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How to invert from the expense function to the indirect utility
function?

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Final answer:

Indifference curves further from the origin represent higher levels of utility because they consist of larger quantities of goods. Lower utility levels are represented by curves closer to the origin. The substitution effect shows the change in consumption as prices vary, viewed as a shift along the indifference curve.

Step-by-step explanation:

To determine which indifference curves represent higher or lower levels of utility, we rely on the understanding that each curve represents a combination of goods or services that provide a consumer with the same level of satisfaction or utility. Thus, the farther an indifference curve is from the origin, the higher the level of utility it represents, as it combines larger quantities of goods or services. Conversely, if an indifference curve is closer to the origin, it represents a lower level of utility.

Indifference curves are graphical representations of different bundles of goods between which a consumer is indifferent. In reciprocal relationships between expense functions and indirect utility functions, we often employ mathematical techniques to invert functions. To invert from an expense function to an indirect utility function, we apply duality in consumer theory, which utilizes the convexity and monotonicity properties of preference relations that underpin the consumer's choice behavior.

The substitution effect, mentioned in Exercise B5, helps illustrate changes in consumption as prices vary, holding utility constant. This is often visualized on an indifference map where the original indifference curve is drawn tangent to the budget constraint before and after a price change, marking the shift from point A (initial equilibrium) to point C (new equilibrium after substitution effect) and showing the change in consumption of goods.

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