Under Mixed Member Proportional representation there are two types of members of parliament some representing constituencies and others elected from closed party lists. Shouldn't members representing constituencies be paid more than list members because they have to do plenty of constituency work while list members are not connected to any geographical constituency?
You seem to be under the impression that list members will not be doing any case work. I don't think this is necessarily the case.
In a lot of places where MMP is used, these list members will represent a state or other region, rather than the whole country. For example, in Germany, each of the list members represent a state within the country.
Residents of this state have the ability to approach list members with their concerns in the same way as a constituency member. In fact, many will probably approach a list member before a constituency member if the constituency member is not from their preferred party.