100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Summary Mathematical Economics 1 UvA 2021 $8.02
Add to cart

Summary

Summary Mathematical Economics 1 UvA 2021

 49 views  3 purchases
  • Course
  • Institution

This summary contains material for the course Mathematical Economics 1. Note that almost all subjects are covered, excluding the topics that can only be learned by making exercises. Therefore, I recommend you to use this document as an addition to the course material, but not a replacement.

Preview 2 out of 13  pages

  • February 20, 2022
  • 13
  • 2020/2021
  • Summary
avatar-seller
Over view lecture 1
Axioms


1
Complete Ness

It 't
'
' ' '

t × × E X either X or × ×
,
utility function
,
.




2
Transitiviteit A function U :
IRI → IR is called a

' ' '
't 't
' '
For × , × × EX If × × × ×
any ,
utility the
,
represented
,

function
'
then x 't ×
relation if
.




prefereren 2

3 continuit '

) xo EIRI
'

ulx
'
) ± ulx
'
⇐ Ex t xo, ×


For an X C- IRI ,
L (x ) and I (× ) are
- invariante to positive monotonie

closed in IRI .




transformaties .




4 Local non -
satiation
→ IK ) =
{ × 1×2×03=9×1 ulx ) zulk ) }
For an I C- IRI and HE > 0
,
] some
is called a
superiors set .




'
X E B , (xo ) such that × > × .




Quasi concavity
5 Strict monotone city "


let f :D → IR ,
where DE IR and convex .




ER ?
'
xozx
'

xo It
'
t
,
x :
.


if ,
then ×
' '
* Quasiaancare iff t x
,
× E D
xo >
'
It
'
.


if ×
,
then ×

text ) { f- (x ) f- LI ) }
'
= min
6
,




Convexity '
with xt =
tx
'

+ ( 1- f) x t te [0,13
XIX EIRI
' ' '
t
,
it X 2X ,
then
* Quasi c o nvex

( 1- f) Ik
'
[ 0,13
'
tx 1- × t te

f- txt ) { f- (× ) f- ( x2 ) }
'
E Max ,



7 Strict convexity
' '

IRI
'
t xo # X E If × 2x ,
then
,




)
' '
1- × t ( i -



E) xo ×
× t te ( 0,1




S. Veeling
ij

, Over view lecture 2


Utility maximization
problem
.


Budget set B =

Ex ) XE IRI , D. × Ey } Marginet rate of substituties MRS


Max ulx ) ⇐ (x ) * MRS =
d at =

#
in
u

B die Itxz P2

sit .




p
-



×
Eg
is the optimale t condition


This can be explained by the
following
Calculatie
:
solution
*
optimal

f. ( × 7) =
ulx ) X ( p )

ya
se " Eso units of goed 1
,
which
×
y
-
-
-




,




deoeasesyovr utility by I c .




* KKT conditions
pas
-




:
JX ,


- om × :
Xi 20 Xi I =
0 I to with the extra
, , → nou
you buygood 2

di di
income units
E-
p ,
,
so
you buy E.pe

t
.




→ om 2 A zo X 0 I to
pz
: =
, ,

JX .




utility by
¥-2 Eppi
This i n c re a s e
-




*
17 ulx ) Strictly quasicomcare , then UMP
→ In optimal situation those two are equal .




has a
Unique Solution .





Ja EPI = < ⇐ MRS

* Solution to UMP Maxlp ) is called I §
, , y

the Marshallion demand function .




S. Veeling
ij

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying these notes from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller SuusV. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $8.02. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

53068 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$8.02  3x  sold
  • (0)
Add to cart
Added