Where have you spent more money to live small than to "live large"? We have experienced it when purchasing a small refrigerator, the apartment itself, and cabinetry (which had to be customized to fit our tiny kitchen space).
We think we probably spend more in our small spaces because every move counts. When you're living in a small apartment, you are constantly in close contact with your furnishings, appliances, storage. So you'll pay a premium to make it nice. Also, more care in design is required to make compact electronics or efficient storage. This price is likely passed on to the consumer. Maybe as small living becomes more prevalent, the cost of living small will come down. What's your theory?