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 (��) and all other goods (��). Vlad’s utility function is quasilinear and non-monotonic: ��(��, ��) = −0.01(�� − 100)2 + �� . Note that it is non-monotonic because too much heat makes Vlad worse off (there’s a ‘right’ temperature). Let �� be the numeraire (���� = $1) and, for simplicity, also suppose that ���� = $1. With rent fixed at $500, Vlad’s budget constraint is then simply: �� + �� = 500. a) How much �� 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 (���� = $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?1 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)? e) What’s the maximum Vlad would be willing to pay in rent for a heat-included contract?
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 (��) and all other goods (��). Vlad’s utility function is quasilinear and non-monotonic: ��(��, ��) = −0.01(�� − 100)2 + �� . Note that it is non-monotonic because too much heat makes Vlad worse off (there’s a ‘right’ temperature). Let �� be the numeraire (���� = $1) and, for simplicity, also suppose that ���� = $1. With rent fixed at $500, Vlad’s budget constraint is then simply: �� + �� = 500. a) How much �� 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 (���� = $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?1 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)? e) What’s the maximum Vlad would be willing to pay in rent for a heat-included contract?
Chapter10: Consumer Choice Theory
Section: Chapter Questions
Problem 6P
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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 (��) and all other goods (��).
Vlad’s utility function is quasilinear and non-monotonic: ��(��, ��) = −0.01(�� − 100)2 + �� .
Note that it is non-monotonic because too much heat makes Vlad worse off (there’s a ‘right’
temperature). Let �� be the numeraire (���� = $1) and, for simplicity, also suppose that ���� = $1. With
rent fixed at $500, Vlad’s budget constraint is then simply: �� + �� = 500.
a) How much �� 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 (���� = $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?1
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)?
e) What’s the maximum Vlad would be willing to pay in rent for a heat-included contract?
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