See the comparison here
Mostly in every aspect Powershot SX150 is superior to A4000, why is A4000 priced higher than SX150?
Comparing the features its should be priced way lower than SX150 but its priced more than it. Why so?
The difference is not that big, and you are right, the SX150 is a much better camera.
The main advantage of the SX150 is that it has full manual controls with a rear control dial and makes it much better for creative photography. It also has 50% more zoom. Plus, it has twice the battery-life with 320 shots per charge instead of 175. If you do the comparison on my site, most differences are automatically highlighted.
This brings us back to your question. Why would the better one by cheaper? It is hard to guess but the main difference is that the A4000 comes with a battery included, since its a proprietary one and goes for about $40 USD. It also comes with a charger which also costs money. With the SX150 IS, you need to buy your own AAs (Good ones cost $16 for 4, so you get two sets!) and charger or you may use ones you already have.
Most likely because the A4000 is smaller, almost half the weight of the SX150 and uses a proprietary lithium-ion battery.
The only real improvement the SX150 seems to have is much better video recording.