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Complete, such that all points on an indifference curve are ranked equally preferred and ranked either more or less preferred than every other point not on the curve. So, with (2), no two curves can intersect (otherwise non-satiation would be violated since the point(s) of intersection would have equal utility).
If you do not find a tangency point within the domain then the utility maximising indifference curve for the given budget constraint will be at an intersection between either the x or y axis (depending on whether the slope of the indifference curve is strictly greater than or less than the slope of the budget constraint) - this is a corner ...
By varying the weighting parameter b, one can trace out the entire contract curve: If b = 1 the problem is the same as the previous problem, and it identifies an efficient point at one edge of the lens formed by the indifference curves of the initial endowment; if b = 0 all the weight is on person 2's utility instead of person 1's, and so the ...
If the curves cross (as shown in Fig. 4) then they divide the immediate neighbourhood into four regions, one of which (shown as pale green) is preferable for both consumers; therefore a point at which indifference curves cross cannot be an equilibrium, and an equilibrium must be a point of tangency.
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]
For example, every point on the indifference curve I1 (as shown in the figure above), which represents a unique combination of good X and good Y, will give the consumer the same utility. Indifference curves have a few assumptions that explain their nature. Firstly, indifference curves are typically convex to the origin of the graph.
Under the standard assumption of neoclassical economics that goods and services are continuously divisible, the marginal rates of substitution will be the same regardless of the direction of exchange, and will correspond to the slope of an indifference curve (more precisely, to the slope multiplied by −1) passing through the consumption bundle in question, at that point: mathematically, it ...
An indifference graph, formed from a set of points on the real line by connecting pairs of points whose distance is at most one. In graph theory, a branch of mathematics, an indifference graph is an undirected graph constructed by assigning a real number to each vertex and connecting two vertices by an edge when their numbers are within one unit of each other. [1]