Which income and consumption theory states that an individual's consumption in any time period depends on resources available to the individual, the rate of return on his or her capital, and the age of the individual?

Introduction / Context:
In macroeconomics and consumption theory, several hypotheses attempt to explain how individuals decide how much to consume and how much to save. These include the Absolute Income Hypothesis, Relative Income Hypothesis, Life Cycle Hypothesis, and Permanent Income Hypothesis. This question asks you to identify which specific hypothesis emphasizes that consumption depends on lifetime resources, rate of return on capital, and the age of the individual.

Given Data / Assumptions:

• Consumption decisions are not based only on current income.
• The individual considers total resources or wealth available over the whole life.
• The rate of return on capital affects how savings grow and support future consumption.
• Age matters because individuals move through working years and retirement.

Concept / Approach:
The Life Cycle Hypothesis, associated with Modigliani and others, suggests that individuals plan their consumption and saving behaviour over their entire lifetime. People work and earn in some years and retire in others, and they aim to smooth consumption across life. Consumption in any period depends on lifetime resources, expected income, rate of return on savings and assets, and where the individual currently is in the life cycle. Other hypotheses focus on different aspects: the Absolute Income Hypothesis links consumption mainly to current income, Relative Income Hypothesis focuses on income relative to others, and Permanent Income Hypothesis, associated with Friedman, emphasizes permanent income rather than temporary fluctuations, but does not stress age in the same way as the Life Cycle approach.

Step-by-Step Solution:
Step 1: Identify key cues in the question: resources available, rate of return on capital, and age of the individual. Step 2: Recall that the Life Cycle Hypothesis explicitly models consumption decisions over the life span, from working years to retirement, which naturally involves age. Step 3: Recognize that rate of return on capital is important in life cycle models because it determines how savings grow to finance future consumption. Step 4: Match this description to the Life Cycle Hypothesis and select it as the correct option.

Verification / Alternative check:
A quick check is to recollect that the Life Cycle Hypothesis often uses diagrams showing income and consumption over time, with higher income during middle age and declining income in retirement, while consumption is smoother. Age is central in those diagrams. Other hypotheses do not place equal emphasis on age and life stages. This confirms that the Life Cycle Hypothesis is the best fit for the description given in the question.

Why Other Options Are Wrong:
Absolute Income Hypothesis: Proposes that consumption mainly depends on current absolute income, without detailed consideration of age or lifetime planning.
Relative Income Hypothesis: Emphasizes that consumption depends on income relative to others in society and on past peak income, rather than directly on age and rate of return on capital.
Permanent Income Hypothesis: Focuses on permanent income versus transitory income and how people smooth consumption, but age and life cycle structure are not as central in its basic form as they are in the Life Cycle Hypothesis.

Common Pitfalls:
Students often mix up the Life Cycle and Permanent Income Hypotheses because both involve smoothing consumption over time. The key difference for exam purposes is that the Life Cycle Hypothesis explicitly structures decisions over different life stages, making age a crucial variable, whereas the Permanent Income Hypothesis emphasizes expected long term average income. Keeping this distinction clear helps avoid confusion in theory based questions.

Final Answer:
The theory described is the Life Cycle Hypothesis of consumption.