Consider the following economy: There are three goods, legume, tillip and quillip, two consumers (called 1 and 2), and two firms (called x and y). Firm x is owned entirely by consumer 1 and makes tillip out of legume according to the simple linear production technology t :::; 3l . That is, for every unit of legume input, this firm produces three times as many (or less) units of tillip. Firm y is owned entirely by consumer 2 and makes quillip out of legume according to the production technology q = 4l. Each consumer initially owns 5 units of legume. Consumer 1 has utility function u1(t, q) = 6 + .4ln(t) + .6ln(q). Consumer 2 has utility function ui(t, q) = 8 +ln(t) + ln(q). (a) What is the general equilibrium of this economy? Assume that firms take prices as given and are profit maximizers, and consumers take prices as given. When you give prices, normalize them so the price of legume is $1. What would be the general equilibrium if the shareholdings were reversed? If each consumer held a half-share in each furn? (b) What is the set of all feasible, Pareto efficient allocations for this econ omy?
11 11. Consider the following economy: There are three goods, legume, tillip and quillip, two consumers (called 1 and 2), and two firms (called x and y). Firm x is owned entirely by consumer 1 and makes tillip out of legume according to the simple linear production technology t :::; 3l . That is, for every unit of legume input, this firm produces three times as many (or less) units of tillip. Firm y is owned entirely by consumer 2 and makes quillip out of legume according to the production technology
q = 4l. Each consumer initially owns 5 units of legume. Consumer 1 has utility function u1(t, q) = 6 + .4ln(t) + .6ln(q). Consumer 2 has utility
function ui(t, q) = 8 +ln(t) + ln(q).
(a) What is the general equilibrium of this economy? Assume that firms take prices as given and are profit maximizers, and consumers take prices
as given. When you give prices, normalize them so the price of legume is $1. What would be the general equilibrium if the shareholdings were reversed? If each consumer held a half-share in each furn?
(b) What is the set of all feasible, Pareto efficient allocations for this econ omy?
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