Candice and Dominica are engaged in exchange over two goods: boxes of pens (x)
and boxes of paper (y). They both have inequality averse preferences as defined by
the following equation.
[(x, y), (x, y)] = − mx[ − , 0] − mx[ − , 0]
We assume that and are identical for Candice and Dominica. In this interaction,
the two players each treats themselves as player and their co-participant as player .
The two players have the following initial endowments. Candice has 16 boxes of pens
and 4 of paper. Dominica has 4 of boxes pens and 46 of paper.
a. Graph the Edgeworth box for the exchange between Candice and Dominica
when they each have utilities that are Cobb-Douglas and take the following
form:
1 1
2₁,2
Ui = x+y;
x²
YiCandice knows Dominica's utility takes this form, and vice versa. They use
this information when constructing their
functions. Derive the equation of
the contract curve. In your Edgeworth box, show their initial allocations, their
initial indifference curves, and the contract.
b. Referring to your Edgeworth box, explain the shape of the indifference curves
and how we determine a Pareto efficient allocation in the Edgeworth box.
What would happen if
increased? Explain by referring to your Edgeworth
box. It is useful to think about what happens to marginal utility with changes in
the consumption of pens and paper when changes.
