Not all other prices are set by competition. There's much manipulation through things like subsidies, tariffs, tax incentives, and bailouts.

Also, having lived in Singapore for years, it's a wonderful city and I love it, but the wage story isn't necessarily one to mimic. It might look grand as a foreigner, but your cleaning lady is probably sharing a 3 bedroom apartment with 16+ other women and doesn't see her family more than a few times a year.