Antonio Stasi
1. Utility
2. Utility…lets talk in math terms
3. Utility…basics of comparative
statics
4. Utility and policy
5. How to measure utility
Utility
• What is?
– Adimensional Measure of Consumers’
Satisfaction
• If it is adimensional, How it is used?
– Used to make consumers among
consumers (only if measured always
in the same way)
• What we need to know:
– How can I practically use it for
policy/managerial purposes
Utility
• The RATIONALE behind utility refers
to the HEDONISTIC principle
– Consumers behave rationally and
selfishly (egoistically), maximizing their
own satisfaction
• Which are the determinants of
utility?
• Which are the cause of utility?
• What could potentially change the
level of utility a consumer achieves?
Utility
• We can say that individuals choose to
buy/eat/consume a product when
utility is at its maximum level given the
budget constraint
• Utility is max when the perceived
quality is max and the quantity is also
max….depending on the budget…of
course
max(U) = max(Quality,Quantity)
subject to: Y = sum(pq)
Utility
max(U) = max(Quality,Quantity)
subject to: Y = sum(pq)
Utility
Budget Constraint
Max U for that
person
Quality
Utility…lets talk in math terms
• If Utility is assumed to be a linear
function of quality and quantity…
U = a1Qt + a2Qual
• Because of Lagrange Theory,
budget constraint can be included
into the equation, giving rise to…
U = a1Qt + a2Qual - bP
Utility…basics of comparative
statics
• How much utility would increase if
budget increases by 1 euro (unit)?
– By means of the partial derivative with
respect to price, we have
∂U/ ∂P = -b
• How much utility would increase if
quality increases by 1 unit?
∂U/ ∂Q = a
Utility…basics of comparative
statics
• TRADE-OFF
– How much should I increase quality if I
increase the price and I want to keep
people buying my product?
• If an individual already buys, Utility
is max
• Utility was already maximized
initially, when for example Qual = 1
and Price =1
U = a1 – b 1
Utility…basics of comparative
statics
• What if I want to increase price to 2? How
much should I increase quality to keep
consumer’s utility at the max level?
Umax = a1 – b 1
now
a(Q?) – b 2
therefore
a1 – b 1 = a(Q?) – b 2
hence
Q? = (a+b)/a
So I would increase quality from 1 to Q?
Utility…basics of comparative
statics
• What if I want to produce higher quality
(from 1 to 2) products? How much should I
ask consumers to pay?
Umax = a1 – b 1
now
a(2) – b P?
therefore
a1 – b 1 = a2 – b P
hence
P? = (a+b)/b
So, if quality goes from 1 to 2, I would
increase price from 1 to P?
Utility…basics of comparative
statics
• This concept keeps the name of
WILLINGNESS TO PAY for an
increase of quality (WTP)
• “a” measures consumers’
perception of quality
• “b” measures consumers’
sensitivity to price changes
Utility and Policy
• Quality can be intended in various ways
– Organoleptic quality
– Level of information provided to consumers
(labeling)
– Level/Presence of some ingredients
(sulfites in wine, genetically modified
ingredients…, level of fiber, level of
alcohol…)
– Combination of product attributes
• The evaluation of utility could be used for
understanding the best policy
How to measure Utility
• E.g. take more than one product
with fixed characteristics
• Ask people:
– Ranking/Ordering
• Say which is the first choice for you, the
second, the least
– Scoring
• Assign a score for each product
– Choice Probability
• Which one among those is your
effective choice?
How to Measure Utility
• The following measure are reliable
approximation for Utility
– Ranking/Ordering
– Scoring
– Choice Probability
U = Prob = Rank = Score
How to measure Utility
• Remember the equation?
U = aQual - bP
– For the moment we have U
– How about Qual and P?
• Those are observable characteristics
we can see on the shelves
– How about a and b?
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