By Michael Pohst
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Extra resources for Algorithmic Methods in Algebra and Number Theory
A corner solution. ” Given the household’s budget line, the highest indifference curve it can reach is at point A, representing the situation in which the household spends all its income on “all other goods” and does not buy a GPS. Point A is the point of maximum satisfaction. It is an equilibrium position because no other point on AC would be more satisfying to the household, and therefore, the household has no incentive to move from point A. 6) does not hold. 8) holds (see mathematical note 6).
Geometrically, point c is the point of tangency between the budget line and the highest attainable indifference curve, U3 . At point c the household’s marginal rate of substitution of food for “all other goods” (represented by the slope of U3 at point c) equals the rate at which food and “all other goods” exchange for each other in the marketplace (represented by the slope of the budget line). Recall that the marginal rate of substitution is the rate at which the household is willing to exchange “all other goods” for food.
The knowledge is obtained through extremely detailed questionnaires filled out by sample consumers. 9. Maximization of satisfaction at point c. The satisfaction-maximizing combination of food and “all other goods” can be found by putting the household’s indifference curves together in the same figure as its budget constraint. Obviously, the satisfactionmaximizing combination of “all other goods” and food will be somewhere on the budget line. The fact that households prefer more to less ensures that there are combinations on the budget line the family prefers to any given point to the southwest of the budget line.
Algorithmic Methods in Algebra and Number Theory by Michael Pohst