Linear utility

Article summary

In economics and consumer theory, a linear utility function is a function of the form: :: u(x_1,x_2,\dots,x_m) = w_1 x_1 + w_2 x_2 + \dots w_m x_m or, in vector form: :: u(\overrightarrow{x}) = \overrightarrow{w} \cdot \overrightarrow{x} where: * m is the number of different goods in the economy. * \overrightarrow{x} is a vector of size m that represents a bundle. The element x_i represents the amount of good i in the bundle. * \overrightarrow{w} is a vector of size m that represents the subjective preferences of the consumer. The element w_i represents the relative value that the consumer assigns to good i . If w_i=0 , this means that the consumer thinks that product i is totally worthless. The higher w_i is, the more valuable a unit of this product is for the consumer. A consumer with a linear utility function has the following properties: * The preferences are strictly monotone: having a larger quantity of even a single good strictly increases the utility. * The preferences are weakly convex, but not strictly convex: a mix of two equivalent bundles is equivalent to the original bundles, but not better than it. * The marginal rate of substitution of all goods is constant. For every two goods i,j : :: MRS_{i,j} = w_i/w_j . * The indifference curves are straight lines (when there are two goods) or hyperplanes (when there are more goods).…

Key claims

No claims recorded.

Discussion questions

1. Summarise the article in your own words. Which single claim would you verify first, and why?
2. Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
3. If two sources disagreed about one of these facts, what would you need in order to trust one over the other?

Bibliography

No sources recorded.