=Paper=
{{Paper
|id=None
|storemode=property
|title=Mechanism Design for Foreign Producers of Unique Homogeneity Product
|pdfUrl=https://ceur-ws.org/Vol-1000/ICTERI-2013-p-329-338-ITER.pdf
|volume=Vol-1000
|dblpUrl=https://dblp.org/rec/conf/icteri/Kobets13
}}
==Mechanism Design for Foreign Producers of Unique Homogeneity Product==
https://ceur-ws.org/Vol-1000/ICTERI-2013-p-329-338-ITER.pdf
Mechanism Design for Foreign Producers of Unique
Homogeneity Product
Vitaliy Kobets1
1
Kherson State University, 1, 40 rokiv Zhovtnya Street, 73000, Kherson, Ukraine
vkobets@kse.org.ua
Abstract. Paper concerns to impact on custom receipts of duty rate changing
from single to differentiated ones by customs house for foreign producers. To
get maximal custom receipts for achieving of social goal state may introduce
differentiated duty rates for foreign producers of unique product. Success of this
state policy will depend on effectiveness of incentive compatibility conditions
for these producers.
Keywords. Mechanism design, single duty, differentiated duty, custom policy,
social choice function
Key terms. MechanisnDesign, RevelationPrinciple, SocialGoal, Mathemati-
calModel, IncentiveCompatible
1 Introduction
Mechanism is a mathematical structure, modeling an institute and determining the set
of rules, regulating actions accessible to the participants and determining as partici-
pants strategies in given communication system are transformed in results. In the
absence of co-operation mechanism between participants the final result can substan-
tially differ from social optimal one. A mechanism implements given objective func-
tion, realizing it on participants types space [2; 8].
Mechanism structure includes [7]:
1. Social choice function (SCF is a final result demanded by the society)
2. Implementation mechanism (realization of SCF by the payoffs and distributive
functions of product and money);
3. Revelation mechanism of participants types (by a social planner);
4. Motivating mechanism (it is intended to make conditions for revelation of true
information by participants about their types [6]).
Objective function F is a composition of messages and result h (fig.1).
330 V. Kobets
Fig. 3. Mechanism M and objective function F
Mechanism can enforce to cooperation rules, when participants accomplish ac-
tions, violating set rules [4]. Two extremes of mechanisms’ types are centralized
(planned system) and decentralized (such as competition market), between them are
continuum numbers of other mechanisms.
The decentralized mechanism (saving confidentiality mechanism) implies the pri-
vate expenditure (for collection and verification of information reliability) [1]. Exis-
tent mechanisms can be complemented or substituted by the new ones, for example,
by the means of legislation changes.
Reasons of new mechanism introduction:
Revelation of unsatisfactory aspects activity of existent economic systems or insti-
tutes (market failures)
Established economic system gives advantage only for certain participants
Mechanism tasks:
To ground social choice function with the desirable characteristics for society
To develop compatible conditions for participants to reveal their true types (reser-
vation price, costs etc.)
To make implementation process of social choice function by the help of chosen
mechanism (direct or indirect)
The direct mechanisms provide direct transfer of the truthful private information
about their types by the agents to the public planner (not realistic mechanism). The
indirect mechanisms create motive, under which to the agents more profitable to open
true information, than to conceal or to distort it (more realistic mechanism) [10].
During organizing of customs mechanism, as well as any other, to the participants
concerns of social planner (government) and agents (payers of the customs tax). The
agent is selfish person, who has private information only about him or her own type
(for example, personal income, costs, profit).
Economic environment is exogenous variable, given by nature or received from the
last periods (competition type, technology, rule of custom policy). In model neither
the agents, nor mechanism designer do not know prevailing environment. Mechanism
designer knows: (i) class of environments, for which should be developed the mecha-
nism; (ii) desired criterions for SCF [5; 9].
Mechanism Design for Foreign Producers of Unique Homogeneity Product 331
SCF represents criterions for result estimation, but not a means of goal achieve-
ments as mechanism does.
For customs house SCF mapping types space (average costs of production for im-
porters) in results space (custom receipts). The participant type (average costs) de-
fines its message (invoice cost of the goods), which causes final result (custom re-
ceipts).
So the purpose of customs mechanism can be maximization of receipts from cus-
toms taxes in the state budget under creation of the appropriate motivating system for
the importers (increase of the invoice price, preferential duty rates regime).
This paper has a following structure. We make a literature review in this, first, part.
Problem statement and basic assumptions of model are presented in the second part.
Part 3 deals with main results for participants under fixed and differentiated duty
rates. Last part concludes.
2 Problem Statement
Search of effective ways of state budget replenishment by the means of indirect taxes
requires introduction of flexible duty customs for foreign producers foreseen by the
proper government laws in relation to payment of custom payments. Criteria, after
which the state aims to set the duty rate on import commodities, and to foresee protec-
tionism principle for domestic producers, profitableness principle for the state and
utility principle, for domestic consumers.
Peculiarity of optimization for import duty rate is that foreign producers, forming a
competition domestic market, will maximize own profits, taking into account a mar-
ket price [3], whereas for state size of custom rate depends on invoice cost of com-
modity, which can be corrected by a custom house in the direction of increase and
have to corresponds to prevailing (equilibrium) market price.
Product invoice price indicates cost of commodity, which transfers through custom
border of Ukraine. If the invoice price indicated in freight customs declaration below
of average price in the base of Government custom service of Ukraine, there is the
rise of product price to average level before getting customs clearance for product.
From the customs value of product duty and VAT is counted, that countries are trans-
ferred in a budget.
Customs takes place as follows:
B t TRN ,
where B – duty sum; TRN – part of product invoice price, that exceeds an un-
taxable size (in UAH); t – duty rate (in per cent) from the product invoice price,
which now in Ukraine is equal 10%.
For construction of model, that describes co-operation of foreign producers and
customs we assume:
332 V. Kobets
n foreign firms produce homogeneous product, which is supplied to the domestic
market and has no domestic analogues;
between firms there is quantitative Cournot competition;
cost functions of all firms are linear on production quantities (constant scale re-
turn), and reverse domestic market demand function is linear on the quantity of
foreign products;
information about average costs of foreign firms and domestic market demand is
uniformly (symmetrically) distributed between all participants (foreign producers,
domestic consumers and government).
Participants’ objective functions:
Foreign producers:
Total cost of producer i consists of variable cost (fixed cost we assume zero in long-
run period, vi is average (variable) cost of producer i) and duty sum:
TCiF vi qi t P qi , where Pf P is invoice price of unit product.
Profit of producer i: iF P qi vi qi t P qi or
iF (1 t ) P qi vi qi
i q 0
max , i 1,..., n , t is endogenous vari-
able, i.e. duty rate determined by government.
1. State (Ukrainian Income and Duty Ministry)
n
Tax proceeds to state budget is: B t Pf q .
i 1
i
2. Domestic market:
n
Reverse linear function of domestic demand is P b c Q b c q ,
i 1
i
where P is market price of product, b - maximal price of foreign product on do-
mestic market (under zero import supply).
3 Results
3.1 Custom Receipts Model Construction for Fixed Duty Rate
3.1.1 Producer profit maximization
After substitution of market price to profit function of producer i we obtain:
n
iF (1 t ) b c qi qi vi qi , i 1,..., n . First order condition (FOC)
i 1
Mechanism Design for Foreign Producers of Unique Homogeneity Product 333
iF
of profit give us: (1 t ) b 2c qi c qi vi 0 . Similarly we
qi j i
get partial derivatives for profit function of all producers. Algebraic transformation
yields:
v1
2 q1 q2 ... qn b c (1 t ) ,
v2
q1 2 q2 ... qn b ,
c (1 t )
...................................................,
vn
q1 q2 ... 2 qn b c (1 t ) .
Solving of system by matrix approach give optimal value of foreign producer sales
(duty rate 0 t 1 ):
1 (n 1) v j n v
qj b , j 1,..., n , (1)
(n 1) c 1 t
n
v i
where v i 1 - average product cost of all foreign producers. If in equation
n
(1) average cost of producer j lower than average cost of all producers: v j v , then
after increasing of duty rate t , its optimal sales will rise. And vice versa: if v j v ,
then optimal sale of producer j will decrease.
Total quantity of foreign producers with using of (1) will equal:
n
n (1 t ) b v
Q qj . (2)
j 1 c (n 1) (1 t )
Thus growth of duty rate always will lead to decreasing of total quantity of unique
dQ
good for foreign producers at domestic market: 0.
dt
3.1.2 Budget Custom Receipts Maximization
The receipts from foreign producers’ duty customs after substitution of total sales of
import quantity in expression (2) will give:
t 0
B t Pf Q max , where Pf const – product unit invoice price.
334 V. Kobets
First order condition for maximization of custom receipts is determined by condi-
dB
tion 0 or equivalent to following equation: bt 2 2b t b v 0 , from
dt
here equilibrium duty rate will be equal:
v
t 1 . (3)
b
Equilibrium single duty rate (3) will have inverse relation with average cost of all
foreign producers and direct relation with maximal domestic product price.
Thus the invoice price of product will be set at a level P b c Q or taking into
accoun (2) and (3) we will get the equilibrium indexes of invoice price and sales
accordingly:
Pf*
b b n v , Q n b b v .
*
(n 1) c (n 1)
.
Farther from expression B t Pf Q we will define that the equilibrium
(maximal) custom sum will form:
b v b n v .
2
n b
B* (4)
c (n 1) 2
Consider dependence between equilibrium duty state and custom receipts on fig.2.
Dependence of custom receipt on duty rate
100000
80000
60000
custom receipts
B
40000
Bd
20000
0
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
-20000
duty rate, %
Fig. 2. Laffer curve – dependence between custom receipts and duty rate
Mechanism Design for Foreign Producers of Unique Homogeneity Product 335
(n=10, b=40, v=5,25, c=0,01, P=24,04) t=73%.
3.2 Custom Receipts Model Construction for Differentiated Duty Rate
3.2.1 Producer profit maximization
Profit of foreign producer I is presented by next expression:
(1 ti ) P qi vi qi
i
F qi 0
max , where ti is differentiated duty rate for
foreign producer i. FOC for profit function gives ( i 1,..., n ):
iB
(1 ti ) b 2c qi c qi vi 0. .
qi j i
Similarly we obtain partial derivatives for profit functions of others foreign pro-
ducers.
b v1
2 q1 q2 ... qn c c (1 t ) ,
1
b v1
q1 2 q2 ... qn ,
c c (1 t2 ) .
...................................................,
b v1
q1 q2 ... 2 qn c c (1 t ) .
n
System solving by matrix approach give optimal sales values for foreign producers
on domestic market (duty rate 0 ti 1 , i 1,..., n ):
1 nvj v
qj b i , j 1,..., n . (5)
(n 1) c 1 t j i j 1 ti
3.2.2 Budget custom receipts maximization
Receipts from taxation of differentiated duty rates for foreign producers of homogene-
ity products will equal:
n
Bd Pf ti qi
ti 0,i 1,..., n
max , where Pf const – invoice price per
i 1
unit product for foreign producers.
FOC for maximization of custom receipts is defined by following n conditions:
dBd
0 , where i 1,..., n . Obtained n-equation system with n unknown duty
dti
336 V. Kobets
rates ti after equivalent algebraic transformations define reaction curves (6)
ti fi (t i ) , which demonstrate dependence duty rate of i-th producer ti and duty
rates of all its rivals t i . In this function duty rates for foreign producers have to
change in a same direction. Thus increasing optimal duty rate by one of the producers
requires rising of duty rates for all others foreign producers.
vi (1 t j )
j i
ti 1 , i 1,..., n . (6)
vj
b
j i 1 t j
Such adjustment change of duty rates will proceed until the equilibrium size of
each duty rates will not be set.
System solving of n equation formed from functions (6) gives the following sizes
of equilibrium duty rates for foreign producers:
v1
ti 1 , i 1,..., n . (7)
b
Obtained result shows reverse dependence between the average cost and size of
dti
duty rate for import product: 0 and shows direct dependence between
dvi
maximal price of domestic market and duty rate.
From expression (7) follows that more effective producers (with average cost
lower than industry average cost) will be assessed after the higher duty rate, than less
effective ones for maximization of custom receipts. Now equilibrium invoice price
and quantity sale with using of expression (7) and linear function of domestic demand
will be set at the appropriate levels:
n
n
b b vi b n b vi
Pfd * i 1 , Qd* i 1 .
(n 1) c (n 1)
It is important circumstance that after differentiation of duty rates for the foreign
producers, import of product on domestic market will drop Q Q , that will result
d* *
in rising of price for consumers. Additionally, possibility of charging lower duty rates
for one producer and higher for another ones will generate corruption actions. To
prevention it, necessary objective indexes for differentiation of these rates. Expedi-
ence of differentiated rate introduction will arise only after condition of increase of
custom receipts Bd B in comparison with the fixed duty rate (fig. 3).
Mechanism Design for Foreign Producers of Unique Homogeneity Product 337
82500
82000
81500
Bd
B
81000
80500
80000
71% 71% 72% 72% 73% 73% 74% 74% 75% 75% 76%
Fig. 3. Comparison of influencing of the differentiated and fixed duty rates on customs receipts
(n=10, b=40, v=5,25, c=0,01, P=24,04)
4 Conclusions
So if as to differentiation of tariffs to take public accountant reports from the financial
records audit of firm in part of total cost forming, it will decrease possibilities of re-
alization of unfounded duty rates differentiation by custom house.
At the same time more effective producers will be interested not to disclosure in-
formation about true total cost with purpose to drop size of duty rates. Less effective
producers vice versa will have motives to reveal its total cost, which below than aver-
age cost per unit.
Thus if less effective producers will prove that the effective ones gave false infor-
mation, it will become foundation for the rise of duty rates to more effective produc-
ers and decrease of duty rate for less effective. Thus such custom policy will allow to
the state will put information transaction cost about producers from itself on less ef-
fective producers. From one's part, more effective producers will have motives to
prove that less effective producers set too high the size of its inefficiency.
Collusion between all foreign producers about non-disclosure information about
own costs will be highly unlikely when number of foreign producers will be grow and
collusion will be high-probability when firm concentration will be high.
To receive maximal custom receipts for achieving of social aim state may imple-
ment differentiated duty rates for foreign producers of unique product which depend
from producers’ cost. Success of this state policy will depend on effectiveness of
incentive compatibility conditions for these producers, which mean extracting of true
information about cost from foreign producers by the means of firms cross-sectional
audit.
338 V. Kobets
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