Wow ok you guys don't really know what you're on about.
You can get a career with a psych degree. There are all sorts of options like Human Resources, PR, management, counselling, health psychology, etc and that's just with a three year, undergraduate BA qualification. These are degrees that don't specify a psych degree is required, but having completed a psych major will hold you in good stead.
If you want to do an accredited course, this means you need to do honours, and some specific subjects (at USyd it's Abnormal Psych in third year). To get into honours, you also need to have done both second and third year stats courses, and achieved a distinction average overall.
Doing an accredited course will mean you can go on to do research and such, OR you can pursue things like clinical psych which requires another 2-3 years of study or several years supervised work in the clinical field.
You can ABSOLUTELY do a double major, even if you want to major in psych and go on to do an honours year in psych. The only problem is if the requirements of third year subjects don't fit with the requirements of third year economics. Or, if you do B Psych (different to a BA), then you have to do 30 credits of psych in third year to meet the requirements, whereas normally it's only 24 credits.