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An example of how indifference curves are obtained as the level curves of a utility function. A graph of indifference curves for several utility levels of an individual consumer is called an indifference map. Points yielding different utility levels are each associated with distinct indifference curves and these indifference curves on the ...
The indifference curves are L-shaped and their corners are determined by the weights. E.g., for the function min ( x 1 / 2 , x 2 / 3 ) {\displaystyle \min(x_{1}/2,x_{2}/3)} , the corners of the indifferent curves are at ( 2 t , 3 t ) {\displaystyle (2t,3t)} where t ∈ [ 0 , ∞ ) {\displaystyle t\in [0,\infty )} .
A set of convex-shaped indifference curves displays convex preferences: Given a convex indifference curve containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex set.
The more usual solution will lie in the non-zero interior at the point of tangency between the objective function and the constraint. For example, in consumer theory the objective function is the indifference-curve map (the utility function) of the consumer. The budget line is the constraint.
An indifference curve is a set of all commodity bundles providing consumers with the same level of utility. The indifference curve is named so because the consumer would be indifferent between choosing any of these bundles. The indifference curves are not thick because of LNS.
In a model where competitive consumers optimize homothetic utility functions subject to a budget constraint, the ratios of goods demanded by consumers will depend only on relative prices, not on income or scale. This translates to a linear expansion path in income: the slope of indifference curves is constant along rays beginning at the origin.
For a minimum function with goods that are perfect complements, the same steps cannot be taken to find the utility maximising bundle as it is a non differentiable function. Therefore, intuition must be used. The consumer will maximise their utility at the kink point in the highest indifference curve that intersects the budget line where x = y. [3]
A consumer's indirect utility (,) can be computed from their utility function (), defined over vectors of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector (,) by solving the utility maximization problem, and second, computing the utility ((,)) the consumer derives from that ...