery store as affecting the full price of purchasing groceries, in which case, we get a change in behavior that is consistent with what you described without needing to deal with changing preferences.
-Bryan
Knut P. Heen
Nov 14 2024 at 5:52am
Is she blond?
James
Nov 14 2024 at 4:45pm
If all prices and incomes go up by the same amount, there will be no change in behavior. If there are other products W and Z available, the consumer may switch to them if their prices did not also double. If there is a progressive tax on nominal incomes, the consumer will not be able to maintain the previous consumption patterns.
Bryan Cutsinger
Nov 17 2024 at 8:09pm
James,
You make a great point about the interaction of taxes and inflation on wages. The IRS indexes wage income taxes to inflation, so, leaving inflation measurement issues aside, the interaction shouldn’t have an effect. To the best of my knowledge, the IRS does not index interest income and capital gains to inflation, so in this case, even if this person’s income increased by the same amount as the prices of X and Y, they may consume different amounts of X and Y.
Bryan
Sam Branthoover
Nov 20 2024 at 3:09pm
My intuition is that relative prices aren’t changing, so the slope of the budget constraint isn’t changing. But higher prices means lower income, which means lower Q bought of both but at a proportionately equal rate. But then you’re also positing a proportionate increase in income, which means we’re compensating the individual for the change in prices, and the intersection of tangencies between the budget constraint and indifference curve is exactly the same (because the slope of the budget constraint hasn’t changed, and neither has the indifference curve). Which means no change in quantity.
Just spitballing.
Bryan Cutsinger
Nov 26 2024 at 10:35am
Sam,
Your answer is similar to my own. Of course, we can consider some interesting implications…suppose the price of one of the two goods rises faster than the other or income adjusts more slowly than prices. In those cases, clearly the quantity of goods X and Y this person buys will change.
I’ll post my solution soon!
-Bryan
GG
Dec 3 2024 at 6:40am
My answer is similar to Sam’s- in terms of the Budget line being tangent to the indifference curve at the same equilibrium combination of X and Y.
Since preferences are not changing, the Indifference Curve map remains the same. Doubling the prices of both X and Y brings the budget line inwards parallelly depicting fall in real incomes at same relative price as before. This could have led to disproportionate fall in units of X and Y consumed depending on the shape of the indifference curves, but… doubling money income brings the budget line back to its earlier position as well. So the equilibrium consumption bundle of X and Y remains the same.
Bryan Ferguson
Dec 3 2024 at 8:18am
She will only consume the same quantities of each if the relative values don’t change. Suppose she buys potatoes and lottery tickets before the price increase. To her, a lottery ticket is worth n potatoes. If the price of lottery tickets double but the expected value does not double too, she’s better off buying more potatoes.
Comments are closed.