The correct answer to this open question is the following.
There is no question here. Just a statement.
What is your question? What do you want to know?
You also forgot to mention the time in history and the place for this situation. It could be in European medieval times, it could be in the United States one century ago, it could be in New Spain.
We are going to assume that you are referring to medieval times in Europe.
If this is a true or false question, the correct answer is "false."
It is false that due to a growing peasant population there was "a growing shortage of land". This was a consequence of a growing population.
The portions of land belonged to the rich landlords and the monarchies. Nobles and Kings were very rich and had many servants and peasants dedicated to serving them. Peasants, of course, farming the fields to produce crops.