Saxman
Much the same overheads that are involved with anything else on the menu. Admittedly the actual 'chef' work is less, but it still needs a maitre d' or headwaiter, waiter, kitchen porter, bar steward, cellarman, on the premises to open and serve you your ice-cream.
Then there are the premises-related costs, which are the same whether you are occupying the seat for an hour eating fillet steak and champagne or nursing a pint until the rain stops.
The rough costing for restaurants is 1-3 of the menu price is the ingredient cost. However, this would put some dishes (such as the fillet steak) unaffordably high, so the cheaper dishes are usually the more profitable. You will almost always get a bad deal ordering the cheapest dishes, a veg soup starter that costs pennies to make with rechauffee1 vegetables will sell for £3 on the menu, subsidising the langoustine which should really be marked up to £9 but is actually on at £6.
The second from first and second from last dishes in a menu section are the ones most ordered - restaurants will often put their most profitable dishes their.
Also people tend to look at the menu price for main course but not notice puddings, drinks, etc - those prices are loaded so the restaurant makes more profit.
Owain
1 That's the polite term for plate-scrapings