A puzzle on the Kingdom of Prosperity

Four hundred years ago in the kingdom of Prosperity lived 450 adults. Out of those 450 adults, 400 were farmers and 50 were managers/administrators, including the king, queen, accountant, auditors, guards etc. Each farmer had one hectare of land and they only knew how to grow wheat. Each farm produced about one ton of wheat per year and the total production was just sufficient to feed the entire Kingdom of Prosperity.

Producing one kilo of wheat required about 1000 liters of water and since the Kingdom of Prosperity was located in a desert, there was no rain and the farmers used the water of the nearby river to irrigate their crops.

Q1) Estimate the total volume of water extracted by the farmers of the Kingdom of Prosperity.

The total annual flow of river was about 700 million liter, out of which 100 million liters was lost to evaporation and other phenomena. Whatever was left after the extraction for agriculture was used for fish breeding to provide necessary protein to the population and in the end about 150 million liters of water was released downstream for the wildlife living in the jungle next to the kingdom. Sometimes the villagers went to the jungle to fetch some bush meat when they were fed-up of eating fish and bread all the time. It truly was a kingdom of prosperity and everyone lived happily. The news of its wealth reached distant lands and a curious economist decided to visit the Kingdom of Prosperity.

The curious economist suggested the King to estimate the GDP of the kingdom using the international selling price of wheat, which was about $250 per ton.

Q2) Estimate the GDP of the Kingdom of Prosperity.

The king was so impressed with the economist and his way of measuring production that he renamed his city to the Kingdom of GDP. The economist also suggested that if they start producing rice, their GDP might increase further since the market price of rice is about 60% higher than that of wheat. The king hired an agriculturalist from a distance land and trained the farmers to grow rice.

Compared to wheat, growing rice consumed at least twice the amount of water for the similar yield and without irrigation, the rice yield was negligible. Since there wasn’t enough water in the river to irrigate all the rice fields, farms that were close to the river received more water than those that were far.

Q3) Estimate the maximum amount of rice that can be produced and estimate the new GDP of the Kingdom of GDP.

The farmers started to extract whatever water they could get their hands on, drying out the river and destroying the fish pollution and wildlife downstream. Even though the GDP of the kingdom was greater than before, its population was starving and income inequality was increasing since the farmer who managed to produce rice sold it to the neighboring town and assembled assets. There simply wasn’t enough food for everyone. At the beginning of the next planting season, the king of the Kingdom of GDP died of depression.

The queen took over the management and called upon the council, which consisted of a tax advisor, an MBA, a farmer, a treasurer, a technician and a guard. The tax advisor suggested that the income needs to be distributed from the rich to the poor so the poor can buy food from the neighboring town. To that point, farmer argued that the farmers need to find work and they will not sit at home and live on other’s income.

The MBA suggested that they need a taxation system that dis-incentivizes people to use too much water and effectively makes farmers indifferent to growing rice or growing wheat*. If they effectively tax the water, they might sustain the whole ecosystem and manage to bring back the fish population and wildlife.

Q4) Estimate the tax rate per thousand liters of water to implement this strategy.

The queen quite liked the idea but was concerned about how to smoothly introduce the proposed taxation without societal backlash and how to enforce and monitor it. To that, the treasurer suggested that the income tax could be reduced and public services, such as health care and education, could be made further better. To address the issue of enforcement, the technician and the guard teamed up to come up with state of the art monitoring and enforcement system. The council decided to implement this strategy and it worked as expected with some minor issues.

The queen died after a couple of years but she changed the name back to the Kingdom of Prosperity because that is what it truly was.

Ans1. 400 million liters

Ans2. $100,000

Ans3. 300 tons; $120,000

Ans4. $ 0.15 per thousand liters

 (These are my own personal views and do not necessarily reflect the views of any organization I am associated with)

Image: wikipedia