This analogy seems confused.
If someone in Chicago moves to Seattle, then our policy options are (1) no new condo in Seattle or (2) new condo in Seattle.
Under policy 1, the new buyer from Chicago must outbid locals for the fixed housing supply; they will wind up buying older housing stock, which otherwise would have gone to existing local residents. Prices go up.
With policy 2, the new entrant buys the new condo and does not compete for pre-existing housing stock.
In this scenario, whatever house is freed up in Chicago is irrelevant to the housing stock in Seattle. I'm not sure why you included it.
The entire question can be contained by the assumption that "there is someone new coming to Seattle" and whether it would be better to have a new condo unit to sell to them or have them compete for existing fixed stock. The whole bit about the Chicago housing market is a distractor, because it stays the same under either policy.
If someone in Chicago moves to Seattle, then our policy options are (1) no new condo in Seattle or (2) new condo in Seattle.
Under policy 1, the new buyer from Chicago must outbid locals for the fixed housing supply; they will wind up buying older housing stock, which otherwise would have gone to existing local residents. Prices go up.
With policy 2, the new entrant buys the new condo and does not compete for pre-existing housing stock.
In this scenario, whatever house is freed up in Chicago is irrelevant to the housing stock in Seattle. I'm not sure why you included it.
The entire question can be contained by the assumption that "there is someone new coming to Seattle" and whether it would be better to have a new condo unit to sell to them or have them compete for existing fixed stock. The whole bit about the Chicago housing market is a distractor, because it stays the same under either policy.