Exercise: Consider two households, A and B and two goods, and . Overall, there are 10 units of good and 8 units of good that the households A and B can share.
The utility that household A gathers when consuming xA units of good and yA units of good is given by A = xA + 4yA − 1/2 (yA )^2 .
The utility that household B gathers when consuming xB units of good and yB units of good is given by B = xB + 6yB − 1/2 (yB)^2 .
Q1. Characterize all allocations of the goods that maximize total welfare measured as A + B.
Q2. Assume that each household owns some positive initial endowments of the goods such that, overall, they have 10 units of good and 8 units of good . Assume as well that they set up a market where the price of good is €1. Find the equilibrium price for good and the resulting consumption of good for each household.