Bananas and Potatoes: A Solution to the Weekend Puzzle


Paul's weekend puzzle below requested answers to the question "What would happen if a community that only produces bananas decides to save more?" It's no longer the weekend, so I figured I'd answer separately:


Forgive my ignorance, but exactly how does one "save" a banana?

It's not durable; once picked, it must be consumed within seven days. Now potatoes kept in premium conditions can last about six months. So, in order to save for the future, banana growers have to buy more potatoes; to finance their purchases, they try to sell more of their fruit to potato-growing communities. They've been selling fruit for some time, I gather, and market prices have been at an equilbrium for ages, say at 2 bananas for 1 potato.

Let's use the elementary economics of a barter economy -- that way relative prices incorporate interest rates: What happens first? Banana growers preferences change, though potato growers preferences remain the same. Let's assume that B-growers' discount rates decrease -- that is they value utility in the future more than before. Yet quantity currently available of B and P are fixed. Banana growers, wanting potatoes, reduce their own banana consumption, and increase the supply of bananas on the market. That is, banana growers begin to offer more bananas for every additional potato to entice potato growers to exchange further, and finding it worthwhile, the potato growers agree to these exchanges.

The equilibrium market price (of potatoes per banana) falls; to get one potato, B-growers must give up now, say 3 bananas for one potato. Quantity exchanged increases. For banana growers, present consumption of B decreases, consumption of P decreases (they've become more expensive relative to B), and saving of P increases. Potato growers consume more B, decrease consumption of P (again, substitution-price effects), and we don't know about the net effect on saving of P (they can get more B for them, but they're decreasing consumption of P).

Now, we know potato growers are better off, or they wouldn't trade for more bananas. But banana-growers had a change in preferences, so it's unclear if they are better off or worse off; while the new market order has made them better off than immediately after their preferences changed, it is impossible to say (without examinining specific forms of the before and after utility functions) whether they have higher utility after the change in preferences than before. Do they really do valuing saving that much???

This is a four-part model:

1) Evenly-rotating old market order: 2 B for 1 P
2) Change in B-prefs
3) Short-Term New Market Order: 3 B for 1 P *P growers better off
4) Long-Term New Market Order

How do B and P growers respond to the short-term new market order? That all depends on the marginal cost of producing additional potatoes. The greater number of bananas per potato available in the market means some P growers see an opportunity to profitably produce more; they set higher future yeilds so that their own marginal cost is lower than the expected future market price of potatoes to bananas. However, the lower number of potatoes per banana hits the high-cost marginal banana producer hard; he leaves the farm and works as a middle-man facilitating the burgeoning banana-potato trade.

And "interest rates"? They're the differential you have to pay in order to acquire command of resources now instead of later. Hence they're directly related to consumption preferences.

[Present Value] = [Future Value]/(1+r)^n

In our model, both bananas and potatoes can be consumed, but only potatoes can be saved. B growers decide to consume more later and less now. They want more potatoes, less bananas. The change in preferences increases the present value of future consumption, decreasing the cost of current consumption (bananas). Interest rates decline.

Extra: Let's say banana-growers want to save LESS. They decrease banana supply. Quantity exchange decreases, and prices for bananas rise (number of potatoes per banana). Potato growers are made worse off because the cost of eating bananas has risen, but again, we can't see what happened to banana-growers.


Go big time. Add cattle and wheat.

Bananas can be processed into various long-term food products. I'm working my way thru a bottle of Jufran banana hot sauce right now.

One can also dry and save the stringy part of the peel...


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This page contains a single entry by Kevin published on March 7, 2006 8:11 AM.

For Hedonists it is without Parallel was the previous entry in this blog.

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