Description

Scientific paper

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Related Documents

Share

Transcript

ACTA UNIVERSITATIS DANUBIUS Vol 8, No. 1/2012 164
An Analysis of the Substitution Effect and of Revenue Effect in the Case of the Consumer’s Theory Provided with a CES Utility Function
Catalin Angelo Ioan
1,
Gina Ioan
2
Abstract
In the consumer’s theory, a crucial problem is to determine the substitution effect and the revenue effect in the case of one good price’s modifing. There exists two theories due to John Richard Hicks and Eugen Slutsky which allocates differents shares of the total change of the consumption to these effects. The paper makes an analysis between the two effects, considering the general case of a CES utility function and introduces three indicators which will characterize these shares.
Keywords:
CES; substitution; revenue; utility
JEL Classification:
D11
1. Introduction
In the consumer’s theory, a crucial problem is to determine the substitution effect and the revenue effect in the case of one good price’s modifing. The theory due to John Richard Hicks consider after a modifing of a price, first a new allocation of goods preserving the utility, but modifing the revenue and after taking into account that the revenue is the initial one the changing in allocation due to a different utility. The theory of Eugen Slutsky consider a combined displacement of the relative consuming obtained a share of the substitution effect or of revenue effect depending only from the parameters of the utility. The problem is to determine these shares for both methods and to inquire which effect is uppermost.
1
Associate Professor, PhD, Danubius University of Galati, Faculty of Economic Sciences, Romania, Address: 3 Galati Blvd, Galati, Romania, tel: +40372 361 102, fax: +40372 361 290, Corresponding author:
catalin_angelo_ioan@univ-danubius.ro
2
Assistant Professor, PhD in progress, Danubius University of Galati, Faculty of Economic Sciences, Romania, Address: 3 Galati Blvd, Galati, Romania, tel: +40372 361 102, fax: +40372 361 290, e-mail: gina_ioan@univ-danubius.ro
AUDŒ, Vol 8, no 1, pp. 164-175
ŒCONOMICA
165
2. The Analysis
Let two goods A and B with the initial prices
A
p
and
B
p
and an utility function of a CES type U=
( )
λ−λ−λ−
β+α
1
YXT,
α
,
β
>0,
λ
>0, where X and Y are the consumed quantities in order to obtain an utility U. Let also, at a given time, V – the consumer’s revenue. In order to have the maximum utility for the revenue V it is known that we must have:
+==
YpXpV
ppUU
BABAmBmA
where U
mA
=
( )
111
YXTX
−λ−λ−λ−−λ−
β+αα
and U
mB
=
( )
111
YXTY
−λ−λ−λ−−λ−
β+αβ
are the marginal utilities corresponding to the two goods A and B respectively. We have now:
+==βα
−λ−−λ−
YpXpV
ppYX
BABA11
Let note, in what follows:
ϕ
=
βα
, r
1
=
BA
pp
and: S=
1111
r
+λ−+λλ
ϕ+
. We have therefore: XrXppY
1111111AB
+λ+λ
−+λ−
ϕ=
βα=
XrppV
11111BA
ϕ+=
+λ+λ
−
=Xprr
B111111
ϕ+
+λ+λ
−
We obtain now:
ACTA UNIVERSITATIS DANUBIUS Vol 8, No. 1/2012 166 X
1
=
A11
SpVr
+λλ
, Y
1
=
B11
SpV
+λ−
ϕ
and the corresponding utility is: U
1
=
B111
pSTV
λ+λ−λ−λ−
ϕβ
. Let suppose now that it is a change in the price of one of the goods, let say B, from
B
p
to
B
'p
, but the revenue V remains constant. Let note now: r
2
=
BB
p'p
and, of course:
BA
'pp
=
21
rr
. Let note, also: R=
111211
rr
+λ−+λλ−+λλ
ϕ+
, Q=
SR
. We have, from the upper relations: R-S=
−
+λλ+λλ−+λλ
121211
r1rr
121211
r1SrR
+λλ−+λλ−+λ−
−−=ϕ
Now: X
3
=
A1211
RpVrr
+λλ−+λλ
, Y
3
=
B211
pRrV
+λ−
ϕ
and the corresponding utility: U
3
=
λ+λ−λ−λ−
ϕβ
1B211
RprTV
. We shall apply now the Hicks method for our analysis. At the modify of the price of B, for the same utility: U
1
=
B111
pSTV
λ+λ−λ−λ−
ϕβ
we shall have: U
1
=
λ+λ−λ−λ−
ϕβ
1B211
Rpr'TV
ŒCONOMICA
167therefore:
λ+λ−λ−λ−λ+λ−λ−λ−
ϕβ=ϕβ
1B211B111
Rpr'TVpSTV
implies that:
λ+λ−λ+λ−
=
112
RSVr'V
With the new revenue, we obtain: X
2H
=
A1111211
pRVSrr
λ−λ+λ−+λ+λ
λ
Y
2H
=
B1111
pRVS
λ−λ+λ−+λ−
ϕ
. The substitution effect (which preserves the utility) gives us a difference:
∆
1H
X=X
2H
-X
1
=VrSpQQr
11A11112
+λλλ−λ−+λ
−
∆
1H
Y=Y
2H
-Y
1
=VSpQQ1
11B11
+λ−λ−λ−
ϕ−
The difference caused by the revenue V instead V’ is therefore:
∆
2H
X=X
3
-X
2H
=
VrrRpQr1
1211A12
+λλ−+λλλ+λ
−
∆
2H
Y=Y
3
-Y
2H
=VpRrrQ1
11B221
+λ−λ+λ
ϕ−
named the revenue effect.

Search

Similar documents

Tags

Related Search

Art Film: An Analysis of Terrence Malick's ThAn analysis of the rules and procedures of reAn analysis of the rules and procedures of reAn analysis of the outgrower's scheme among tAn Analysis of the Notion of a Failed StateAn Analysis of Seaport ClustersPUNJABI COLOR CATEGORIES: AN ANALYSIS OF WORLAnalysis of Edward Albee's The Zoo StoryAN ANALYSIS OF RURAL POVERTY, AGRICULTURAL RISpatio Temporal Analysis Of Earthquake Time S

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks

SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...Sign Now!

We are very appreciated for your Prompt Action!

x