3(b)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 U, (t,q) = 6+4 In(t) +.6 In(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+ In (t) + In(a). 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 (u',u) is a weighted sum with weight 2 on the lesser of u' 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?
3(b)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 U, (t,q) = 6+4 In(t) +.6 In(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+ In (t) + In(a). 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 (u',u) is a weighted sum with weight 2 on the lesser of u' 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?
Microeconomics A Contemporary Intro
10th Edition
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Chapter6: Consumer Choice And Demand
Section: Chapter Questions
Problem 2QFR
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Transcribed Image Text:3(b)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 U; (t,g) =6+.4 In(t) + .6 In(q) (where t is the amount of tillip 1
consumes and q is the amount of quillip). Consumer 2 has utility function U; (t,q) = 8 + In (t) + In(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 afunction of
(u",u") is a weighted sum with weight 2 on the lesser of u' and u' 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?
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