Monday, October 20, 2008

A Sushi Model of Capital Consumption

Robert P. Murphy "(...) Without further ado, let's examine a hypothetical island economy composed of 100 people, where the only consumption good is rolls of sushi.

The island starts in an initial equilibrium that is indefinitely sustainable. Every day, 25 people row boats out into the water and use nets to catch fish. Another 25 of the islanders go into the paddies to gather rice. Yet another 25 people take rice and fish (collected during the previous day, of course) and make tantalizing sushi rolls. Finally, the remaining 25 of the islanders devote their days to upkeep of the boats and nets. In this way, every day there are a total of (let us say) 500 sushi rolls produced, allowing each islander to eat 5 sushi rolls per day, day in and day out. Not a bad life, really, especially when you consider the ocean view and the absence of Jim Cramer.

But alas, one day Paul Krugman washes onto the beach. After being revived, he surveys the humble economy and starts advising the islanders on how to raise their standard of living to American levels. He shows them the outboard motor (still full of gas) from his shipwreck, and they are intrigued. Being untrained in economics, they find his arguments irresistible and agree to follow his recommendations.

Therefore, the original, sustainable deployment of island workers is altered. Under Krugman's plan for prosperity, 30 islanders take the boats (one with a motor) and nets out to catch fish. Another 30 gather rice from the paddies. A third 30 use the fish and rice to make sushi rolls. In a new twist, 5 of the islanders scour the island for materials necessary to maintain the motor; after all, every day it burns gasoline, and its oil gets dirtier. But of course, all of this only leaves 5 islanders remaining to maintain the boats and nets, which they continue to do every day. (If the reader is curious, Krugman doesn't work in sushi production. He spends his days in a hammock, penning essays that blame the islanders' poverty on the stinginess of the coconut trees.)

"Any talking head on CNBC who doesn't understand capital consumption is going to give horrible policy recommendations."

For a few months, the islanders are convinced that the pale-faced Nobel laureate is a genius. Every day, 606 sushi rolls are produced, meaning that everyone (including Krugman) gets to eat 6 rolls per day, instead of the 5 rolls per day to which they had been accustomed. The islanders believe this increase is due to use of the motor, but really it's mostly due to the rearrangement of tasks. Before, only 25 people were devoted to fishing, rice collection, and sushi preparation. But now, 30 people are devoted to each of these areas. So even without the motor, total daily output of sushi would have increased by 20%, assuming the islanders were equally good at the various jobs, and that there were plenty of fish and rice provided by nature. (In fact, the contribution of the motor was really only the extra 6 rolls necessary to feed Krugman.)

But alas, eventually the reduction in boat and net maintenance begins to affect output. With only 5 islanders devoted to this task, instead of the original 25, something has to give. The nets become more and more frayed over time, and the boats develop small leaks. This means that the 30 fishermen don't return each day with as many fish, because their equipment isn't as good as it used to be. The 30 islanders making sushi are then in a fix, because they now have an imbalance between rice and fish. They start cheating, by putting in smaller pieces of fish into each roll. The islanders continue to get 6 rolls per day, but now each roll has less fish in it. The islanders are furious — except for those who are repulsed by the idea of ingesting raw fish.

Being a trained economist, Krugman knows what to do. He suggests that 2 of the rice workers and 2 of the sushi rollers switch over to help the fishermen. Now with 34 workers, the islanders are able to catch almost as many fish per day as they were in the previous months, even though they are now using tattered nets and dilapidated boats. Krugman — being very sharp with numbers — moved just enough workers so that the fish caught by the 34 islanders matches up perfectly with the rice picked by the remaining 28 islanders who go to the paddies every day. With this amount of fish and rice, the 28 workers in the rolling occupation are able to produce 556 sushi rolls per day. This allows everyone to consume about 5 and a half rolls per day, with a bonus roll left over for Krugman.

The islanders are a bit concerned. When they first followed Krugman's advice, their consumption jumped from 5 rolls to 6 per day. Then when things seemed to be all screwed up, Krugman managed to fix the worst of the discoordination, but still, consumption fell to 5.5 rolls per day. Krugman reminded them that 5.5 was better than 5. He finally got the crowd to disperse by talking about "Cobb-Douglas production functions" and drawing IS-LM curves in the sand.

Because this is a family-friendly website, we will stop our story here. Needless to say, at some point the 5 islanders devoted to net and boat production will decide that they have to cut their losses. Rather than trying to maintain the original fleet of boats and original collection of nets with only 5 workers instead of 25, they will instead focus their efforts on the best 20% of the boats and nets, and keep them in great shape. At that point, it will be physically impossible for the islanders to prop up their daily sushi output. In order just to return to their original, sustainable level of 5 sushi rolls per person per day, the islanders will need to suffer a period of privation where many of them are devoted to net and boat production. (We can only hope that Professor Krugman has been rescued by the Swedes by this time.)

The 5 people looking for ways to synthesize gasoline and motor oil will have to abandon that task, because it was never appropriate for the islanders' primitive capital structure. The islanders will of course discard the motor brought to the island by Krugman once it runs out of gas.

Finally, we predict that during the period of transition, some islanders will have nothing to do. After all, there will already be the maximum needed for catching fish with the usable boats and nets, and there will already be the corresponding number of islanders devoted to rice collection and sushi rolling, given the small daily catch of fish. There would be no point in adding extra islanders to boat and net production, because then they would end up building more than could be sustained in the long run. Hence, the elders rotate 10 people every day, who are allowed to goof off. They could of course go try to catch fish with their bare hands, or go gather rice that would just be eaten in piles by itself, but everyone decides that this is a waste of time. Given the realities, it is decided that during the transition, 10 people get the day off, even though everyone is hungry. That is just how bad Krugman's advice was."


JoaoMiranda said...

Muito bom.

Miguel Madeira said...

A gasolina é suposta ser uma injecção de capital sem poupança prévia?

CN said...

Suponho que possa assim ser visto, embora a injecção de moeda não faça aparecer capital que não existia, apenas desloca capital de outras sítios e no final acaba mesmo a consumir capital existente para a ilusão temporária que a produção/consumo aumentou.