Optimal transfer price: optimizing resource allocation 
Tomáš Buus*
Second draft. Please do not quote without prior author’s permission.
1
Introduction
„A transfer price is the price attached by business enterprise to transactions between
different divisions or affiliates under its ownership.“1 This definition tells us what the transfer
price is, but not too much on how to deal with it. Due to the increasing role of multibusiness
or even multinational companies and their impact on national welfare, on effectiveness of
economic policies and on quality of our lives, we should have tremendous interest to clearly
and well understand how to deal with transfer pricing issues. „Yet interestingly, in recent
years, as public concern has grown about transfer pricing (especially in developing
countries) this literature2 has attempted to play down this aspect of corporate strategy. This
does not indicate that the scope or impact of transfer pricing has decreased, only that this
practice is more discreet and more closely monitored by national governments.“3 Compared
to macroeconomic issues, equity premium or many other microeconomic issues, transfer
pricing gets much less attention than it deserves.
Theory and practice are quite contrary about what shall be optimal transfer price equal
to (will be shown later in this article) mainly because theory is about the microeconomic point
of view, whereas practice is about the macroeconomic point of view and tax issues. Our
concern will concentrate on the optimal transfer price from the point of view of a
multibusiness (multinational) company, which experiences different income tax rates in
countries, where its affiliates have their seats.
Former microeconomic literature on transfer prices concludes that optimal transfer
price should be equal to marginal cost of production of the supplying business entity
(company). This opinion is known since the beginning of the 20th century thanks to article
(Schmallenbach, E., 1908) and in anglo-saxon literature then (Hirshleifer, J., 1956). Of
course, there are limiting conditions, which are explicitly stated to be held while setting the
transfer price that way. We we will try avoid breaking. On the other hand the conclusion
reached in the above mentioned articles could be true only under such unrealistic conditions,
that they are unable to be met in reality, as we will show. Other topic of interest is optimal
level of transfer price in multinational enterprise with different tax levels in different
countries.
2
Recent literature
Either elder or new literature on transfer pricing is mostly based on considering the
best transfer price on the level of marginal cost. In the first line we could mention pioneering

This article is supported by Czech Grant Agency programme GAČR 402/05/2163 Teoretické aspekty
oceňování podniku v ČR.
*
Department of Corporate Finance and Business Valuation, University of Economics in Prague
1
(Eatwell, J. – Milgate, M. – Newman, P., 1998), p. 682
2
International business literature offering advices on the use of transfer prices to maximize net profits
3
(Eatwell, J. – Milgate, M. – Newman, P., 1998), p. 683
articles (Schmallenbach, 1908) and (Hirchleifer, 1956). Newer works as (Gatti and Grinell
and Jensen, 1997), (Baldenius and Melumad and Reichelstein, 2004) or in the czech literature
(Soukup, 2003) and (Roun, 2004) still consider marginal cost of supplying division as the best
solution at least from the short-run point of view.
In (Gatti and Grinell and Jensen, 1997) authors came to conclusion that the best
transfer price in the short run is marginal cost. In long run, however the authors consider to be
highly recommendable to use transfer price on free market price level. In (Baldenius and
Melumad and Reichelstein, 2004) authors extend the Hirshleifer’s solution of optimal transfer
price in a tax-free world, that is the marginal cost of the supplying division, by tax issue. After
that these authors argue that „optimal internal transfer price should be a weighted average of
the pre-tax marginal cost and the most favorable arm’s length price.“ Roun (2004) clearly
states that optimal transfer price should be set on the level of marginal cost of the supplying
division and the same conclusion could be found in (Hirschey, 2003) and many other
textbooks on managerial economics. Among significant textbooks noting the marginal cost as
the best transfer price in no-tax and no-imperfections world can be also counted (Lutter et al.,
1998).
Among the others that argue against transfer price at the marginal cost level and offer
another approaches (mainly negotiated transfer prices) are (Sunil and Anctil, 1999) which
advocate for using of negotiated transfer prices. Another article is (Baldenius and
Reichelstein, 2004) which solves the problem of intracompany trade under conditions of
monopoly power of supplying division.4 Market imperfections, differences in marketing cost
and smaller risk that receivables would not be paid in intracompany transactions cause that
optimal transfer price should be market price minus some discount. We could mention many
other authors, who argue for market prices or negotiated prices, but their argumentation is
based on a solution of some specific problem (information asymmetry, solution of investment
allocation distortion, agency cost, etc.)
In contrary to the literature on corporate finance and microeconomics there is (often
implied) assumption emerging in articles and books aimed on tax issues of transfer pricing.
As one example for all could serve Transfer Pricing Guidelines for Multinational Enterprises
and Tax Administrations. Methods of treating transfer prices based on comparable prices
advised by OECD to be used by particular national tax authorities, are derived from market
prices, which only in few extraordinary cases could be on the level of marginal cost. Armslength price can be rather viewed as an average or range of market prices. Under these
conditions almost no multinational or multibusiness company optimizing only its output (not
tax paid) would meet requirements of tax authorities because it would set the transfer price as
marginal cost of supplying division. However, marginal cost are equal to market price only
very rarely.
3
Optimal transfer price in tax free world
Since (Schmallenbach, 1908) is as an optimal transfer price regarded marginal cost of
intermediate product production. This model considers neither taxes (or tax differential) nor
information asymmetry, incentives of managers to cheat (agency problems), etc. Let us take a
few words to descript this approach in short. Suppose there is a multibusiness company
consisting of two companies, A and B . A supplies B with product a . We do not impose
any assumptions about existence of external market of an intemediate product. B uses good a
4
But while there was lack of capacity constraints and market imperfections and other above mentioned
imperfections, the best transfer price should be again marginal cost of supplying division, see pages 3 and 4.
to produce b . For simplicity let us consider, that ratio of a needed for production of b is
constant and denote it k .
Both A and B carry cost related to the production of their products
TC

total
cos t , MC  m arg inal cos t , AC  average cos t ) and get revenues from selling
(
their goods TR  total revenues, MR  m arg inal revenues, AC  average revenues . We
consider being of use to stress, that we under TC b understand cost without price for
intermediate product. Profit functions are then
A  Qa PT TCa ,
where PT is transfer price and

B
 Q b  Pb  TC
b
(1)
 Q b  k  PT ,
(2)
where
k 
Qa
,
Qb
(3)
 B
Company B maximizes its profit at
 0 . After some rearrangement we get
Qb
MRb  MCb  k  PT ,
(4)
Difference between marginal revenues and marginal cost, called net marginal revenue
(NMR) is the highest amount which company B would pay for quantity k of product a . On
the other hand also company A optimizes its profit and the result is, similarly to the company
B:
MRa  MC a .
If the multibusiness company was one entity, we could rewrite equation (4)
MR b  MC b  k  MC a
(5)
and from equating (4) and (5) we get

(6)
PT  MCa
This way we got the result, which appears in most textbooks on intermediate
microeconomics nowadays. As we have mentioned above, we could see these conclusions for
example in (Roun, 2004). Characteristics of profit functions needed for the result of the
optimization was maximum of the profit function are that the profit functions are strictly
concave (  2   Q 2  0 ) and cost and revenues functions are differentiable all over their
domains.
Let us suppose now, that the market for intermediate product a is perfectly
competitive. Under this condition the only solution for price of intermediate product is
marginal cost of production of intermediate product, just because of the nature of the market.
In the long run all companies sell their production at the lowest possible price – at the
minimum of average cost on perfectly competitive market. This average cost is also marginal
cost for that given quantity of intermediate product.
If market of intermediate product was imperfectly competitive, slightly different
situation could emerge. On the imperfectly competitive market supplying division (company
A ) could chose any price within range determined by shape and corners of demand curve (of
course with regard to its cost function). Nevertheless in this case could be marginal cost also
suitable as a price of intermediate product. Monopoly profit, achieved on the sales of the
intermediate product a to external consumers enables supplying company not to use its
monopoly power in case of sales to B and set price for intragroup deliveries on the level of
marginal cost.
Quite different situation occurs, when market of intemediare product does not exist. In
this case there is no external power forcing company A to sell at minimum of average cost
and depending upon character of the final product there can or does not have to be space for
shifting price of intermediate product.
4
Problems with transfer price on level of MC
We have concluded in previous paragraphs that it is possible to use marginal cost as
optimal transfer price in world without taxes (tax differentials), agency cost, etc., but
according to our opinion it is particularly due to the fact that external conditions either enable
or even force and fix transfer price on such level. We consider marginal cost of intermediate
good production not to be good measure for setting transfer price even in world without taxes
and agency cost.
Let us start proving this statement on model with perfectly competitive market of final
product b and with absence of market of the intermediate product a . We have imposed only
those constraints in the previous paragraphs, which ensure that the result of optimization is
maximum of profit function and it can be reached. Hirshleifer (1956), Schmallenbach (1908)
or Baldenius, Melumad and Reichelstein (2004) implicitly assume that the function of average
cost is equal to the function of marginal cost (as will be evident from further text). We
consider this assumption (even not explicitly stated) too strong. Under our conditions,
situations where marginal cost and average cost functions are not equal, can emerge:
MCQ  ACQ .
Q
(7)
Because of the fact that cost functions have to be differentiable all over their domains,
we can also say that there is more than one such a quantity Q that fits equation (7). In fact
(providing that intermediate product can be divided into infinitely small amounts), there is
infinite number of quantities Q meeting condition (7). It is obvious that if optimal quantity


(8)
Q   MC 1 MC  , where MC  MC Q 
falls within the range described by (7), the supplying company would get economic profit or it
would suffer economic loss (cost of capital are not fully covered at least). This situation is not
efficient and under our assumptions, i.e. perfectly competitive market of final product b and
with absence of market of the intermediate product a , it would finally lead to complete loss
of competitiveness of our model company on the market of final product. Compared with
another company, producing the same final product, but as one enterpreneurial entity

(variables will be marked with ) it becomes obvious. Let us suppose that at the beginning
there are one or more non-multibusiness companies. Its/their profit functions would be
   Qb  Pb  TCb  TC a ,5
whereas profit function of multibusiness company as an economic entity would be
  Qb  Pb  TCb  Qb  k  MCa   k  Qb  MCa  TC a  ,
5
(9)
(10)
We could assume that profit and cost functions of all firms on the market are the same because of the nature of
the perfectly competitive market.
which after some rearrangements could be written in the same way as (9). Difference between
(9) and (10) is in the division of profit between the particular parts of multibusiness company.
In the single company including both production of a and b revenues are divided according
to the factor (labour, capital) cost and those are fully covered by revenues, thus in perfect
competition profit equals zero.
If the transfer price was set on level of marginal cost of supplying division in the case
of multibusiness company, revenues would be divided differently from factor cost. This
situation would lead either to shifts and change of shape of production and cost functions or,
in case that managers realized that inefficiency to backward shifts in profit, compensating
wrong transfer price. All companies operate at the lowest possible average cost on the
perfectly competitive market, so that if managers of multibusiness company did not realize
the inefficiency, changes in the cost functions would lead to complete loss of competitiveness
in long run because of inability to acquire either enough capital or enough labor. If we
assumed that managers of multibusiness company arrange backward shifting of profit, we
would get to the same state as in equation (9), except the fact that shifting of profit is
connected with non-zero cost (thus again in long run multibusiness company would probably
lose ability to compete its rivals).
Under conditions of absence of market for intermediate product and perfectly
competitive market of final product we can say that transfer price at a level of marginal cost is
unstable and would earlier or later lead to cease of existence of multibusiness company.
If a market for intermediate good existed, but was not perfectly competitive, the
situation would be a bit more complicated, because the optimal level of a transfer price
depends among other factors upon characteristics of market of the final product. Transfer
price could fall within range of prices, which could also include marginal cost of intermediate
good production, without loss of competitiveness. Would each of those prices be also at level
ensuring efficient allocation of resources? We think it would not. Even in this case the best
solution for the multibusiness company is that one that equates marginal cost of production of
intermediate good and net marginal revenue.
MRb  MCb  k  MCa ,
(5)
If market for intermediate product were perfectly competitive, what would happen?
This is the only situation in which the rule

PT  MCa
is generally valid, because companies operate at lowest possible average cost, which are also
equal to marginal cost.
It is obvious that there has to be „something rotten in the Denmark“ either with
arguments underpining the opinion that optimal transfer price in world without taxes,
information asymmetry, agency cost, etc. should be set on the level of marginal cost or with
the other opinion stated above. We have to admit that our analysis is quite simplified, but we
consider it to be sufficient for our purposes. Crucial problem lies in implicit assumption,
which is built in equations (1) and (2) – that transfer price should remain constant for every
possible quantity of intermediate good a . If we wanted to explicitly state the problem of
dependence between cost, prices and quantity, we would have to rewrite (1) and (2).
 A Qa   Qa  PT Qa   TC A Qa  ,
(11)
 B Qb   Qb  Pb Qb   TC B Qb   Qb  k  PT Qa  ,
(12)
and
which is in fact implicitly understood when we write these equations without this dependency
expression, except the the fact that transfer price is a function of quantity too. The special case
of transfer price constant through its whole domain occurs only if market for intermediate
product is perfectly competitive. In that case both supplier A and consumer B can sell and buy
any quantity of intermediate product for a constant price. Now the question is how to set the
transfer price. Principles of profit maximization still hold (optimal quantity of intermediate
product is set at (10)), but we have to respect that transfer price could change. Then maximal
profit will be reached if derivatives of (11) and (12) are equal to zero
PT Qa   Qa 
PT Qa 
 MC A Qa   0 ,
Qa
(13)
Pb Qb   Qb 

Pb Qb 
P Q  
 MCB Qb   k   PT Qa   Qa  T a   0 .
Qb
Qa 

(14)
and
Because of
PT Qa 
(15)
Qa ,
the result is the same as if we optimized (1) and (2), except the assumption of constant
transfer price and optimum will be reached at
MRA Qa   PT Qa   Qa 
MRA Qa   NMR .
(16)
If transfer price was set ex ante by multibusiness company headquarters on the level of
marginal cost of supplying business, there would probably be only one Qa for which (16)
holds, which would not have to be neccessarilly the optimal quaintity

Qa .
If the transfer price was set upon negotiation between A and B , transfer price could
reflect shapes of cost and revenues curves of both companies A and B . There could be
several situations on which were discussed above:
1)
Market for the intermediate product is perfectly competitive, then PT
 
exogenous to examined multibusiness company and equal to MC A Qa

is

2)
Market for the intermediate product does not exist and market for the final
product is perfectly competitive. The only one price for which intermediate
product could be exchanged between A and B without lost of efficiency is
PT  AC A , based on equating (2) with non-multibusiness company’s profit
function (9)
3)
Market for the intermediate product does not exist and market for the final
product is not perfectly competitive (negative slope of demand curve).
Then PT  AC A is the lowest possible level for business A and the best
possible result of negotiation for B . Because of negotiation we can assume
that economic profit could be split between A and B , thus
PT  ACA ; ACA 
B   A
.
Qa
(17)
Transfer price higher than AC A could induce investments and innovations
in business A , which would be made if multibusiness company was one
entity.
4)
Market for intermediate good exists, but it is not perfectly competitive.
Optimal transfer price has to be higher than average variable cost AVC A in
short run and higher than average cost AC A in long run. Due to the
monopoly power A gets some profit from deliveries to external subjects
and it can share this profit with B . From the point of view of the selling
division (the best result of negotiation) would be efficient
Qa
 NMR dQ
a
PT 
0
Qa
(18)
,

which is nothing else than
PT   ARB  AC B   k .
(19)
The worst outcome of negotiation about transfer prices from this point of
view would be for the supplying company the state when the whole
economic profit is allocated to the buying company and PT  ACA . Again
transfer price could fall into range
PT  ACA ; ACA 
B   A
.
Qa
(17)
In this case the optimal quantity would be set upon equating marginal cost
of production of the intermediate product both to the net marginal revenue
and the marginal revenue from selling the intermediate product to
economic subjects outside multibusiness company.
We can consider these levels of transfer price as fully optimal under following
conditions (some of them were expressed in the beginning of this article)6:
1) no tax
2) no information asymmetry
3) managers can negotiate about transfer prices
4) no agency cost (there is no need to shift the profit to prevent managers from
private consumption on account of acompany).

Summing up the above conclusions, optimal quantity QA sold on the intracompany
market is set upon
 
 
 
MR B Q B  MC B Q B  k  MC a Q A
and the optimal transfer price should fall into range
6
Among other conditions is for instance inability of transfer prices to have signaling function. We seriously
doubt about the possibility of transfer price to have signaling function, as mentioned in (Göx, 1998), because
transfer prices are mostly not directly observable. Signaling function can have only variable that is directly
observable without any distortion to the recipient of the information.
PT  AC A ; AC A 

Qa
7
.
When the profit of multibusiness company is equal to zero, the optimal transfer price would
be at the level of the average cost of the supplying division. In the case supplying or buying
division has a monopoly power and can create economic profit, it is convenient not to use
transfer prices on the level of market transfer prices because (depending upon the type of
price discrimination used by the subject that has monopoly power) part or the whole buyer's
or seller's surplus can be usurped by the monopolist. Such a state could of course have bad
impact on intracompany relationships, morale and also on investments.
5
Conclusions
Both older and recent literature on transfer pricing are not unified about the opinion
whether the optimal transfer price should be equal to marginal cost of supplying company and
set by centralized decision (of a multibusiness company headquarters) or whether it should be
set by negotiation or even set on the level of market (arms-length) price. Those, who argue for
setting transfer price by negotiation or at the market price levels, base their arguments on
market imperfections like information asymmetry, motivation of managers, et cetera. We
have proved that the optimal transfer price should be equal to average cost of the supplying
division plus part (or the whole) of economic profit of the multibusiness company,
independent on the market conditions at the market of either intermediate or final product.
Every other way of setting transfer price is inefficient and would earlier or later lead to loss of
multibusiness company’s ability to compete its rivals. If market conditions allowed the
multibusiness company not to gain any economic profit, then optimal transfer price would
equal to average cost of supplying division. We base our conclusions on financial resources
deficiency that would occur if marginal cost were used. Although we have not explicitly
analysed influence of managerial incentives and agency cost in this article, we could state that
personal objectives of particular divisions’ managers would lead to the same conclusions as
we have come to.
In spite of the above stated, one of the basic conclusions stated in classic literature on
transfer pricing holds. That one is that optimal quantity of intracompany deliveries and
optimal transfer price is set upon equating the net marginal revenue of the buying division and
the marginal cost of the supplying division.
References
Dutta, Sunil – Anctil, Regina M.(1999): Negotiated Transfer Pricing and Divisional versus
Firm-Wide Performance Evaluation.
http://papers.ssrn.com/sol3/Delivery.cfm/99021113.pdf?abstractid=149771&mirid=2 .
January 1999.
Baldenius, T. – Melumad, Nahum D. – Reichelstein, Stefan J. (2004): Integrating
Managerial and Tax Objectives in Transfer Pricing. Accounting Review 79, no. 3, July 2004,
pp. 591-615.
Baldenius, T. - Reichelstein, Stefan J. (2004): External and Internal Pricing in
Multidivisional Firms.
7
All proofs of propositions needed for this conclusion are evident from the above stated text.
http://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID491662_code199489.pdf?abstractid=4916
62&mirid=1. 2004.
Dawson, Peter C. - Millet, Stephen, M. (2000): TRANSFER PRICING IN THE
DECENTRALIZED MULTINATIONAL CORPORATION.
http://www.econ.uconn.edu/working/2000-06.pdf. 2000.
Eatwell, J. – Milgate, M. – Newman, P. (1998): The New Palgrave A Dictionary of
Economics. Macmillan Reference Limited, 1998.
Gatti, James F. – Grinnell, D. Jacque – Jensen, Oscar W. (1997): Replicating a Free Market
for Internal Transactions: An Alternative Approach to Transfer Pricing. JOURNAL OF
BUSINESS & ECONOMIC STUDIES, Vol 3, No 2, 1997.
Göx, Robert F. (1998): Strategic Transfer Pricing, Absorption Costing and Vertical
Integration. Management Accounting Research, Vol. 11, No. 3, S. 327-348.
Hirschey, M. (2003): Managerial Economics. Thomson South-Western, 2003.
Hirshleifer, J. (1956): On the Economics of Transfer Pricing. Journal of Business, 172 –184.
1956.
Li, Jian (2005): International transfer pricing practices in New Zealand. University of
Auckland Business Review, Autumn 2005.
Lutter, M. – Scheffler, E. – Schneider, Uwe H. et al. (1998): Handbuch der
Konzernfinanzierung. Verlag Dr. Otto Schmidt KG. Köln, 1998.
Organisation for Economic Co-operation and Development (2001): Transfer Pricing
Guidelines for Multinational Enterprises and Tax Administrations. OECD, 2001.
Pappas, J. L. - Brigham, E. F. - Hirschey, M. (1983): Managerial Economics. Dryden Press.
Chicago, 1983.
Roun, V. (2003): Funkce předacích cen v podnikových uskupeních. University of Economics
in Prague. 2004. Dissertation work.
Schmallenbach, E. (1908): Über Verrechnungspreise. Zeitschrift für handelswissenschaftliche
Forschung 3, 1908/1909, pp. 165 – 185.
Soukup, J. (2003): Mikroekonomická analýza – vybrané kapitoly. Melandrium, 2003.
Shrnutí
Starší i novější literatura k transferovým cenám není jednotná v názoru na to, zda by
optimální transferová cena měla být rovna mezním nákladům dodávajícího podniku (v
koncernu) a určena centralizovaným rozhodnutím koncernové centrály nebo zda by měla být
stanovena na základě vyjednávání či dokonce na úrovni tržní ceny (dosažené při transakci
nepropojených subjektů). Ti, kteří argumentují pro optimální tržní cenu na základě
vyjednávání nebo na úrovni tržní ceny, zakládají svá tvrzení na tržních nedokonalostech jako
jsou informační asymetrie, motivace manažerů, atd. V tomto článku dokazujeme, že optimální
transferová cena by měla být rovna součtu průměrných nákladů dodávající divize a části
(nebo celého) ekonomického zisku koncernu, nezávisle na tržních podmínkách na trhu
meziproduktu i na trhu finálního produktu. Jakýkoliv jiný způsob stanovení transferové ceny
je neefektivní a dříve nebo později vede ke ztrátě konkurenceschopnosti. Transferové ceny
stanovené na základě vyjednávání dominují centralizovaně stanovené transferové ceny i
transferové ceny na úrovni tržních cen. Omezujícími podmínkami jsou: neexistence daní,
neexistence informační asymetrie, žádné agenturní náklady a konečně možnost vyjednávat o
transferových cenách.
Summary
Both older and recent literature on transfer pricing is not unified about the opinion
whether optimal transfer price should be equal to marginal cost of supplying company and set
by centralized decision (of multibusiness company headquarters) or whether it should be set
by negotiation or even set on level of market (arms-length) price. Those, who argue for setting
transfer price by negotiation or at the market price base their arguments on market
imperfections like information asymmetry, motivation of managers, et cetera. We prove that
optimal transfer price should be equal to average cost of the supplying division plus part (or
whole) economic profit of the multibusiness company, independent on the market conditions
at the market of either intermediate or final product. Every other way of setting transfer price
is inefficiend and would earlier or later lead to loss of multibusiness company’s ability to
compete its rivals. Transfer prices based on negotiation dominate centralized transfer price
setting and transfer prices on the level of the market prices. Limiting conditions under which
these conclusions are valid are: no taxes, no information asymetry, no agency cost and finally
possibility to negotiate on transfer prices.
Key words:transfer pricing; multibusiness company; average cost
JEL classification:D21, D29, G39