Q2 1. For this and the following three problems, consider a partial equilibrium model withtwo households with preferences given by u1(r1, m1) = 2ln(x1 + 1/6) + mị andu2 (x2, m2) = 3 ln(x2+1/3)+m2, and two firms with cost functions for the productionof good 1 given by c1 (y1) = yỉ and c2(y2) = y3. Find the demand function for good1 of each household and the market demand function for good 1, and illustrate eachhousehold demand and the market demand curves in a graphic.2. Find the supply function for good 1 of each firm and the market supply function forgood 1, and illustrate each firm supply and the market supply curves in a graphic.3. Find the competitive equilibrium price for good 1, as well as the equilibrium de-mand of each household, the equilibrium supply for each firm, the households' utilityin equilibrium, the firms' equilibrium profits, the consumer surplus, the producersurplus, and the total surplus.4. Suppose that a price ceiling of 1 is put in place. Under the assumption of efficientrationing, find the supply of each firm, the consumption for each household, the newconsumer surplus, the new producer surplus, the new total surplus, and the surplusloss in relation to the competitive outcome.

The market supply curve refers to the graphical representation of the relationship between the price…

Answered: Find the supply function for good 1 of…

Find the supply function for good 1 of each firm and the market supply function for good 1, and illustrate each firm supply and the market supply curves in a graphic.

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

1. For this and the following three problems, consider a partial equilibrium model with
two households with preferences given by u1(r1, m1) = 2ln(x1 + 1/6) + mị and
u2 (x2, m2) = 3 ln(x2+1/3)+m2, and two firms with cost functions for the production
of good 1 given by c1 (y1) = yỉ and c2(y2) = y3. Find the demand function for good
1 of each household and the market demand function for good 1, and illustrate each
household demand and the market demand curves in a graphic.
2. Find the supply function for good 1 of each firm and the market supply function for
good 1, and illustrate each firm supply and the market supply curves in a graphic.
3. Find the competitive equilibrium price for good 1, as well as the equilibrium de-
mand of each household, the equilibrium supply for each firm, the households' utility
in equilibrium, the firms' equilibrium profits, the consumer surplus, the producer
surplus, and the total surplus.
4. Suppose that a price ceiling of 1 is put in place. Under the assumption of efficient
rationing, find the supply of each firm, the consumption for each household, the new
consumer surplus, the new producer surplus, the new total surplus, and the surplus
loss in relation to the competitive outcome.

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Step 1: Define the Market supply curve

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Step 2: Derive the supply function

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Step 3: Plot the graph for supply fucntion for Good 1 in both the firm and the market supply curve

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For this and a and b problems, consider a partial equilibrium model with two households with preferences given by u1(x1, m1) = 2 ln (x1 + 1/6) + m1 and u2(x2, m2) = 3 ln(x2+1/3)+m2, and two firms with cost functions for the production of good 1 given by c1(y1) = y 2 1 and c2(y2) = y 2 2 Find the demand function for good 1 of each household and the market demand function for good 1, and illustrate each household demand and the market demand curves in a graphic. a. Find the supply function for good 1 of each firm and the market supply function for good 1, and illustrate each firm supply and the market supply curves in a graphic. b. Find the competitive equilibrium price for good 1, as well as the equilibrium demand of each household, the equilibrium supply for each firm, the households’ utility in equilibrium, the firms’ equilibrium profits, the consumer surplus, the producer surplus, and the total surplus.