Consider a two-good economy (good z and good y) with two consumersand one firm. Consumer 1 has only 10 units of good x as her endowment.Consumer 2 has 25 units of good y as her endowment. The firm producesgood x by using good y. Its production function is x = 2/y. Consumer 1fully owns the firm. Consumer 1's utility function is given by U1[¤1, Yı] =In x+ln y1. Consumer 2's utility function is given by U2[c2, Y2] = VT2Y2.Let p be the price of good x and q the price of good y. Derive the generalequilibrium.

General equilibrium in economics is a situation where all markets within an economy are in balance…

odecor good y) and one firm. Consumer 1 has only 10 units of good x as her endowment. Consumer 2 has 25 units of good y as her endowment. The firm produces good x by using good y. Its production function is x = 2√. Consumer 1 fully owns the firm. Consumer 1's utility function is given by U₁[1, 1] In ₁+In y₁. Consumer 2's utility function is given by U2[2, 32] = √√√2Y2. Let p be the price of good x and q the price of good y. Derive the general equilibrium. =

odecor good y) and one firm. Consumer 1 has only 10 units of good x as her endowment. Consumer 2 has 25 units of good y as her endowment. The firm produces good x by using good y. Its production function is x = 2√. Consumer 1 fully owns the firm. Consumer 1's utility function is given by U₁[1, 1] In ₁+In y₁. Consumer 2's utility function is given by U2[2, 32] = √√√2Y2. Let p be the price of good x and q the price of good y. Derive the general equilibrium. =

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Consider a two-good economy (good z and good y) with two consumers
and one firm. Consumer 1 has only 10 units of good x as her endowment.
Consumer 2 has 25 units of good y as her endowment. The firm produces
good x by using good y. Its production function is x = 2/y. Consumer 1
fully owns the firm. Consumer 1's utility function is given by U1[¤1, Yı] =
In x+ln y1. Consumer 2's utility function is given by U2[c2, Y2] = VT2Y2.
Let p be the price of good x and q the price of good y. Derive the general
equilibrium.

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Step 1: Define general equilibrium

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Step 2: Consumer 1's optimisation

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Step 3: Consumer 2's optimisation

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Step 4: Firm's optimisation

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Step 5: Market clearing condition

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Step 6: Price adjustment

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