# Utility Function

Here is an excerpt from a journal article:

"A solicitor's input decision on a given case can be thought of as a labour supply decision, with the movement towards standard fees altering the budget constraint the solicitor faces (Gray et al., 1996). Start with fee-for-service remuneration. Assume that solicitors derive utility from consumption $(C$) and leisure $(L)$, $U(C, L), U_i > 0, U_i{_i} < 0, i = C, L$."

Here are my two questions: 1. What do $U_i>0$ and $U_i{_i}<0$ mean? Is this the British way of denoting prime and double prime? 2. Assume utility is derived from three variables; the two indicated by the author and a third, say... happiness ($H$). How would this be expressed? I have only seen utility expressed as a function of two factors and I'm curious how more than two are dealt with.

1. What do $U_i>0$ and $U_{ii}<0$ mean? Is this the British way of denoting prime and double prime?
1. Assume utility is derived from three variables; the two indicated by the author and a third, say... happiness ($H$). How would this be expressed? I have only seen utility expressed as a function of two factors and I'm curious how more than two are dealt with.
The utility function is now $U(C,L,H)$. we still end up with first and second condtions being $U_i>0$ and $U_{ii}<0$ except now $i=C,L,H$.