$..(14$ points$)$ Consider an endowment economy that consists solely of Apples and Bananas

just like the one discussed in lecture. Jane is endowed with $40$ apples and $20$ bananas

while Tarzan is endowed with $20$ apples and $30$ bananas. Notice, then endowment is

just like in lecture.

Unlike lecture, let Jane and Tarzan have different utility functions. The utility function

for Tarzan is:

UT $=3$ ln$($aT $)+$ ln$($bT $)$

The utility function for Jane is:

UJ $=$ a

$(3/4)$

J

b

$(1/4)$

J

where ai

is the number of apples and bi

is the number of bananas consumed by i $=$

$\{$T$,$ J$\}.$

$($a$)(3$ points$)$ What is the Contract Curve here?

$($b$)(5$ points$)$ Give a sketch of the Edgeworth Box $($including the contract curve and

indifference curves$).$ Use the diagram to explain what part of the contract curve

we would expect to see trade take place.

$($c$)(6$ points$)$ What prices would Jane and Tarzan trade at in a competitive market?

Note: to make your life easier assume one of the goods is a numeraire good $($set

Pi $=$ $$1).$ Explain what the final outcome in the market will be after trade takes

place.