What am I not understanding about marginal utility?

[Jackson]

I was watching this: http://www.youtube.com/watch?v=DFe-PRKud5g#t=48m40s and Salerno gets to a little quiz to see if the students are understanding the concepts of marginal utility. I believe I failed.

The question is as follows: You are a farmer with five animals, three horses and two cows. You value ends the animals can provide in this order:

1. the first horse, which you use to plow your fields.

2. the second horse, which you use to assist the first horse in plowing your fields.

3. the first cow, which you use for milk.

4. the second cow, which you use for cheese and butter.

5. the third horse, which you use for pleasure riding.

The barn where you house these animals is burning and you can only save four, which four do you save? Which animal has the lower value, “the cow or the horse”?

My answer to this is that ol’ Seabiscuit is left in the barn while the first two horses and the two cows are saved.

He goes on to say that yes, the horse has the lower value and it is left in.

…but he says that the horse has the lowest value. I’ll just quote what he says directly as I’m losing something and I don’t want to obfuscate this further. “yeah, the horse has the lower value. even though it serves the the highest end (this might be what’s confusing me as it looks like he’s pointing to the first horse, the one that does the plowing), we don’t look at the highest end in the term of value (does highest mean the first horse that is plowing or the third horse which is for pleasure riding?) we always look at the lowest end. You would lose the least amount of satisfaction if you allowed the third horse to stay in the barn (which I get).”

but I only get it briefly. He then asks “Once that happens though, which animal is more valuable, the cow or the horse?”

I have no idea what he’s asking. Now I’m left with four animals. I know that if wolves attack my unsheltered livestock and I can only protect three, I’m going to sacrifice Bessy the cheese and butter cow. But Salerno says “now the horse becomes more valuable?”

um…which horse? weren’t the first two horses always more valuable. for instance, in the initial barn burning if I were only allowed to save two animals, I would pull out the two horse plowing team because they meet my most desired ends.

He keeps confusing me “But with these five (pointing to the original list), even though the horse (I thought there were three horses) serves the first two ends, the more valuable animal is the cow because its marginal utility is higher. It’s the satisfaction from the fourth rank down.” well yeah, the cows are more valuable than the horse that is for pleasure riding…but how are they more valuable than the horses that provide the first two ends? and after the fifth horse is burnt up, he seems to say that the second cow is the most valuable because its marginal utility is the highest on the list. wouldn’t it be the case that since the cow is where it is on the list, it is the least valuable - and the next one on the chopping block should circumstances demand?

I don’t know if I’m missing something or if Salerno just butchered this (which I am hesitant to consider).

I hope this made sense. I’m completely befuddled and I don’t know if I can properly communicate right now.

[motoman]

I believe what he means is that before the fire, horses (as a category of goods) are less valuable than cows because there is a horse last on the list. Yes, horses hold the 1st and 2nd positions on the list, but they also hold the 5th position, and therefore as a category of good, that places them lower on the owner’s value scale than cows. You might say the owner has an excess of horses relative to cows.

However, once the third horse (which is valued 5th on the list) is lost to the fire, then as a category of goods horses are now more valuable than cows since now cows hold the 4th position on the list and the lowest valued horse is now 2nd on the list. The idea being that the more units of a good you have the lower you will value that particular good and concurrently, the less of a good you have, the higher you will value that good.

I don’t know if any of this helps. Does any of it make more sense now?

[nirgrahamUK]

you must remember that each horse from the set of horses is homogenous in the sense that each of them could provide each of the horsy services the farmer might want, and so too each of the cows could provide each of the cowish services.

Therefore, a horse might be used for a high end, and cows for a few lower ends and a horse for a lower end still. yet any horse would fit to the highest or the lowest service, they can be swapped. Their marginal utility is equal. they are equally capable of being put to use. Because a horse will always be assigned to a higher end logically prior to a lower end, this means that the marginal utility of each individual horse of all your horses will be equal to the service that the logically last (the most diminished) horse is serving.

Back to the example, if you lose any physically differentiable horse, you will always reassign whichever of the remaining horses to be the plow-your-fields-horse. and another to be the assist the plowing horse, and you will always have lost your pleasure riding horse. This is independant of which physical horse was doing what role before you lost whichever physical horse you lost.

The order of your horse ends, effectively determines which logical horse you will lose when you lose a physical horse (you loose the physical horse that you had used to assit plowing the fields, but logically you still have such a horse, since the physical horse that was previously used for pleasure riding is now logically the horse that you use to assist plowing the fields.

When the example has gone down to 4. your answer is correct the because chees and butter service is the lowest end that a cow services whcih is lower than any end your horses are services then each cow has a lower marginal utility than each horse and you would more happily sacrafice a cow than a horse. an Salerno says that exactly. You choose to keep a horse over a cow. horse has a higher marginal utlity (value) than a cow .

Its not a question of which horse among all of your horses has the higher marginal utlity; all of the horses you own have the same marginal utility because they could each be fit to each horse end.

um…which horse? weren’t the first two horses always more valuable. for instance, in the initial barn burning if I were only allowed to save two animals, >>I would pull out the two horse plowing team because they meet my most desired ends.

we are not imagining that your plow-the-fields-horses are more skilful or stronger than your pleasure ride horse and so are more worth of being saved than it. rather any two horses that you save will logically be horses that you will put to plowing the fields no matter what you had used those physical horses to do before.

[gabriel.syme]

Yes, as others have pointed out this question is rather confusing unless you assume that the animals are fungible. It’s a bad example, IMO.

[Jackson]

thanks, that cleared things up.

I suppose raising quarter horses while I grew up in Alabama made that example nearly impossible to get.