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In the realm of economics, understanding consumer behaviour is crucial for predicting market trends and making informed decisions. One of the key theories that help us decipher this behaviour is the Consumer Choice Theory.

This theory, first developed by economists Vilfredo Pareto and John Hicks, provides a framework for understanding how consumers make choices about what goods and services to purchase, given their limited resources.

At the heart of this theory lies the concept of utility, which economists use to explain consumer satisfaction. A 'basket of products' is employed to represent different combinations of goods and services, each offering a unique level of satisfaction, or utility, to the consumer.

The model of the optimal consumption bundle, as it's known, is a product of Pareto and Hicks' work on consumer choice theory and utility maximization. This optimal bundle represents the most preferred combination of goods and services within a consumer's budget.

The budget constraint line, another essential element in this theory, shows the combinations of goods that fit within the consumer's budget. Falling prices cause this line to shift to the right, increasing the level of consumer satisfaction, as more combinations become affordable. Conversely, rising prices cause the budget constraint line to shift to the left, reducing consumer purchasing power.

The indifference curve, another key component, illustrates the combinations of goods that produce utility equally. The higher the indifference curve, the higher the utility consumers get from a combination of products. Lower indifference curves represent a reduced level of utility.

The intersection of the budget line and the indifference curve shows the level of satisfaction with the same nominal income. This point, known as the consumers' equilibrium, represents the optimal bundle, the most preferred combination of goods and services within the consumer's budget.

Utility theory, a fundamental concept in economics, attempts to answer why a consumer prefers one basket over another. The utility function, a mathematical representation of this theory, quantifies the satisfaction a consumer gets from consuming different bundles of goods.

The Consumer Choice Theory also adheres to several axioms, including the transitivity of preference. This axiom states that if a consumer prefers bundle A over bundle B, and bundle B over bundle C, then the consumer also prefers bundle A over bundle C.

Moreover, two baskets are considered different bundles if the quantity of one item is different, even if they contain the same items.

An example of three different consumption bundles containing apples and oranges, with varying quantities, can help illustrate these concepts. Each bundle represents a unique combination of apples and oranges, each offering a different level of utility to the consumer.

In conclusion, the Consumer Choice Theory provides a powerful tool for understanding consumer behaviour and decision-making. By understanding the concepts of utility, budget constraints, indifference curves, and the optimal bundle, we can gain insights into why consumers make the choices they do, and how these choices impact the market.