Utility Function

Question

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.

Answer 1

1. What do $U_i>0$ and $U_{ii}<0$ mean? Is this the British way of denoting prime and double prime?

Seems like it. It just indicates the all the first and second derivatives that exsist in this context.

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.

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 $i=C,L,H$.

Hope this helps.