Problem
Consider the following exchange economy. There are two goods and two consumers. The two goods are called tillip and quillip and the two consumers are called 1 and 2. Consumer 1 has utility function U1 (t, q) = .4ln(t) + .6ln(q) (where t is the amount of tillip 1 consumes, and q is the amount of quillip). Consumer 2 has utility function U2(t,q) = .Sln(t) + .Sln(q). Consumer 1 is endowed with 10 units each of quillip and tillip. Consumer 2 is endowed with 10 units of quillip and 5 units of tillip.
(a) What is the Walrasian equilibrium of this economy? (If there is more than one equilibrium, give them all.)
(b) Suppose a social dictator wished to implement an allocation that makes U1 (t, q) + U2(t, q) as large as possible at the equilibrium. Give all the possible reallocations of the endowment that give the dictator's optimal endowment as a Walrasian equilibrium.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.