Summary EC123 term 1 warwick formulas

, Week 2

One Variable Optimisation
Choice between two options a and b with utility u(a. b)
↳ If pa =pis , optimal choice implies that the
marginal utility of each choice must be equal
↳ U'blaI
Utpaabl
=




Pb



Note
µ ,
sometimes the maxima and minima
when the slope are horizontal


É
occur .




I



t
(
dyq=o) such as the
However
graph on the left
other times the maximum
.




i " ,


I i. I :-. and minimum have
points dont a
¥
:


horizontal slope
a ✗0 A
a b
such as on the
right
but other points do .




Convex and Concave Functions

first

limtcctmn-tcclh-oitt.cn
derivative =
t.ca =




yo tcm is
increasing over D
'
it t (a) to tent is decreasing over D



it f ca) > otcx) is strictly 4
'
over D

it 1- (a) { of (a) is
'

strictly * over D




Convexity 1- (a)
"
deal with the functions
and
Concavity second derivative

Definition : Given that it is twice continuously differentiable ,




t
'
f-
"
function is D if (a) 20 cat I
1) A convex over
t (a)
'
f-
"
I
2) A function is concave over D if (R) & O