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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.

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.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Q3 solution needed. another pic is just for helping material

1. Assume that income for household 1 is mi, and let the price of good x be p. Then household l's problem is max 2 In (x1 +) + m, subject to px, + m, s ĩ, Since household 1 will always consume as much as possible to get the most utility, we will have px, + m, = mg. You can then solve for m, and substitute into the utility function. Then take a first- order condition with respect to x1. Solve for x, to get household 1's demand for good 1. You can solve a similar problem for household 2 and then add the two together to get market demand, 2. Each firm needs to produce where MC = price. If you then solve each of these equations for y, and y2. you will have the supply functions for each of the firms. You just add these two together to get market supply. Helping material 3. These should be pretty straightforward calculations. (Let me know if they don't seem that way!) 4. This is going to be a binding price ceiling, so there will be a shortage. Find the quantity supplied by each firm by substituting a price of 1 into the supply function, and find the quantity demanded by each household by substituting a price of 1 into the household demand functions. Consumer surplus, producer surplus, and total surplus will be found similarly to #3, except with a different price and different bounds on your integrals.
Transcribed Image Text:1. Assume that income for household 1 is mi, and let the price of good x be p. Then household l's problem is max 2 In (x1 +) + m, subject to px, + m, s ĩ, Since household 1 will always consume as much as possible to get the most utility, we will have px, + m, = mg. You can then solve for m, and substitute into the utility function. Then take a first- order condition with respect to x1. Solve for x, to get household 1's demand for good 1. You can solve a similar problem for household 2 and then add the two together to get market demand, 2. Each firm needs to produce where MC = price. If you then solve each of these equations for y, and y2. you will have the supply functions for each of the firms. You just add these two together to get market supply. Helping material 3. These should be pretty straightforward calculations. (Let me know if they don't seem that way!) 4. This is going to be a binding price ceiling, so there will be a shortage. Find the quantity supplied by each firm by substituting a price of 1 into the supply function, and find the quantity demanded by each household by substituting a price of 1 into the household demand functions. Consumer surplus, producer surplus, and total surplus will be found similarly to #3, except with a different price and different bounds on your integrals.
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.
Transcribed Image Text: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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