There are two households in an exchange economy. These households have preferences that are represented by the following utility functions:

$U_7(x,y)=x^{0\mathrm{.}5}{y}^{0\mathrm{.}5}$

$U_2(x,y)=xy$

Initial endowments of each household is given by $(x_1,y_1)=(16,4)$;$(x_2,y_2)=(8,8)$

a$.$ Draw the Edworth box and show the initial endowments on the Edworth box.

b$.$ Is the initial endowment point Pareto Efficient? Explain.

c$.$ Draw the indifference curves that go through the initial endowment.

d$.$ Show the set of bundles that are Pareto improvement $($that Pareto dominates$)$ the initial endowment on your Edgeworth box.

e$.$ Identify a competitive equilibrium for this exchange economy. $($Relative prices, and final allocations such that quantity demanded equals quantity supplied for each good at the relative prices.