How could only 20% tax of 7 years of plenty be sufficient for the subsequent 7 years of famine?

Joseph said to Pharaoh in Ge 41:

34 "Let Pharaoh proceed to appoint overseers over the land and take one-fifth of the produce of the land of Egypt during the seven plentiful years.

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Store 1/5 of the produce for 7 years.

35 And let them gather all the food of these good years that are coming and store up grain under the authority of Pharaoh for food in the cities, and let them keep it. 36 That food shall be a reserve for the land against the seven years of famine that are to occur in the land of Egypt, so that the land may not perish through the famine.”

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How could only 20% tax of 7 years of plenty be sufficient for the subsequent 7 years of famine?

In the average year, Egypt produced more food than it consumed. So, you don't need to double your average production to cover the 7 years of famine. Each of the seven years of plenty produced more than the average yearly yields.

During the famine years, food was distributed carefully to make it last. People were consuming less than the average year.

There were some levels of harvest in the first 2 years. Joseph spoke to his brothers in Ge 25:

6 "For the famine has been in the land these two years, and there are yet five years in which there will be neither plowing nor harvest.

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13 You must tell my father of all my honor in Egypt, and of all that you have seen. Hurry and bring my father down here.”

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Strict rationing was likely implemented in the later years.

The farmers traded in their animals for food in Ge 47:

16 And Joseph answered, “Give your livestock, and I will give you food in exchange for your livestock, if your money is gone.” 17 So they brought their livestock to Joseph, and Joseph gave them food in exchange for the horses, the flocks, the herds, and the donkeys. He supplied them with food in exchange for all their livestock that year.

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Though not explicitly mentioned, during the plentiful years, Joseph might have implemented extra farming run by the government.

Let's say that in the average year, Egypt produced 100 units of food.
Let's say that 20 units were exported.
Let's say that the minimum to stay alive was 60 units.
To keep everyone alive for 7 years, they needed 60 *7 = 420 units.

Now, let's say that each plentiful year, they produced 130 units.
20% tax for 7 years = 130 * 0.2 * 7 = 182 units.
Let's say that in year 1 of famine, they produced 60 units.
Year 2, they produced 50 units.
The extra government farming produced 10 units/year. Total was 70 units.
Their livestock was worth 60 units of food.
182 + 60 + 50 + 70 + 60 = 422 units.

422 was 2 units above the requirement for feeding all the Egyptians for 7 years.

How could only 20% tax of 7 years of plenty be sufficient for the subsequent 7 years of famine? Even on an average year, Egyptians produced more food than they consumed. They exported food. The plentiful years were extraordinarily productive. Joseph might have introduced extra farmland during the seven plentiful years. During the famine years, they tightened their belts and consumed less. They sold their livestock in exchange for food for a year.