From a distant time and a distant country ...
Genesis of the old testament
Pharaoh dreamed that he was standing by the river, and seven cows came up from the river, fat and beautiful, grazing on the grass; Seven cows came up from the river, thin and ugly, and ate the seven fat cows, so Pharaoh woke up. After falling asleep again, I dreamed that seven ears of wheat grew, fat and beautiful, and then seven ears of wheat grew, thin and dry, and swallowed them. Pharaoh woke up and called a man named Yue Se to explain the dream. Yue Se told Pharaoh that there would be seven bumper years and then seven famine years in Egypt, and suggested that when there were seven bumper years, Pharaoh should collect one-fifth of Egypt's land to store food for the famine years, which involved an economic problem. If so, how should Egypt deal with these fourteen years?
In 2002, Hamermesh2002 made an analysis in the paper "How miserable the biblical famine is" in Economic Express.
First of all, Pharaoh faced a two-stage problem: 7 years of abundant years and 7 years of barren years, and solved the optimal decision in 14 years. In the Old Testament, Yue Se suggested that one-fifth of the land should be expropriated in the seven-year bumper year, so that the food saved could last for seven years of famine.
Assuming that the harvest in good years is 1 and the harvest in bad years is 0, Yue Se suggested that Pharaoh store 1/5(0.2), that is, the consumption in good years is 0.8. The age of grain storage is:
Pharaoh's goal is to optimize the food consumption in two periods. Suppose Pharaoh's social time preference is (simply understood as myopia or hyperopia, myopia is 0, and farsightedness is regarded as 1).
Suppose the Pharaoh's utility in each period, and C is the consumption in each period. In the second stage, the unit grain price is zero relative to the first stage, so the intertemporal utility is maximized as follows:
Since it is known that it is 0.8 (the current consumption value suggested by Yue Se), the shift term is obtained as follows:
The consumption in the poor harvest year is equal to the supply in the poor harvest year, that is:
Harvest failure rate in famine years:
Then, given Pharaoh's social time preference and food decay rate, the failure rate of famine years can be calculated.
Hammermesh believes that it is reasonable to set the sum of assumptions to 0.25 and 0.2 respectively, and the corresponding crop failure rate is 0.65, that is, the harvest in the poor year is about one third (0.35) of that in the rich year, which provides a new knowledge increment for the Old Testament.
The analysis method is simple and the story is quite interesting. I recommend it to the followers!