According to the classical Malthusian theory of population, how do population growth and food supply increase in relation to each other over time?

Introduction / Context:
This question examines understanding of the classical Malthusian theory of population, an important idea in economics and demography. Thomas Robert Malthus proposed a relationship between population growth and food supply that had deep implications for resource scarcity, poverty and policy debates. Many competitive exams include at least one conceptual question on this theory, so it is important for learners to remember the exact way in which Malthus described the relative growth rates of population and food production.

Given Data / Assumptions:

• The question refers to the original Malthusian theory, not later modifications by other economists.
• We need to compare how population and food supply increase over time.
• Options mention different combinations of geometric, arithmetic and harmonic types of growth.
• The correct option must match the classical statement made by Malthus.

Concept / Approach:
According to Malthus, population, if unchecked, tends to grow in a geometric ratio, meaning it can double at regular intervals, similar to exponential growth. In contrast, food supply, limited by land and technology, was assumed to increase only in an arithmetic ratio, that is, by a fixed amount each period. This imbalance between a potentially very rapid population increase and slower growth of food resources leads to pressure on resources, resulting in famine, disease and other checks. The approach to answering is simply to recall this exact pairing: population geometric, food supply arithmetic.

Step-by-Step Solution:
Step 1: Recall the core statement of the Malthusian theory. Malthus wrote that population tends to grow faster than the means of subsistence. Step 2: Remember the technical description he used: population increases in a geometric ratio (for example 1, 2, 4, 8, 16) while food supply increases in an arithmetic ratio (for example 1, 2, 3, 4, 5). Step 3: Check the options and identify which one states population increases in geometric ratio and food supply increases in arithmetic ratio. Step 4: Option a clearly states population increases in geometric ratio and food supply increases in arithmetic ratio. Step 5: Confirm that none of the other options represent the original Malthusian formulation and select option a.

Verification / Alternative check:
A quick mnemonic to verify is to think that geometry is associated with shapes that can grow quickly in size, so geometric ratio is linked with rapid growth. Arithmetic suggests simple addition by the same amount. In Malthusian reasoning, population is the dynamic, fast growing factor, while food supply is the slower changing factor. Therefore, population must correspond to geometric growth, and food supply to arithmetic growth. If any option reverses this pair or introduces harmonic growth, that option is inconsistent with the original theory and can be rejected.

Why Other Options Are Wrong:
Population increases in arithmetic ratio, food supply increases in geometric ratio: This option completely reverses the Malthusian idea, suggesting food grows faster than population, which is not what Malthus argued.
Population increases in a harmonic mean, food supply increases in geometric ratio: Harmonic growth is not a term used in the classical formulation of this theory, so this option does not match the standard description.
Population increases in a harmonic ratio, food supply increases in an arithmetic ratio: Again, harmonic ratio is not part of the original theory, which only uses geometric and arithmetic comparisons.

Common Pitfalls:
Students sometimes confuse which one is geometric and which one is arithmetic, especially under time pressure. Another common error is overcomplicating the theory by imagining more advanced mathematical patterns than Malthus actually used. A simple way to avoid this is to memorise the phrase population grows geometrically, food grows arithmetically. This short association helps keep the pairing clear and improves accuracy when facing similar questions in exams that focus on economics, population studies or human geography.

Final Answer:
The correct statement is that population increases in geometric ratio, food supply increases in arithmetic ratio according to the classical Malthusian theory of population.