Density is more expensive. Not just because of demand for the area (though that doesn't help), but because density requires different building methods. Your single family house can be built so cheaply because it doesn't have to support the weight of many floors above; nor does it need to be fireproof because in the rare fire you can evacuate. (density means more people are displaced, fires are more likely, and longer distances to get away)

Density is also more expensive because higher costs are worth it. A rural area cannot afford things like library in walking distance of every farmer (every farmer would have to pay for a personal librarian), but in a dense area it is only a couple bucks for each one - but that all adds up to hundreds of dollars in extra costs that less dense areas do without. (you decide if it is worth the cost)