John and Karl can live together in a two-bedroom apartment for $500 per month, or each can rent a single-bedroom apartment for $350 per month. Aside from the rent, the two would be indifferent between living together and living separately, except for one problem: John leaves dirty dishes in the sink every night. Karl would be willing to pay up to $175 per month to avoid John’s dirty dishes. John, for his part, would be willing to pay up to $225 to be able to continue his sloppiness. a. Should John and Karl live together? They live together. If they do, will there be dirty dishes in the sink? . b. If John would be willing to pay up to $30 per month to avoid giving up his privacy by sharing quarters with Karl, should John and Karl live together?

A: Together their flat is $500, however if they were to live separately it'd be $350 per month. 350x2= 700. They save $200 by sharing a flat. However, if Karl plays John $175 a month to keep the dirty dishes away, then 200>175. Therefore, they should live together.

Karl could just live alone and pay the $350 to live alone with no dish problem. Since Karl will play $175 to rid the dish problem the highest rent he'll pay is 350-175=175. John would pay 500-175=325<350 this shows it better for John to live with Karl.

B: If living alone, John would pay £ 350. The highest monthly rent he would be willing to pay for the shared apartment is: £ 350- £ 30 = £ 320. This means that Karl would need to pay at least: £ 500- £ 320 = £ 180. But the highest monthly rent Karl would be willing to pay is : £ 175. They should live separately.

hope this helps you out a bit, I know its a lot. But its math, what do we expect. lol