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A collection of (selected) indifference curves, illustrated graphically, is referred to as an indifference map. The slope of an indifference curve is called the MRS (marginal rate of substitution), and it indicates how much of good y must be sacrificed to keep the utility constant if good x is increased by one unit.
A standard indifference-curve map for an individual has these properties and so is an ordering. Each ray from the origin ranks (conceivable) commodity bundles from least preferred on up (no ties in the ranking). Each indifference curve ranks commodity bundles as equally preferred (all ties in the ranking).
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. In the usual case, constrained utility is maximized on the budget constraint with strictly positive quantities consumed of both goods.
Created Date: 8/30/2012 4:52:52 PM
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 )} .
The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve surface; The Welfare function is analogous to the indifference-curve map; The Possibility function is analogous to the budget constraint
To maximize social welfare, a point on the UPF would be chosen that also falls on the highest indifference curve for society. The shape of the utility possibility curve is often represented as being concave to the origin, as cardinal utility is often assumed. Cardinal utility implies that consumers can rank their preferences over goods (utility ...
If the axes depicting coconut collection and leisure are reversed and plotted with Crusoe's indifference map and production function, [1] figure 2 can be drawn: Figure 2: The Robinson Crusoe economy's production function and indifference curves. The production function is concave in two dimensions and quasi-convex in three dimensions. This ...