Vlad lives in Siberia. It gets really cold there. He has $1,000 in monthly income. He pays $500 of his income in rent for his apartment and spends the remaining $500 on two things: Fuel for heating the apartment (H) and all other goods (Y). Vlad's utility function is quasilinear and non-monotonic: u(H,Y) = -0.01(H — 100)² + Y. Note that it is non-monotonic because too much heat makes Vlad worse off (there's a 'right' temperature). Let Y be the numeraire (py = $1) and, for simplicity, also suppose that PH = $1. With rent fixed at $500, Vlad's budget constraint is then simply: H+ Y = 500. a) How much H does Vlad consume? b) Suppose the landlord is considering including heat in the rent. She offers Vlad a heat-included rental contract of $560 per month (under this contract, heat would be free to Vlad). Should Vlad take the deal? c) Suppose heating fuel costs the landlord the same as the tenant (PH = $1). How much would the landlord have to charge for a heat-included rental contract to break even, i.e., to make as much money as with the old heat-not-included contract? d) Would Vlad be better or worse off under the 'breakeven' heat-included contract from part c) compared to paying $500/month in rent and buying heating fuel separately (part a)? What's the maximum Vlad would be willing to pay in rent for a heat-included contract?

Fig: 1