Principles of Microeconomics by Martin Kolmar

Author:Martin Kolmar
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

If f(x) is a monotonic increasing function, then one knows that

However, this implies that

And, thereby, that

The transfer from preference orderings to utility functions bears some risk of misinterpretation. Because utility functions assign numbers to alternatives, it is tempting to use these numbers and perform all types of operations with them, like calculating differences (, hence and thus the individual must be three units better off) and comparing them between different individuals (individual A has 8 units of utility, whereas individual B only has 3 units, which makes individual A 5 units better off than individual B). These calculations are mathematically well defined, but economically meaningless, because absolute values of utility or differences in utilities have no meaning if the underlying, primary concept is a preference ordering. What remains, however meaningful, is the marginal rate of substitution MRS, because it is independent of the exact utility representation used. To see this, return to the two representations used above, u(x) and , and use the following notation: alternative x i consists of the quantities and of the two goods 1 and 2. One can express the marginal rate of substitution by the total differential of the utility function. One can start with the representation u(x) to get the total differential

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