Trade Incentives and Whoppers: A Finger Exercise
Nick Rowe was looking for the role of money in the Heuristic Macro Model, which is often used to introduce students to Trade economics. The problem he discovered is that there is only a role for money if there is friction in the model, and therefore a two-household (or household-firm or firm-firm) model makes money if not superfluous, then at least a poor substitute to direct barter.
Following is a “finger exercise” for introductory economics the way (I think) it should be taught, using that heuristic model and the Whopper story that often is used at the start of Introduction to Economics.1
Telling a Whopper
The Whopper story basically has the eager student challenging talk about scarcity and optimal reource allocation by saying, “But I can go into Burger King and get a Whopper for $1 and I can keep ordering $1 Whoppers all night.” The general Professorial Counter runs “well, that wouldn’t really happen because you run out of money and/or they run out of supplies,” which is a missed opportunity.
First, relax all of the normal constraints. You have an unlimited cash availability, and the Burger King has unlimited supplies and is open 24/7. Both the workers and any other customers are nether going to be irritated by you buying a new Whopper every five or ten minutes nor start calling their friends/hitting social media to get others to see the “spectacle” (no external incentives to start or stop). Oh, and the $1 price includes any taxes.
All Hail Declining Marginal Utility
For the first few rounds, both parties will act in keeping with the premise. You get your second, third, fourth, and even fifth Whopper and have spent $5.
You also are now less hungry than when you bought the first Whopper. That first Whopper cost you $1–and you valued it at least that much, if not more (consumer surplus >=0). The second was almost as good as the first; still well worth its dollar. The third, fourth, and fifth aren’t being eaten to satisfy hunger pangs, but you enjoy them at the $1 price.
You always have the same choice: give a dollar, get a Whopper. But sooner or later,2 you will decide that keeping that next $1 in your pocket is worth more than eating another Whopper (consumer surplus<0).
On to the Model
From this foundation, the two-household trading model finds the value of money.
Household A grows bananas. It produces enough bananas to feed the Household. Household B grows Apples. It produces enough apples to feed the Household.
Let’s make it easy: each Household consists of one person. And the people are both such that they could subsist on eating only apples, only bananas, or a combination of both.3
So there is no need to trade for subsistence. Both Households are Price Makers.
There are two scenarios at t0: either the parties can agree on a rate by which they exchange bananas for apples or they cannot. In the first case, the market clears (total consumer surplus >=0). The second is more interesting.
In the Beginning
Assume, for instance, that the banana grower is willing to trade 2.3 bananas for an apple (23 bananas=10 apples). However, the apple grower wants at least 2.6 bananas/apple. So, in terms of bananas, the best possible offer would be 2.3:1 while the best possible bid requires accepting 2.6:1.4 At t0, no deal can be made. As a classroom example, the banana maker initially offers 2 bananas per apple, while the apple grower requires 3.
From time t1, both sides know no trade means that they must continue eating only bananas(apples). Their total (and individual) Utility depends on the trade-off between their desire for variety in their diet and their willingness to shift their offered price.
Sooner or Later
As with the Burger King example above, the Utility of sameness declines over time. Therefore, the willingness to trade must grow. At tn, the offers will have moved such that they come closer and the difference (initially 0.3 and 0.4) between the offers and the Utility of variety will narrow (Total Consumer Surplusn < Total Consumer Surplus0). Eventually, the parties will trade, at some level between 2.3 and 2.6 (Consumer Surplustotal >=0). The “market” moves with new information, which in this case is that one or both parties is more tired of eating only apples(bananas) than determined to trade at their initial offering level.
With money as a vehicle for intermediation, the added certainty of pricing will both shift some from Price Makers to Price Takers and adjust Utility calculations. Throw in the uncertainty of future price changes and differences in time horizons, and you get to trading quicker.
So, in the two-party Heuristic Model, money is time.
1Feel free to substitute McDonald’s/Big Mac or similar.
2Probably before the store would have run out of supplies even if we hadn’t relaxed the constraints
3Don’t try this at home.
4Apple offer=Banana bid
You have reduced dfmensionality when switching to an unlimited flow and a changing utility. Then, correctly show, the envelope theorem applies, that your optimization function is still convex. All correct.
But money became instant, and we end up neglecting the changing utility of money holdings. So pricing is not part of the equation at all, it is all about the changing utility of apples vs bananas when supply is unlimited.
Mostly . . . 🙂