Lesson 3 - 7 ottobre 2014: Exercises 1. Pareto efficiency: Let us

Lesson 3 - 7 ottobre 2014: Exercises
1. Pareto efficiency:
Let us assume there exists only one consumption good and 3 individuals.
Individuals derive satisfaction from consumption of a given good, based on their
respective subjective utility functions and on the quantity consumed. Alternative
allocations of a given amount of good among individuals produces different levels
of utility, as indicated in the chart below.
INDIV. 1
INDIV. 2
INDIV. 3
Allocation A Allocation B
5
8
7
7
12
12
=> Which allocation is efficient according to the Pareto criterio based on
individuals’ satisfaction?
2. Pareto efficiency and non confrontability of individuals preverences
INDIVIDUO 1
INDIVIDUO 2
INDIVIDUO 3
SITUAZIONE A SITUAZIONE B
5
8
7
6
12
12
=> Which allocation is efficient according to the Pareto criterio based on
individuals’ satisfaction?
=> UTILITY is ORDINAL NOT CARDINAL
3. Pareto efficiency and non confrontability of individuals preferences and value
judgments
INDIVIDUO 1
INDIVIDUO 2
INDIVIDUO 3
SITUAZIONE A SITUAZIONE B
5
25
70
60
18
80
=> THE CRITERION Pareto does NOT TAKE ACCOUNT INITIAL INCOME
DISTRIBUTION (poverty).
Adv. Publ. Econ. 2014-15/ Briotti
Pag. 1
Chart: efficient allocation (Pareto criterion) and non confrontability of individuals’
preferences
Bice
Andrea
P. a
6
2
2 indiv. 1 good
P. h
P. g
P.e
6
9
3
4
2
8
How to choose? Value judgement!
Adv. Publ. Econ. 2014-15/ Briotti
Pag. 2
How do we know that we are in a Pareto optimum?
1 EXCHANGE (ALLOCATIVE EFFICIENCY IN CONSUMPTION):
EQUALITY OF Marginal Rate of Substitution (MRS) FOR EACH PAIR OF GOODS
BETWEEN CONSUMERS
2 PRODUCTION (ALLOCATIVE EFFICIENCY IN PRODUCTION:
EQUALITY OF Marginal Rate of Technical Substitution MRTS FOR EVERY COUPLE OF
FACTORS (INPUT) BETWEEN VARIOUS PRODUCTIONS
3 EFFICIENCY "GENERAL" (MRT = MRS) EQUALITY BETWEEN MRSubstitution in
consumption and MR Transformation in production
Exercise 4: Exchange
SMS => Rate at which 2 goods can be substituted at the margins keeping constant
same level of utility (indifference curve).
If different between 2 consumers => exchange improves utility
1. SMS different!
Bice
1 dvd for 3 Cloth => SMS?
Andrea 1 dvd for 4 cloth =>SMS?
2. With exchange => 1dvd / 4 teli
Bice
-1 dvd + 4 teli higher utility
Andrea
+1 dvd -4 teli same utility
Conclusion: Allocation 1 is PO? Why?
Exercise 5: What happens if we go on exchanging the two goods?
Equality of SMS! Why? Bice lower Andrea higher because of higher and lower
consumption of cloth, respectively
Having reached the equality of MRS is no longer possible through exchanges to
increase, the satisfaction of one without reducing the satisfaction of someone else
=> = Equality of MRS satisfies the condition of efficiency in the exchange
Same with production and general efficiency conditions
Adv. Publ. Econ. 2014-15/ Briotti
Pag. 3
Teli ordinata; Dvd ascissa
B smt (3:1) teli su dvd < sms (4:1) teli su dvd
Scostamenti a destra di B rappresentano miglioramenti paretiani
Adv. Publ. Econ. 2014-15/ Briotti
Pag. 4

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