When looking at utility functions, how do you compare preferences? I understand the economic concepts, but the math part is holding me down from understanding a lot in the textbook. (I am not typing this so that someone can 'do my homework for me'). For example, given these three functions, how do I compare the different consumer's preferences for the two goods? I think this is pretty straightforward. I just need a quick explanation to understand how I interpret these numbers. Thanks!

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  • $\begingroup$ Hi! What exactly do you mean by "compare [...] preferences"? $\endgroup$
    – Giskard
    Nov 22 at 8:26

1 Answer 1


Given that the problem is "compare the preferences of the individuals below":

The first two are Cobb-Douglas utility functions. The general function is: $$ U(x,y)=x^{\alpha}y^{\beta} \space ,\space \alpha,\beta\in (0,1) \space and \space \alpha +\beta=1 $$ In this equation the higher the exponent $\alpha$ (or $\beta$) the more that particular good is important for the consumer.

We can take the $ln(U_{Steve}(n,c))$ and compare the 3 functions.


We can clearly see that Steve and Patrick have the same preferences. While Jeff shows a utility function which is not the standard cobb-douglas, but if we have to apply the same reasoning even for Jeff, then he prefers good $n$ and $c$ more than the other guys. Plus he has one unit of utility even withouth consuming $n$ or $c$.


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