Problem $2$: Competitive equilibrium

$2$

Intermediate Microeconomics NYUAD

$($a$)$Assume that consumer A$$s initial endowments of good X

and Y are $($x $,$ y $)=(4,2),$ and consumer B$$s initial en$-$ AA

dowments of the two goods are $($x $,$y $)=(4,2).($Note BB

that this means that the total endowments are the same as in part Problem $1$ part $($a$)).$

$($i$)$IllustratetheinitialendowmentsintheEdgeworthbox$,$ and draw an indifference curve for each consumer going through their endowment.

$($ii$)$Illustrate the set of points in the Edgeworth box that are Pareto superior to the endowment.

$($iii$)$Illustrate the set of Pareto optimal allocations in the Edgeworth box that are Pareto superior to the endow$-$ ment.

$($iv$)$In this economy there is a unique competitive equilib$-$ rium. Normalizing the price of good Y to pY $=1,$ find the competitive equilibrium price of good X $($i$.$e$.,$ pX$)$ and the competitive equilibrium allocation $($i$.$e$.,$ x$$A$,$ yA$,$ x$$B$,$ and yB$).$

$($v$)$Which consumer benefits most from trade in the com$-$ petitive equilibrium?

$($b$)$Assume$,$ instead, that consumer A$$s initial endowments of good X and Y are $($x $,$y $)=(6,3),$ and consumer B$$s

AA

$3$

Intermediate Microeconomics NYUAD

initial endowments of the two goods are $($x $,$ y $)=(2,1).$ BB

$($Note that this means that the total endowments are still the same as in Problem $1$ part $($a$)).$

$($i$)$IllustratetheinitialendowmentsintheEdgeworthbox$,$ and draw an indifference curve for each consumer going through their endowment.

$($ii$)$Illustrate the set of points in the Edgeworth box that are Pareto superior to the endowment.

$($iii$)$Illustrate the set of Pareto optimal allocations that Pareto superior to the endowment.

$($iv$)$In this economy there is a unique competitive equilib$-$ rium. Normalizing the price of good Y to pY $=1,$ find the competitive equilibrium price of good X $($i$.$e$.,$ pX$)$ and the competitive equilibrium allocation $($i$.$e$.,$ x$$A$,$ yA$,$ x$$B$,$ and yB$).$

$($v$)$Does consumer B benefit more from trade now than under the initial endowments from part $($a$)?$