I see this assertion time after time -- that we must feed 8, 10, 15 billions of people -- without asking the question, "Does the planet need that many people?"
There are many problems with your reasoning.
First, fertility rates are plummeting. Much of the world (including the USA) is already below replacement rate, leading to problems such as population aging and cultural weakening. Some countries still have large fertility rates, but even there it is falling fast. As a result, world population is projected by the UN to peak at 9B or maybe 10B, then start falling.
Second, much of the world is obese, and 1/3 of the food is not even eaten - it is thrown away at any of the several stages of production. Food production per capita is growing. Starvation is not caused by lack of food, it is caused by civil wars, terrorism, or corrupt, authoritarian and incompetent governments.
Third, inflation-adjusted price of many commodities have been stable for a century.
Fourth, there is no clear correlation between population density and income per capita.
Fifth: while we compete for primary resources (but see the third point above), when the population grows we share the benefits of more scientists, engineers, musicians, writers, philosophers, etc.