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Economics 420K
Problem Set 3
More Demand Theory
Bronars
1. Crusoe lives on an island alone.
He owns 10 coconuts and 2 bananas.
He knows that at the
neighboring island he can trade coconuts oneforone for bananas.
a. Illustrate Crusoe's constraint now, and if he goes to the neighboring island.
b. After drawing Crusoe's preference map, show the maximum number of coconuts he'd be
willing to pay you to take him to the other island.
2. For the utility function U= X
1
X
2
a. Derive the demand functions for X
1
, and X
2
, assuming the consumer buys some of both goods
b. For I=40, P
1
=1 and P
2
=2, find the consumer’s optimal choices and utility
c. Explain what happens to optimal choices and utility if the P
1
were to increase to 2.
d. Find the EV of this price change In other words, when prices are P
1
=1 and P
2
=2, how much of
a loss in income would generate an equivalent loss in utility (compared to the price increase)?
a. X1=I/2P1 and X2=I/2P2
b. X1=20 and X2=10 and U=200
c. X1=10 and X2=10 and U=100
d.V=I
2
/(4P1P2) so that when P1=1 and P2=2, V= I
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 Fall '09
 Bronars
 Economics

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