The correct answer is: A. Population increases arithmetically.
Thomas Malthus was an English economist and demographer who proposed the theory of population in his 1798 book An Essay on the Principle of Population. Malthus argued that population growth is exponential, while the growth of food production is linear. This means that population will eventually outstrip food production, leading to famine and disease.
Malthus’s theory has been criticized for being too simplistic and for not taking into account technological advances in agriculture. However, it remains a influential theory in economics and demography.
Option B is incorrect because food production does not increase geometrically. Food production does increase, but it does so at a slower rate than population growth. This is because it takes time to develop new agricultural technologies and to bring them into widespread use.
Option C is incorrect because population does not increase geometrically. Population growth is exponential, but it does not increase at a constant rate. This is because the rate of population growth is affected by a number of factors, including birth rates, death rates, and migration.
Option D is incorrect because both A and B are incorrect.