All societies must take decisions on collective resources should be allo- cated. In democratic societies such decisions are often taken by majority voting, as a matter of fact democracy is often associated with majority voting. However, it has for a long time been known that this way of taking collective decisions is associated with certain problems.
All societies must take decisions on collective resources should be allo- cated. In democratic societies such decisions are often taken by majority voting, as a matter of fact democracy is often associated with majority voting. However, it has for a long time been known that this way of taking collective decisions is associated with certain problems.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
part C and D
![All societies must take decisions on collective resources should be allo-
cated. In democratic societies such decisions are often taken by majority
voting, as a matter of fact democracy is often associated with majority
voting. However, it has for a long time been known that this way of taking
collective decisions is associated with certain problems.
(a) Assume that a small city should decide whether they should build a
new public library (x), a new public swimming pool (y), or improving
the street lightning along the city's main street (z). Only one of
these alternative can be started during the next budget year. The
city population can be divided into three equally large groups, the
members of each group has the following preference ordering for these
alternatives:
1:x > y > z,
2: y > z> x,
3:z > x> y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4748a10c-4a4f-4ce9-8816-6d6a66a7bb52%2F5cf4c0b4-53a0-4366-bb36-408f74deca64%2F6l1gqq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:All societies must take decisions on collective resources should be allo-
cated. In democratic societies such decisions are often taken by majority
voting, as a matter of fact democracy is often associated with majority
voting. However, it has for a long time been known that this way of taking
collective decisions is associated with certain problems.
(a) Assume that a small city should decide whether they should build a
new public library (x), a new public swimming pool (y), or improving
the street lightning along the city's main street (z). Only one of
these alternative can be started during the next budget year. The
city population can be divided into three equally large groups, the
members of each group has the following preference ordering for these
alternatives:
1:x > y > z,
2: y > z> x,
3:z > x> y.
![Show that with majority voting between pairwise alternatives, each
alternative can win dependent on the order in which the pairwise
voting take place (the winner in the first vote goes on to a second
round of voting against the remaining alternative).
(b) The problem that the above example illustrates is that majority vot-
ing is vulnerable to manipulation. Assume that the person that de-
cides the voting-order between pairwise alternative, belongs to group
3. Show how this person (the "agenda setter") can determine the
voting-order so that he/she can assure that his/her best alternative
(z) wins.
(c) According to the first fundamental theorem of welfare economics, a
general equilibrium allocation in a perfectly competitive market econ-
omy is Pareto efficient. However, this allocation can be very unequal,
e.g., one person can get everything and all other nothing. The so-
ciety's preferences other equality can be summed up in a so called
social wel fare function. Discuss different forms of such a function
and what they imply about the inequality of the final allocation.
Discuss also how an allocation, which is optimal according to the so-
cial welfare function, can be implemented as a perfectly competitive
market equilibrium.
(d) Discuss with the help of a so called Edgeworth box-diagram and a
diagram where the consumers' utility possibility sets are illustrated,
where a conflict can emerge between efficiency- and equality goals.
When can it, even in the most egalitarian societies, be optimal with
different distribution of the final utility between citizens.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4748a10c-4a4f-4ce9-8816-6d6a66a7bb52%2F5cf4c0b4-53a0-4366-bb36-408f74deca64%2Fg7h98g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that with majority voting between pairwise alternatives, each
alternative can win dependent on the order in which the pairwise
voting take place (the winner in the first vote goes on to a second
round of voting against the remaining alternative).
(b) The problem that the above example illustrates is that majority vot-
ing is vulnerable to manipulation. Assume that the person that de-
cides the voting-order between pairwise alternative, belongs to group
3. Show how this person (the "agenda setter") can determine the
voting-order so that he/she can assure that his/her best alternative
(z) wins.
(c) According to the first fundamental theorem of welfare economics, a
general equilibrium allocation in a perfectly competitive market econ-
omy is Pareto efficient. However, this allocation can be very unequal,
e.g., one person can get everything and all other nothing. The so-
ciety's preferences other equality can be summed up in a so called
social wel fare function. Discuss different forms of such a function
and what they imply about the inequality of the final allocation.
Discuss also how an allocation, which is optimal according to the so-
cial welfare function, can be implemented as a perfectly competitive
market equilibrium.
(d) Discuss with the help of a so called Edgeworth box-diagram and a
diagram where the consumers' utility possibility sets are illustrated,
where a conflict can emerge between efficiency- and equality goals.
When can it, even in the most egalitarian societies, be optimal with
different distribution of the final utility between citizens.
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