Whether it results in seeking work is different from how prices respond, in fact, an increase in those seeking work may be a direct result of the cost of living

Whether it results in seeking work is different from how prices respond, in fact, an increase in those seeking work may be a direct result of the cost of living increasing. The subsidy in Alaska is per person, thus two families in identical apartments may receive different levels of subsidy. If at any point the management company observes that their tenants are receiving more subsidies (say the average family size per apartment increases) then they could choose to raise rental rates to try to capture this. But it raises the rates on all family sizes, so a 2-person family is now paying more as a % basis than a 4-person family, so it would make it more likely that someone from the 2-person family may need to work more/get a part-time job. Obviously that's a drastic simplification, but I think it illustrates the problem with stimulating demand without trying to control supply or pricing directly.