Problem
Consider the following social choice problem in the setting of consumption of two goods by 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) = 6 + .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) = 8 + ln(t) + ln(q). The social endowment consists of 15 units of tillip and 20 units of quillip.
(a) Suppose that a social dictator has social welfare functional of the following form: Social welfare, as a function of (u1, u2) is a weighted sum with weight 2 on the lesser of u1 and u2 and weight 1 on the greater of the two. What will be the welfare optimum plan chosen by this social planner?
(b) What is the set of all feasible, Pareto efficient allocations of the consumption good for this society?
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.