Indeed, construction costs have likely increased for various reasons, but I would bet that low interest rates along with other subsidies (lowering FHA standards for example) have been the primary drivers of increased home costs.

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I'm curious how much the price has increased in terms of square feet though. Average home price has gone up, but so has average home size.

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This is a little dated, but assuming the trend did not reverse, median home sizes have increased at least 66% since the early 1970s.