### Utility

Utility is a measure of our well-being, of how well off we are. Although well-being depends on many things, webDICE treats utility as a function of consumption. It assumes that as we get richer we are better off. It assumes, however, that the benefits of getting richer still are smaller. This is sometimes called the ‘declining marginal utility of income’. It means that going from, say, poor to middle class produces great benefits, from middle class to wealthy also makes you better off but the gains are smaller. Going from wealthy to incredibly rich produces smaller gains still. The intuition is simply that a dollar matters less to Mark Zuckerberg thanks to a poor person.

You can choose the rate at which the gains from getting richer goes down by choosing the variable called ‘eta’ or $\eta$. If you change eta, the model runs and almost all of the output will unaffected because utility does not enter into most of the calculations. The one place where changing eta will change the results is in optimization. If you increase eta so that the gains from getting richer are smaller, the optimizer will put less weight on the wealthy and more on the poor. The reason is that the optimization focuses on utility. As eta gets larger, giving another dollar to a wealthy person produces a smaller increase in their utility.

One important but technical problem with changing eta is that the graphs of utility with different etas are not comparable. more

Utility is $U=\frac{c^{1-\eta}}{1-\eta}$ where c is consumption. Total utility in each period is the value multiplied by the population in that period.