Editor’s Note: You may have heard that price theory needs a revival. We agree. The economic way of thinking has of late been subsumed by mathematical analysis absent intuition. Fortunately, Professor Bryan Cutsinger is here to help. We are happy to present this first in what will [for now] be a monthly series in which Cutsinger presents price theory questions for your consideration.
Professor Cutsinger will be present for two weeks for feedback in the Comments section, helping you to “solve” each problem. We can’t wait to see your responses!
Question 1:
In his book, Basic Economics, Thomas Sowell (2015) writes, “the price which one producer is willing to pay for any given ingredient becomes the price that other producers are forced to pay for that same ingredient” (p. 20). With that quote in mind, consider the following scenario:
The demand to drink milk rises while the demand for milk in the form of cheese, ice cream, and yogurt remains the same. Assume that the supply of milk is perfectly inelastic. Explain why the elasticities of demand for milk in these other uses determine how much milk will be reallocated from these uses for direct consumption.
READER COMMENTS
David Henderson
Sep 18 2024 at 2:27pm
Quick friendly suggestion re use of the word “intuition.” When I grew up, we used the word “intuition” to refer to some gut feel that came to you absent any reasoning. It was only when I got into economics that I heard the word “intuition” used the way you use it, Bryan. But it’s not intuition. It’s understanding.
Bryan Cutsinger
Sep 19 2024 at 10:24am
Thanks, David!
Amy WIllis
Sep 23 2024 at 8:47am
Hi David,
That wording was mine, not Bryan’s, so he’s innocent. 🙂 We hope that intuition leads to understanding, and that practicing such problems will build it!
Amy
Robert EV
Sep 18 2024 at 2:33pm
Barring theft, demand in a market economy is equal to the dollars put forward to that purposes.
Dollars to drink milk = DM
Dollars for cheese = DC
Dollars for ice cream = IC
Dollars for yogurt = DY
Supply of milk = 1 (constant)
DM + DC + IC + DY = 1
If DM increases, and DC + IC + DY stays the same, then DC + IC + DY must be a smaller proportion of the supply of milk. Since we already know that the demand (aka dollars) for milk for the other uses stays the same, I don’t understand how elasticity factors in here? The elasticity is imposed by the increasing demand for milk to drink, and unwillingness of people to pay more for the other products. This “elasticity” will be directly proportionate with cheese, ice cream, and yogurt each decreasing by an equal fraction of supply, unless suppliers alter the allocation based on profit margin.
E.g. let’s say we have 5000 milk units of drinkable milk (D), 200 milk units of cheese (C), 1000 milk units of ice cream (I), and 600 milk units of yogurt (Y). If demand for drinkable milk increases by 500 units, then allocation for C+I+Y goes from 1800 units to 1300 units. So C = 200 * (1300/1800) = 144.4 units, I = 1000 * (1300/1800) = 722.2 units, and Y = 600 * (1300/1800) = 433.3 units of milk.
I don’t want to do the dollar calculations.
Robert EV
Sep 18 2024 at 2:49pm
I think I get it now. Prices are going to rise for all milk products. People have shown they’ll pay more for drinkable milk, but they haven’t shown how much more they will pay each for cheese, ice cream, and yogurt. There will be a period of trial and error as producers reduce the amount of cheese, ice cream, and milk on the market, raise prices on all milk products, and consumers show which they are willing to buy at what prices. For things like aged cheeses with long lead times, the price increase may be delayed, but will ultimately rise, extending the trial and error time for up to a year or so.
This trial and error will result in some shortages when the less available cheese, ice cream, and yogurt are priced too low. It will also result in some wastage when the reverse happens. Eventually prices and availability will settle down with a varying amount of drinkable milk, cheese, ice cream, and yogurt available. These proportions will likely not be the same as before demand for milk increased, as some customers will stop eating ice cream entirely and instead spend their remaining milk money on cheese and yogurt, and et cetera.
Don Geddis
Sep 18 2024 at 8:06pm
Yes, “demand for drinkable milk” should be in units of “dollars”, not in units of milk. You already knew that (you said “the demand (aka dollars) for milk”), but then later you also tried to measure milk demand in milk units (“If demand for drinkable milk increases by 500 units”). That’s the core mistake.
Also, of course, the price that cheese, yogurt, and ice cream makes pay for their milk ingredient will change, and similarly the price they charge for cheese, yogurt, and ice cream can also change. What is stable is the demand CURVE for cheese, yogurt, and ice cream (which means: the quantity demanded at any given price). But the price will change, and then (based on elasticity) the quantity transacted will then change as well.
Just to take an extreme case: it isn’t at all clear that more quantities of milk will be drunk! Just because there is more demand (dollars) for milk, does NOT mean there will be greater quantities. With perfectly inelastic demand (for cheese, yogurt, and ice cream), you might wind up with the exact same quantities, but simply at higher price points. (This of course isn’t realistic, not the least because cheese, yogurt and ice cream sellers would not have settled at the former “stable” equilibrium if demand for their products actually was perfectly inelastic.)
Robert EV
Sep 19 2024 at 12:27am
I was trying to do calculations and wasn’t up to doing the more complex algebra required to equivalate an increase in dollars for the various milk products versus the actual unit reallocation of those products, so simplified by discounting dollars and going straight to the unit allocations.
The demand curve for a particular product can’t be stable as it’s affected by the price changes of other products. I thought this was particularly apt here as most people who buy dairy buy a variety of milk products. Unless they have the personal wherewithal to absorb the price increases, they will need to cut back what they were previously willing to spend on some categories.
Your extreme case is interesting. Yes, I guess it’s possible for the milk producers to not allocate more milk to the better profit center. This would definitely happen if there’s a long enough lead time to convert or build processing facilities. Since this was a demand question I purposefully ignored supply-side considerations to the extent possible. Your case seems to come back to a unit-based demand situation instead of a dollar-based demand situation, though.
Don Geddis
Sep 19 2024 at 11:02pm
The problem scenario has explicit simplifying assumptions, so you have to be a little careful when applying real-world intuition to the problem. Because, in the real world, those simplifying assumptions would probably be false.
Imagine instead a concrete example: customers pay $1000 for each of milk, cheese, ice cream, and yogurt (total: $4000). The problem states: “The demand to drink milk rises.” So suppose that customers will now pay $2000 for milk. The problem also states: “the demand for milk in the form of cheese, ice cream, and yogurt remains the same.” So the same $1000 will be spent on each of cheese, ice cream, and yogurt (while $2000 is spent on milk; total: $5000).
What happens to quantities transacted, under those conditions?
You need to trace the effect through supply, but don’t forget that “the supply of milk is perfectly inelastic.” So if ANY quantity increases, some other quantit(ies) MUST decrease by the same amount. But the thing you get to change is the market price of each good.
Dale Courtney
Sep 18 2024 at 5:16pm
When the demand for drinking milk rises while the total supply of milk remains unchanged (perfectly inelastic), the available milk must be redistributed from other uses—such as cheese, ice cream, and yogurt—to meet this increased demand. This reallocation happens through price changes in the market and is influenced by how sensitive producers are to changes in milk prices, known as the elasticity of demand for milk in these other uses.
Bryan Cutsinger
Sep 19 2024 at 10:26am
Dale,
You’re on the right track but I think you could go further with your analysis. Specifically, how does the elasticities of demand for milk in other uses affect how much milk will be allocated from these uses to drinking milk?
-Bryan
Dale Courtney
Sep 19 2024 at 2:59pm
You’re absolutely right, and I appreciate the prompt to delve deeper.
The elasticities of demand for milk in its other uses directly influence how much milk is reallocated to drinking milk. If producers of cheese, ice cream, or yogurt have an elastic demand for milk, they are highly responsive to price changes; thus, a rise in milk prices will lead them to significantly reduce their milk consumption, freeing up more milk for direct consumption. On the other hand, if their demand is inelastic, they won’t reduce their milk usage much despite higher prices, meaning less milk is shifted to drinking milk. So, the more elastic the demand in these other uses, the greater the reallocation of milk to meet the increased demand for drinking milk.
Bryan Cutsinger
Sep 20 2024 at 1:48pm
Fantastic!
Knut P. Heen
Sep 19 2024 at 8:26am
If the demand for the other uses does not depend on price, no milk will be reallocated.
If the demand for the other uses does depend on price, some milk will be reallocated.
Bryan Cutsinger
Sep 19 2024 at 10:28am
Knut,
I think it’s reasonable to think that the demand for milk as cheese, ice cream, or yogurt, depends, in part, on the price of milk. Given that this is the case, milk will be reallocated from these other uses towards direction consumption. What we want to know is how the elasticities of demand for milk in these other uses influences the amount of milk that each of these uses will give up and reallocate towards direct consumption.
-Bryan
Knut P. Heen
Sep 24 2024 at 12:49pm
The price elasticity is a function of quantum. As soon as we reduce the consumption of cheese by one unit, the price elasticity of cheese changes (in direction of becoming less elastic). It is therefore incorrect to say that the price elasticity of cheese is elastic or inelastic. The price elasticity refers to a specific point on the demand curve, not to the good itself. It may be elastic at the margin, but that does not imply that it is elastic off the margin. You cannot answer “how much” questions with information about the margin. You need to know the demand curve to give a more precise answer than I gave.
The important information is in dQ/dP (the slope of the demand curve). I don’t understand why multiplying the slope with P/Q is helpful at all. Therefore I do not like to talk about elasticity. I talk about the slope of the demand curve.
Phil H
Sep 19 2024 at 9:29am
My 13 year old is doing economics at school, and I can’t deal with his homework any more than I can deal with this. I need more explanation of why the particular simplified model in use here is a reasonable way for me to start learning. Because everything in this question just seems untrue – which is not uncommon for very simplified beginner work, but needs some measure of justification or trust. And they’re both lacking right now.
“the price which one producer is willing to pay for any given ingredient becomes the price that other producers are forced to pay for that same ingredient” – not if there’s any elasticity in the market. And seeing as in the question, we’re explicitly told to think about elasticity, I can’t see how this generalisation helps us. One producer might pay more for some ingredient because of some variation in transaction costs, internal strategic considerations, willingness to sacrifice profit, etc. This does not mean that they will have the capacity to immediately buy up all of the supply. It does not mean that all other producers will immediately start paying that amount.
“the elasticities of demand for milk in these other uses determine how much milk will be reallocated from these uses for direct consumption” – actually, it would be the combination of elasticity in the consumption demand and the elasticity in demand for other uses.
I wouldn’t mind learning this stuff. But I will need an introduction explaining why you’re presenting it this way, whatever this way is. I’d accept the unrealistic simplifications if you explained how it would lead to greater insight.
Bryan Cutsinger
Sep 26 2024 at 2:24pm
Phil,
I understand your frustration. Perhaps I can write down the problem in a manner that clarifies the question I’m asking.
You’re absolutely right that this question jumps midstream into supply and demand analysis, and without that background, the question may seem odd. That said, I disagree that everything in the question seems untrue. You might argue that the assumption of a fixed supply of milk is unrealistic, as producers are sure to produce more as the price rises. I agree that the quantity of milk supplied will rise as the price of milk rises. However, at any given point in time there is a fixed amount of milk to split between various uses. This question can help us understand how the price system allocates the existing stock of milk between competing uses when the demand for one of those uses changes.
I am assuming, as is common with supply and demand analysis, that demanders and suppliers are price takers. I’m also assuming that the law of one price holds. These are common starting assumptions that we can relax if we want to analyze the considerations you discuss in your comment, e.g., transaction costs, strategic considerations, etc. In my view, it’s better to start simple and make things more complicated rather than the reverse.
The price elasticity of demand for milk to drink is not directly relevant here, as we’re considering a situation where the entire demand schedule for milk to drink has increased. Assuming there’s been no change in demand for milk in non-drinking uses, it’s the price elasticities of demand for these other uses that determines how far demanders of milk for non-drinking uses move up their demand curves.
I will post my answer next week. Hopefully I’ll be able to show you that these unrealistic simplifications provide insight.
-Bryan
John Hall
Sep 19 2024 at 1:03pm
We can call cheese, ice cream, and yogurt together a single good, “non-drinking milk”.
The question proposes that demand for drinking milk increases and demand for non-drinking milk is unchanged. Supply of milk is assumed to be perfectly inelastic.
We also can combine both uses of milk together into a demand for milk. Regardless of the elasticities, we have an upward shift in the demand for milk and inelastic supply means that the total quantity is unchanged and the price increases. Total amount spent on milk also increases.
To think about the breakdown, it can help to consider two scenarios:
1) demand for drinking milk is more elastic than demand for non-drinking milk
2) demand for drinking milk is less elastic than demand for non-drinking milk
In scenario 1, if demand for drinking milk is more elastic, then consumers are more price sensitive for drinking milk vs. non-drinking milk. They are more willing to give up drinking milk and instead consume via non-drinking milk.
In scenario 2, if demand for drinking milk is less elastic, then consumers are less price sensitive for drinking milk vs. non-drinking milk. They are less willing to give up drinking milk. This implies that the increase in demand for drinking milk results in more of the supply of milk getting allocated to drinking milk than in scenario 1.
Bryan Cutsinger
Sep 26 2024 at 2:06pm
John,
I think it helps, at least initially, to simplify the problem by considering two sources of demand for milk, as you’ve done here. In this case, however, the price elasticity of the demand for milk to drink is not as relevant as the price elasticity of the demand for milk in non-drinking uses.
In this scenario, the demand schedule for milk to drink has shifted, perhaps due to a change in people preferences or income, so the price elasticity of demand for milk to drink isn’t as relevant as the price elasticity of demand for milk in non-drinking uses, as that will determine how much milk is allocated away from non-drinking uses to meet the increased demand for milk to drink.
One reason to consider the individual price elasticities for the non-drinking uses of milk is to predict the extent to which milk will be reallocated from each non-drinking use. In my answer that I’ll post next week, I’ll elaborate on this point more.
-Bryan
Monte
Sep 19 2024 at 1:23pm
An increase in the demand for drinking milk, rather than just an increase in the demand for milk (assuming perfect demand inelasticity) would indicate the supply of milk is fixed and would force producers to reallocate milk away from the more demand elastic milk products towards which consumers would be more sensitive to price increases.
Price theory questions aside, you state in your excellent paper, Does Price Theory Have a Future, “Without the disciplining emphasis on rationality, tradeoffs, and market feedback [that traditional price theory provides], abstract mathematics and concrete statistics are more likely to obscure rather than reveal the social realities we seek to explain.” I agree and would surmise that the focus on sophisticated mathematical modeling today is an attempt by economists to make their profession appear more scientific. A careful balance of the two, as you point out, would better inform our understanding of how markets work in reality.
What little I’ve learned about price theory has been garnished from Jack Hershleifer’s superb undergraduate text, Price Theory and Applications (4th ed). I wish you well in your crusade to revive it.
Bryan Cutsinger
Sep 20 2024 at 1:55pm
Monte,
Thank you for your well-wishes! I’m flattered that you read my paper with Alex Salter–hopefully you enjoyed it. Hirshleifer’s book is fantastic…one of the best price theory texts there is, in my opinion.
Your answer to the question is terrific! Elasticities are critical in determining the extent to which the alternative uses for milk will be affected by the higher price. One thing I didn’t quite understand was the distinction between an increase in demand to drink milk and an increase in demand for milk. The demand for milk consists of demands for milk in its various uses, so an increase in demand for milk to drink increases the over demand for milk.
-Bryan
Monte
Sep 21 2024 at 10:46am
Maybe a subtle, but not totally unnecessary, distinction? I assumed an increase in demand to drink milk due to consumer’s preference for milk in beverage form only (perhaps as a result of some breakthrough study and/or marketing campaign promoting its nutritional benefits).
Bryan Cutsinger
Sep 26 2024 at 1:58pm
I see. I think we’re saying the same thing in different ways, as what you just described is the scenario I have in mind.
Cheers!
-Bryan
Glen
Sep 22 2024 at 2:28pm
Three questions:
1. How can I subscribe to get notifications of future posts in this series? I only see “subscribe to our monthly newsletter” at the top.
2. Do you want professional economists like myself to abstain from answering? If so, should we abstain indefinitely or just for some initial period?
3. Will you be posting your model answer at some point?
Amy WIllis
Sep 22 2024 at 11:42pm
Hi Glen.
Glen
Sep 23 2024 at 11:40am
Hi, Amy! I’m not sure I understand your answer to my second question. Do you mean that you do want professional economists to answer, or that you do want them to abstain?
Amy WIllis
Sep 26 2024 at 5:26am
Sorry, Glen, I was unclear, By all means we’d love to hear your response! (And those of other economists…)
Bryan Cutsinger
Sep 26 2024 at 1:56pm
Glen,
As far as I’m concerned, everyone is welcome to answer these questions. As Amy mentioned, she created an RSS feed that you can subscribe to for notifications of when we post new questions. Finally, yes, I’ll post an answer next week.
-Bryan
Robert EV
Sep 22 2024 at 3:42pm
Thinking on this further I predict more wood pulp in cheese products until they become “cheese-like”, “cheese-flavored”, or “cheesy” on their label. More thickening agents in the yogurt. And more eggs, aeration, and thickening agents in the ice cream. This allows all demand for dairy products to be met without a corresponding increase in price.
Bryan Cutsinger
Sep 26 2024 at 1:54pm
Robert,
That’s certainly a possibility, but changing the quality of cheese, yogurt, and ice cream by reducing the milk content would reduce demand for those products. That would offset the rise in price brought about by the higher demand for milk to drink and free-up milk for that use.
-Bryan
Amy WIllis
Sep 23 2024 at 8:45am
Hi, all, At @Glen’s request, we created a Cutsinger RSS feed: https://www.econlib.org/feed/?author_name=bcutsinger
Bryan Cutsinger
Sep 26 2024 at 1:51pm
Thanks, Amy!
Glen
Oct 1 2024 at 12:30pm
Okay, here’s my answer, which I’ve withheld because it seemed fair to let the non-economists go first:
The overall demand for milk is the sum of the demands for specific uses: drinking, yogurt, ice cream, and cheese. This is a horizontal sum, meaning that at each price, we can add up the quantities demanded for the specific uses to find the total quantity demanded. (Note that the demand curve for drinking milk comes from end consumers, whereas the other demand curves come from producers who need milk as an input. But the demands still sum in the way I’ve described.)
Therefore, if the demand for any specific use (such as drinking) increases, the overall demand curve shifts to the right. This drives up the equilibrium price. But the vertical supply curve guarantees that the equilibrium quantity stays the same. Therefore, any increase in one use of milk must be compensated by a decrease elsewhere.
The new higher equilibrium price induces the producers of yogurt, ice cream, and cheese to reduce their milk purchases as described by the specific demand curves for those uses. This would be shown as a movement along those curves. How much the quantities change depends on the elasticities of those demand curves. The uses with the most elastic demand will reduce their milk purchases the most, and the uses with least elastic demand will reduce their milk purchases the least, in response to the same increase in price.
For example, if it’s relatively easy to find substitutes for milk in making ice cream, but relatively hard to find substitutes for milk in cheese, then ice cream producers will reduce their milk purchases more than do cheese producers. (To be clear, substitutability in production is only one possible cause of the differing elasticities.)
I believe that answers the question as posed. But I found myself pondering a different question: How do we know that milk drinkers will indeed purchase more milk? After all, if drinking were the only source of milk demand, and if supply were vertical, then consumers would buy the same amount as before but pay more for it. But it turns out the answer to this question is the same as above: Higher demand leads to higher equilibrium price; higher price induces producers of cheese, ice cream, and yogurt to purchase less; therefore, milk drinkers *must* buy more for total equilibrium quantity to remain the same. In other words, the reduction in purchases by cheese/yogurt/ice cream producers is what enables milk drinkers to buy more.
Fun problem, Bryan. I’m curious to see how closely my answer matches yours.
Glen
Oct 1 2024 at 12:31pm
I am annoyed to see that the bullet points I included in my comments disappeared, leaving unspaced paragraphs. Oh, well.
Comments are closed.