No, you can’t assume without loss of generality that the person who was previously in my parents’ apartment will be willing or able to move to mine. It depends on the relationship between X and Y.
But the set of living spaces is the same as before. Can’t we assume for simplicity that, even if it’s not as simple as two people swapping places with each other, what we have is a ‘permutation’ such that all previously occupied houses and apartments remain occupied?
Then once again we can factor the change into (1) a permutation and (2) a change of rent, and ask whether either of them changes the wealth of the nation. I’m pretty sure that (2) in itself has no effect—it’s just a ‘redistribution’ between landlords and their tenants. Whether (1) has an effect depends on whether or not we’re including the fact that different people may make different assessments of desirability (i.e. whether different people have different preferences about the kind of apartment they’d like to live in.)
Of course you’re quite right that different people do have different preferences—I was merely ignoring this for simplicity—but in any case the statement of the problem says nothing explicit about your or anyone else’s preferences, it only talks about X and Y. Are your apartment-preferences supposed to change depending on the values of X and Y?
You’re right that (2) has no effect, but (1) probably does have effect. I thought we could somehow guess the effect of (1) by looking at X and Y, but now I see it’s not easy.
But the set of living spaces is the same as before. Can’t we assume for simplicity that, even if it’s not as simple as two people swapping places with each other, what we have is a ‘permutation’ such that all previously occupied houses and apartments remain occupied?
Then once again we can factor the change into (1) a permutation and (2) a change of rent, and ask whether either of them changes the wealth of the nation. I’m pretty sure that (2) in itself has no effect—it’s just a ‘redistribution’ between landlords and their tenants. Whether (1) has an effect depends on whether or not we’re including the fact that different people may make different assessments of desirability (i.e. whether different people have different preferences about the kind of apartment they’d like to live in.)
Of course you’re quite right that different people do have different preferences—I was merely ignoring this for simplicity—but in any case the statement of the problem says nothing explicit about your or anyone else’s preferences, it only talks about X and Y. Are your apartment-preferences supposed to change depending on the values of X and Y?
You’re right that (2) has no effect, but (1) probably does have effect. I thought we could somehow guess the effect of (1) by looking at X and Y, but now I see it’s not easy.