Find the Pareto efficient allocation for this economy when the planner is maxi- mizing the sum of utilities as specified in equation (1) above. (b) Find the competitive equilibrium prices of the economy which has the Pareto optimal allocation you have found in (a) as a competitive equilibrium. (c) Find the distribution of the endowments across agents of the economy which has the Pareto efficient allocation you have found in (a) as a competitive equilibrium.

ENGR.ECONOMIC ANALYSIS
14th Edition
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Author:NEWNAN
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Chapter1: Making Economics Decisions
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Consider the following economy with two persons A and B and two goods 1 and 2. The total
endowments of the two goods are
endowment of good i. The utility functions u4 and u for persons A and B respectively are:
wf + wf
= 2 and w +w = 1, where w is person J's
u^(4, 2) = afaf and u (af, a) = af,
B B
= I1
B
B
where x is person J's consumption of good i.
Suppose that a social planner wants to maximize the following sum of person A and B's utility,
3
B
juA (f, ) +
Find the Pareto efficient allocation for this economy when the planner is maxi-
(a)
mizing the sum of utilities as specified in equation (1) above.
(b)
Find the competitive equilibrium prices of the economy which has the Pareto
optimal allocation you have found in (a) as a competitive equilibrium.
Find the distribution of the endowments across agents of the economy which
(c)
has the Pareto efficient allocation you have found in (a) as a competitive equilibrium.
Transcribed Image Text:Consider the following economy with two persons A and B and two goods 1 and 2. The total endowments of the two goods are endowment of good i. The utility functions u4 and u for persons A and B respectively are: wf + wf = 2 and w +w = 1, where w is person J's u^(4, 2) = afaf and u (af, a) = af, B B = I1 B B where x is person J's consumption of good i. Suppose that a social planner wants to maximize the following sum of person A and B's utility, 3 B juA (f, ) + Find the Pareto efficient allocation for this economy when the planner is maxi- (a) mizing the sum of utilities as specified in equation (1) above. (b) Find the competitive equilibrium prices of the economy which has the Pareto optimal allocation you have found in (a) as a competitive equilibrium. Find the distribution of the endowments across agents of the economy which (c) has the Pareto efficient allocation you have found in (a) as a competitive equilibrium.
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