This is an excellent question that has been asked several times before. Here are some of the usual answers as to why only one fifth of the harvest would have been sufficient to last seven years:
Note the comments of Ellicott:
(34) Take up the fifth part of the land.—Heb., let him fifth the land, that is, exact a fifth part of the produce. It has been supposed that it had been usual in Egypt to pay to the king a tithe of the crop, and the doubling of the impost would not press very heavily on the people in these years of extraordinary abundance. As the reason of the enactment would be made known, it would also induce all careful people to store up a portion of their own superabundance for future need.
Benson is more specific:
Let him appoint officers to take up a fifth part — ... why only a fifth part, seeing the years of famine were to be as many as the years of plenty?
- 1st, Because people would live more sparingly in the time of the famine.
- 2d, It is likely that many persons, in all parts of the country, besides the king, would lay up great quantities of corn [= "grain" in modern English], both because they could not easily consume it all, and in expectation of a time of greater scarcity and dearness, when they might either use it themselves, or sell it to their advantage. Add to this,
- 3d, That even the fifth part of the produce of those years of plenty might be more than the half, yea, equal to the whole crop of ordinary years.
Matthew Poole gives almost identical three reasons, as does Gill.