The main user of elec is air conditioning so the cost per month is related to the size of place you live in, the time of year (heat and humidity, how much you use the aircon and the efficiency of the aircon system.
As a guide aircon systems come in three flavours (well five but you won't see a centralised system or 4 pipe fan coil in resi buildings). Firstly window units, these are an all in one box that fits in a hole in a window / wall and has pretty crude controls / thermostats. Secondly split units, these have a condenser / compressor / boxy thing outside and a wall mounted unit inside that will cool / dehumidify and depending on the system heat. Third are cassette units which are not that common in resi buildings and are basically the same as splits but have bigger capacity. Why, you ask, have I set off into aircon world, well window units with their crude controls and thermostats eat electricity especially the old ones where as modern new split units are very good on power use. so what I'm trying to say is it very much depends on what type of systems and how old they are coupled with how cold you like and how big a place you have for how much elec you use.
As an example I have a 600sqft gross apartment (pretty small) equipped with split units. I leave one unit on dehumidify 24-7 and one unit on cool when I am at home in the summer. My elec bill is approx $400 a month (which includes lighting, a plasma tv and a computer on 24-7, but does not include water heating, cooking or tumble dryer as they are gas). One of my mates has a 2800sqft apartment with a range of units from splits to window units (including the biggest window unit I have ever seen) and his bill is $2500 a month.
So to directly answer your question $1500 a month isn't a bad place to start in terms of budget just be aware that the range is pretty big.
Like <above> are saying, it depends on a few factors - size of the apartment, type of aircon, and age/style of building. In my little flat 300-400sq ft (ish) we have split aircon and usually only have one or two units on in the day and one at night. With the modern splits they only come on when the temperature rises above a certain point so they are FAR FAR FAR more effficient. The bill is about 250$ a mnth.
(and we use the washing machines about two times a week so thats pretty cheap)
Its worth noting also, that electricity costs 20% more PER UNIT on the Island and Lamma than everywhere else due to the stupid outdated regulations 'controlling' the electricity industry here...
Is there such a thing as 'peak' and 'off-peak' electricity?
In the UK you can keep the cost of your electricity down by running appliances such as washing machines, tumble dryers during off-peak times i.e. in the evening and over night. These are periods of low demand ie most business use happens during the working day (9-6)
My quesiton is : does such a system exist in Hong Kong? or is one unit of electricity the same price regardless of time of day?
And your washing machine will be a fairly small part of your total electricity bills over the year: you summer bills will likely be 4 times bigger than your winter bills because of the cost of running aircons and dehumidifiers, and you need them when you need them - you can't really timeshift them.
The unit cost of electricity isn't a great deal higher here than in the UK, but the amount you use in the summer will make it feel that way - even as a single person being reasonably frugal with aircon I usually peak at over $1000/month for one or two months each summer.