Busi 8108
Economics for Management
Week 4 - Meetings 1 and 2
2024-2025
Emmanuel Haven
1
Measuring well-being out of consuming goods and services
This week we discussed how we could attempt to
formalize measuring well-being out of consuming a
good or a service.
We discussed that it is a little bit of a -very - ambitious attempt!
Why?
It is very di¢ cult to - precisely - indicate a level of
satisfaction of consuming - say a tomato.
We made the distinction between ordinal and cardinal rankings of utility
2
Formalizing this...?
We discussed discrete value change - using u, when
we de…ned a …rst example using: u(x) = 10x 2x2
x is the quantity consumed of the good and u(x)
yields, given the function 10x 2x2; the level of
satisfaction
The level of utility given the consumption x = 2 or
also x = 3 yields the same level utility = i.e. of 12
utils
We can look at the change of utility, in a discrete valued way: u when we change, in a discrete valued
way the change of consumption of the good: x
We can write, as in class:
u
x
We can also consider ultra small changes in both
utility and consumption of good x
For utility measurement this is really a very ambitious (probably well out of scope of reality) attempt.
But note that for costs and production - ultra small
changes can be calculated - and can be meaningful.
An ultra small change is also called an in…nitesimal
change
We move from discrete change:
change: du
dx
u to in…nitesimal
x
In economics, the above changes bear the name well known in economics: of marginal change.
We can de…ne the marginal utility as:
ultra small change way as: du
dx
u or in an
x
3
The checkpoint rule
Why are we interested in using marginal expressions
du ?
like u
or
in
an
ultra
small
change
way
as:
x
dx
As discussed in class, the e¤ective demand occurring
in some sense can be seen as the result of us, consumers, making decisions over what to buy given our
income constraint
Formally, we maximize utility over goods we pick given our income constraint
This maximization process, which is a mathematical
operation, may well - not - occur in our brain
Behavioural economist will say we probably do not
use such process
But it is an abstraction - and the maximization of
such utility leads to using our checkpoint rule
d a xn = a
We de…ned our checkpoint rule as: dx
n xn 1 where * means multiplication and we shall
replace this henceforth with .
Note also that a is a constant and n is an exponent
d a:xn = a:n:xn 1
As in class, we write then: dx
d (10x
We applied this on our utility function: dx
d 10x
d 2x2 = 10:1:x1 1
2x2) = dx
2:2:x2 1
dx
10:1:x1 1 2:2:x2 1 = 10x0
shown in class
4x and x0 = 1 as
So we note: a = 10 and n = 1 in 10x
We note that: a = 2 and n = 2 in 2x2
Since u(x) = 10x
utility
d (10x
2x2, dx
2x2) is marginal
So marginal utility in this precise case is: 10
4x
As seen in class when - setting - 10 4x = 0 what
we say is that the slope to the utility function, du
dx ,
is zero
As shown in class, this slope is zero at a maximum
or a minimum (we should be more rigorous here but we can leave it as this)
We shall continue on Tuesday next week.