-16-
which, after carrying out the matrix multiplication, can be expressed as

x05 dd £2
(D'/Py)= (@egCi-m,) + eo) +
- a8 ot
+ (08n8 (y22m11 Yi2w21) + ®nj(viiH2i- Yaiaii))det(r) +

ad = -1
+ BB )(08n8 Cre2012 - Yi2w22) + one (yiiu22 - Y2iwi2) Jdet(l) . (26)

Accordingly, three factors determine the total price elasticity of
OPEC's oil exports. The first represents the substitution for alternative
energy sources. The second represents the income feedback effect of oil-
price changes in the absence of policy reactions. The third term captures
the income feedback effect on oil exports arising from policy reactions to
oil-price changes. :

Implicit in equation (26) is the assumption that OPEC knows with
certainty the policy reaction to an oil-price change. To relax this

assumption, suppose only two policy reactions are possible:
soe : : ad 5 : :
--restrictive policy reaction =(G [Pde <0, with probability p,

. : : ad 5 < : ae
--accommodative policy reaction=(G Pia 5% with probability (l-p),
with GB) < 8B).

or oa
Recognition of the uncertainty surrounding policy responses

suggests that the relevant notion of price elasticity is the expected total

price elasticity:

5(o) = 2(B°/B,) = K + {alo((@4/8.) - /B,),) + 7B), )KO, (27)


-10-

import manufactures from developed countries. This increase in OPEC's
imports raises real income in developed countries--and could offset the
direct negative effect. In turn, the stronger activity in developed
countries stimulates imports from developing countries, and thus affords a
higher volume of capital-goods imports and faster output growth in the
latter countries.

An increase in the price of manufactures, induced by higher oil
prices, has an ambiguous impact on the real income of developed countries.
On the one hand, it mitigates the initial deterioration in the terms of
trade, a process that reduces the real transfer to OPEC and thus raises the
real income of developed countries. On the other hand, the increase in Pa
reduces the purchasing power of export revenues of both OPEC and developing
countries with an adverse effect on the exports and GDP of developed
economies. For developing countries, the increase in Pa also has an
ambiguous impact on their real income. On the one hand, it reduces the
purchasing power of existing foreign exchange reserves with an adverse
effect on capital accumulation and output growth. On the other hand, it
stimulates exports of developing countries and thereby enlarges their

foreign exchange reserves.

The Sensitivity of Oil Price Effects to Alternative Parameter Values

On the whole, the above discussion suggests that whether an increase in oil
prices reduces real income or not depends, to a large extent, on the
relative strengths of the direct and indirect effects. For developed

economies, the direct effect of an oil-price increase--the transfer of real


-20-

through both OPEC's revenue recycling and markups on oil prices. The paper
characterizes the effects of oil-price changes using alternative values for
the recycling coefficient of OPEC (8) and for the markup on the price of
oil (r)).

The paper also examines the influence of the income feedback
effects of oil-price changes, as well as the induced policy reactions, on
the optimal price of oil. For this purpose, the model of oil-price effects
is combined with Hotelling's analysis of oil-price determination, and
incorporates unstable demand functions. The motivation for this analysis
stems from the possibility that increases in the price of oil might result
in a reduction of oil revenues if the potentially adverse effects on the
real income of oil importers is not taken into account. The centerpiece of
the analysis is the notion of the total price elasticity of OPEC exports,
which captures the influence of substitution effects, income effects, and
the policy reactions of oil importers in measuring the response of oil.
exports to an increase in the price of oil.

The characterization of strategies for determining optimal oil
prices relies on the behavior of the total price elasticity, which permits
us to establish a formal association between optimal oil prices and policy
stabilization in oil importers. We find that an increased likelihood of a
restrictive policy in response to oil-price increases raises the probability
of loss of oil revenues and thus reduces the optimal price of oil.

While the foregoing conclusions are intuitively plausible, they
are conditioned on a number of simplifying assumptions that need to be
relaxed in future research. First, a more general model of oil-price

effects should allow not only for international trade flows, but also for


Introduct:ion

The effects of increases in oil prices on the world economy have stimulated
research devoted to two concerns--namely, the macroeconomic consequences of
the oil price increases and the underlying factors determining oil prices.
To address the first of these concerns, most investigators have treated oil-
price changes as supply shocks in the context of a small, open oil-dependent
economy. In this framework, an increase in oil prices raises domestic
prices and reduces income and employment, provided oil and labor (and other
domestic factors) are not perfect substitutes for each other in production
Processes. Further analyses have examined the macroeconomic implications of

higher oil prices under alternative policy responses and wage indexation

L
schemes.

Although these analyses enhance our understanding of the effects

of supply shocks, their usefulness in predicting’ the macroeconomic effects

of ano price increase remains limited for several reasons. First, the
effects of oil price increases on a particular economy depend on the
repercussions of these increases on the rest of the world economv. For
example, the transfer of resources from oil -importers to the [countries of
the] Organization of Petroleum-Exporting Countries generated by an oil-price
hike is greatly diminished if OPEC increases its recycling of oil revenues
through an increase in imports. In addition, higher oil prices result in
higher export prices of industrialized countries with further implications
for the growth prospects of developing countries. Yet most analyses

do not incorporate these international linkages explicitly. Second, the
few studies that do consider these linkages give little or no attention to
the implications of higher oil prices for developing countries: therefore

the effects of higher oil prices on a significant portion of the world's

income and trade remain largely unexplained.


-17-

19 .
where K and a (a>0) are constants. As equation (27) indicates, the total
price elasticity ¢ is, in principle, related to both © and the structural
Parameters of the model. Because of our interest in the relationship

between stabilization policies and optimal oil price paths, we focus here on

the role played by p:
ag/ao = af (G/B) - (yp) <0,
or oa

which means that the (absolute) value of the total price elasticity
increases in response to an increase in p. Intuitively, increases in oil
prices reduce oil exports not only because of the associated income and
substitution effects, but also by the reduction in the expected real income
of oil importers that arises from the increased likelihood of a restrictive

fiscal policy.

Characterization of Optimal Pricing Strategies

The cotal price elasticity, equation (27), is a convenient way of
summarizing how the international transmission of oil-price effects feeds
back to the oil exports of OPEC. Our purpose now is to relate this price
elasticity to the determination of optimal oil prices. To this end, OPEC is
assumed to be a monopolist with constant extraction costs; it sets the price
of 011 to maximize the present value of expected future profits subiect to a
demand function and a resource constraint -° Under these circumstances, the
first-order conditions for profit maximization imply that marginal revenue,
m, grows over time at a rate equal to the discount rate, 6:

m, = 6 for all t.


-25-

OPEC is) reduced considerabl

y by the existence of the feedback effects of oil
price changes.

22 It is also possible to examine th
to changes in other parameters.

technological improvement that ra
elasticity et for isd, 2.

@ response of optimal oil prices
In particular, suppose there is a one-time
ises the (absolute) value of the price
Then the optimal response in oil prices is

-((-1/2" ye41-n y)/(141/¢)90 for ixa;
ap* /det = ° °
owe ~((-1/¢" y88)/(141/2) >0 for i=2,

A reduction in the e's (that is, an increase in their absolute value)
reduces the growth rate of optimal oil prices.


-19-
ot 2
aP 4/80 = ~{(-1/2¢ 9)” )Cae/ 80) }/ (141/50) ) < 05 (29)

the associated optimal oil prices are shown in Table 3 and depicted in
Figure 1. Equation (29) indicates that a once-and-for-all increase in the
probability of a restrictive fiscal policy reduces the (contemporaneous)
optimal growth rate of oil prices22 Intuitively, a higher p means a greater
probability that the oil-price increase will be followed by a restrictive
fiscal policy, reducing the real income of oil importers and exacerbating
the expected decline in oil exports and revenues. In effect, the increase
in p raises the probability that the total price elasticity will be less
than minus one implying that an increase in oil prices causes a decline in
oil revenues. Thus it is optimal for OPEC to lower the rate of increase in

oil prices.

Conclusions

The purpose of this paper has been to examine the interdependence between
the effects of changes in oil prices and OPEC's price strategies. The
analysis has relied on a highly specialized multicountry model, which allows
us to determine the channels through which oil-price changes are
internationally transmitted. Despite the relatively strong assumptions

of the model, the impact of an oil-price change on the real income of oil
importers cannot be predicted a priori without specific information about
their policy responses and about the values for structural parameters. The
ambiguity stems from the existence of offsetting effects. In particular, an
increase in oil prices is associated with both a direct effect (the transfer

of real resources to oil exporters) and indirect effects that operate


-14-

¥ < -Craz@ii- Yiz021)/(" Yoam2) »
then an increase in the price of oil and a restrictive fiscal policy reduce

real income of developed countries.

Oil Price Effects And OPEC'S Pricing Policy

The theory of depletion of nonrenewable resources (Hotelling, 1931, and
Dasgupta and Heal, 1979) states that a monopolist's optimal price strategy
should cause marginal profits to grow at the discount rate. An implicit
assumption is that the monopolist faces a stable demand function, which
implies that real income of oil importers can be taken as exogenously given
and therefore unaffected by changes in oil prices. But price changes affect
the real income of oil importers, especially given the possibility of
restrictive policy responses. As a result, the demand for oil shifts and
(if not taken into account in pricing decisions) could lower oil revenues. /®
Consequently, what matters for OPEC's price policy is the total price
elasticity as seen by OPEC, which takes into account the effects of
substitution, income feedbacks, and potential policy responses to an oil
price increase.

In this section we extend the classical analysis of optimal
pricing of nonrenewable resources to allow for the feedback effects of oil-
price changes. Recognition of the feedback effects implies that price
changes themselves shift the demand schedule in ways that are not
necessarily known in advance. We develop the notion of the total price
elasticity of oil demand, which measures the responsiveness of the demand

for oil to changes in oil prices allowing for the international transmission


trade account of the developing countries is in balance except for external

credits and aid, R. Finally, oil imports from OPEC, My in equation (10),

: . : 1
are determined as a function of the terms of trade and real income.

OPEC
The determination of OPEC's income is analogous to the case for
developing countries, The chief difference is that OPEC is assumed to
recycle a constant fraction 6 of export earnings to purchase manufactures
from developed economies, as indicated by equation (14). As development
policies in OPEC evolve, with a corresponding impact on absorption of oil
revenues, the assumption of a constant value for B appears to be a strong

one: it is used here to simplify the comparative-statics derivations. The

effects of relaxing it are studied below.

The International Transmission Of Oil Price Effects

Analytical Solution of the Model

Solving the model begins with totally differentiating the system of
equations (1) - (14); by using the equilibrium conditions (15)-(17), we

obtain a system of three differential equations!“

dd
Yur Ya2 Yu3 dy /Y M1, Wye dP /P

2k o-°
Ya. Yaz 23 qy'/Y = | 421 w22 (18)
Y31 32 33 ay°/y° 31 32 ac*/et

The elements of the matrix Phyl are

d did
Yue l-ecF+ (1-8)¢, us > 9,


-31-

REFERENCES

Behrman, J. 1972. Sectoral investment determination in a developing economy.
American Economic Review 62 (5):825-841.

Brayton, F., and Mauskopf, E. 1985. The MPS model of the United States
economy. Economic Modeling forthcoming.

Bruno, M., and Sachs, J. 1979. Macroeconomic adjustments with import price
shocks: Real and monetary aspects. The Maurice Falk Institute for
Research in Economics, Discussion Paper 793, Jerusalem, Israel.

Bruno, M., and Sachs, J. 1985. Economics of worldwide stagflation.
Cambridge: Harvard University Press.

Caprio, J., and Clark, P. 1983. Oil price shocks in a port folio-balance
model, Journal of Economics and Business 35 (2):221-233.

Cremer, J., and Weitzman, M. 1976. OPEC and the monopoly price of oil.
European Economic Review 8 (2):155-164.

Cukierman, A. 1983. Relative price variability and inflation: A survey and
further results. Paper prepared for the November 1982 Carnegie-
Rochester Conference on Public Policy.

Dasgupta P., and Heal, G. 1979. Economic Theory and Exhaustible Resources.
Oxford: Cambridge-Nisbet.

Dornbusch, R., and Fischer, S. 1980. Exchange rates and the current
account. American Economic Review 70 (5):960-971.

Findlay, R., and Rodriguez, C. 1977. Intermediate imports and macroeconomic
policy under flexible exchange rates. Canadian Journal of
Economics 10 (2):208-217.

Gray, L. 1914. Rent under the assumption of exhaustibility. Ouarterly
Journal of Economics 28 (2):466-489.

Hickman, B. 1983. Global International Economic Models. Amsterdam: North-
Holland.

Hnyilicza, E., and Pindyck, R. 1976. Pricing policies for a two-part
exhaustible resource cartel: The case of OPEC. European Economic
Review 8 (2):139-154.

Hotelling, H. 1931. The economics of exhaustible resources. Journal of
Political Economy 39 (2):137-175.

Krugman, P. 1983. Oil and the dollar. In Economic Interdependence and
Flexible Exchange Rates (J. Bhandari and B. Putnam, eds.)
Cambridge: MIT Press.

Marion, N., and Svensson, L. 1984, World equilibrium with oil price

increases: An intertemporal analysis. Oxford Economic Papers 36:
86-102.


-28-

Table 2

Effects of Oil Price Changes on Real Income:
Sensitivity with Respect to Parameter Changes

Developed Countries Developing Countries
T TM,
8 0 O<m <1 1 ) O<n <1 1
0 - t t - - -
0<B<1 - t + - - -
1 0 - - - - -

The signs shown in this table are obtained by evaluating equation (22) for
the case of developed countries and equation (23) for the case of developing
countries; for example, ¥ 7, = £(8=1, 1,0) = 0. 8 is the recycling
coefficient of OPEC and TM, is the markup on oil prices.


determined. In this context OPEC would face (in addition to the
intertemporal allocation problem) a tradeoff between exploiting the price
inelasticity of oil demand on the one hand, and avoiding the income feedback
effects on the other. In particular, if the price path is too low, then
OPEC is not exploiting the price inelasticity of oil demand and thus incurs
revenue losses. If the price path is too high, then the real income of oil
importers is adversely affected with a detrimental impact on OPEC's
revenues.

The purpose of this paper is to examine the effects of oil-price
changes and the determination of oil prices as one problem, by recognizing
that oil-price changes affect the real income of oil importers and that
changes in the real income of oil importers influence oil-price changes.

The next section presents a simple theoretical model of the world economy to
examine the different channels through which the effects of an exogenous
oil-price increase are internationally transmitted.

The focus of the next two sections is on the comparative statics
of an increase in the price of oil and on the sensitivity of the results to
changes in both parameter vdlues and policy reactions. We find that
increases in oil prices are not necessarily associated with losses in output
if one allows for the international repercussions of oil-price effects. The
following section contains a generalization of Hotelling's analysis of oil-
price determination to allow for the international transmission of oil price
effects. The main result is that Hotelling's r-percent rule remains valid
only in the extreme case in which oil-price changes have no feedback
effects. Moreover, recognition of these feedback effects allows a closer

examination of the influence of stabilization policies in developed


A third limitation of existing analyses is the assumption that oil
importers can be treated as small economies. This is a very convenient
assumption because it allows oil-price changes to be treated as exogenously
set by OPEC. However, this price-taking assumption is of limited
applicability to major oil importers. An increase in oil prices lowers
their real income and oil consumption, and thus OPEC's revenues, thereby
raising the question of why OPEC would increase oil prices. To assume that
oil price changes are exogenous presumes that these changes are optimal,
regardless of their consequences for oil producers. Thus the price shocks
postulated in earlier analyses need not be observed in reality as they may
be inconsistent with OPEC's pricing strategy.

In this regard, the large oil-price increases of the seventies
also renewed the interest in oil-price determinat ton. Typically, OPEC is
characterized as a monopolist determining oil prices in such a way as to
maximize the present value of future oil revenues, subject to a stable
demand function and to a resource constraint. To assume a stable demand
function amounts to assuming that real income--a demand determinant--can be
considered exogenous and thus unaffected by the changes in oil prices, an
assumption that stands opposed to the theoretical and empirical results. To
the extent that higher oil prices affect the real income of oil importers,
there is a feedback effect on the oil exports of OPEC, which should be
recognized in setting an optimal price path.

Earlier analyses of oil-price effects and oil-price determination
have proceeded in a dichotomous manner; what is assumed exogenous in one
kind of analysis is endogenous in the other, and vice-versa. A realistic

analysis should treat oil prices and economic activity as jointly


-15-

of cil-price effects. This notion of price elasticity is then used to

characterize optimal oil-pricing policies.

Total Price Elasticity of Oil Demand

The demand for oil that OPEC faces is

da
Ds M+
fo] oO

Accordingly, the total effect of an increase in the price of oil on D° is

° d & d da d gL QL g
= M
aD° /aP, (amt /aP, +3 ,/2P,) + (Cam§ /ay May" /aP,) + (aMy/ay")(a¥ /4P)),
where the First term on the right-hand side represents the substitution
effect and the second term represents the income feedback effect. This

total price effect can be expressed in elasticity form as

xo x ry g ~d~
(B°7B d= e881 yeore® + (o%n! n){ ee], (25)
fe) o0°o ° oo oo oo co}
YR
oO

1 io .
where 8 =M /D for i=d,2.
° °

Substitution of equation (19) into equation (25) yields

tO 7s _ did Qk
D 1? = ( ae, 1) + 9565) +

did gf%) Py22 -Yi2 11 42] ]1 -1
+(8 n° 8 'n’)
ad > |det(T)
oo 88 en Yh WZ, W22 C/P, ‘ ,


Exports of manufactures to both OPEC and developing countries are
described in more detail below. Here it is simply indicated that they
depend on the terms of trade and on the foreign exchange revenues of these
countries. Oil imports from OPEC, wt in equation (3), and primary-product
imports from developing countries, 4 in equation (4), depend on the terms
of trade and on the real income of developed countries. Finally, the price
of manufactures, Pa in equation (5), is assumed to be a linear markup of
average variable costs, as represented by the prices of primary products,

P_, and oil, P 3
P °

Non-OPEC Developing Countries

In developing countries, it is the scarcity of capital services, not of
aggregate demand, that limits output growth in these economies. Thus real
income of developing countries, ye in equation (6), is determined from the
supply side by using a production function with capital, x’, and fixed
labor, L*, as factors.” Equation (7) defines the capital stock as
accumulated net investment, 1’, which in turn depends on imports of capital
goods, at, from equation (8). This latter relation can be derived by
treating the economy-wide capital stock as an aggregate of a domestically
made component and a foreign-made component, as suggested by McKinnon (1964)
and Taylor (1979). 1°

Foreign exchange constraints may limit output growth in developing
countries In this model, those constraints apply to imports of
manufactures, we in equation (9). If they are binding, then imports of
manufactures will be limited, dampening capital accumulation and income
growth. These imports are financed by foreign exchange revenues (exports

plus aid), net of oil payments to opec}? This assumption implies that the


-21-

asset flows along with exchange rate determination. Similarly, the labor
market and the role of expectations need to be considered in greater detail.
Second, CPEC's interests extend beyond wealth maximization. Competing
models of OPEC behavior, and the implications for the interaction between
oil-price effects and oil-price determination, call for further analysis.
Finally, the model in this paper could be extended by relaxing the
assumption of only one producer in the oil market, and by recognizing that
OPEC is not a coherent decision making bloc. Further analyses that relax or
eliminate the assumptions made in this paper are certain to enhance our
understanding of the interaction of oil-price effects and oil-price

determination.


International Finance Discussion Papers

Number 256

July 1985

THE INTERNATIONAL TRANSMISSION OF OIL PRICE EFFECTS
AND OPEC'S PRICING POLICY

by

Jaime Marquez

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished materials)
should be cleared with the author or authors.


-8-

Consequently, the change in each region's real income can be expressed as a
function of changes in both oil prices and purchases by the governments of

. 5
developed countries}

djyd am
ay ri 9 M1 wp ap /P,
Lk °
dy’/Y = M21 22
im da (19)
ay°/y° Tali, 1 3, 32 dc /G

After carrying out the matrix multiplication indicated by (19),
the impact of an increase in the price of oil on the real income of

developed countries is

~dox + + + + + + ado~ <
YUP =(Cre2@11-Yizi21)* Y22012(6 /P,))/det(T) 5 0, (20)

where the tilde '~' over a variable denotes the percentage change cf that

variable (that is, x = dx/x). For developing countries this impact is
ak > + + - + - + ng >
Y/P (CY iW2i- Yow) ~ Yew 28 /P,) )/det(T 20. (21)

Equations (20) and (21) constitute the first set of results of this paper.
They reveal that the effect of an oil price increase on the real income of
oil importers cannot be predicted a priori, unless further assumptions about

the structural parameters and policy responses are provided. In this

regard, if fiscal policy does not respond to the change in oil prices, and


RRL
Yi2= 1-8) on 384 >0,

Yig= 0,
'

-idoidd
Yair -£ i) nogy <0,

2
Yo2= l+ ont 1 >0,

Yag= 0,
ss ddd
Y31= -F BB oonog, <0,
' LLL
Ys2= -F BB o,n3g5 <0,

Y33= lL.

The elements of the matrix ato! are

_ d 22 8 d,.d <

y= -Q/Y mt - BY (ay9,(1tej~n #4 (ite! )(1-n)) 5%
did
W12= G /Y >0,
" did dd d 2 g <
Wy = -£ i((R/Y Bem, + Ooh _(1+ ef, dato (te, -1)) 5 0,
W22= 0,
dd d ZX & <

wg i= F'DB(G gs (l-m (ite, tog (ite =m )) 5 0,

w32= 0,

where the following notation has been used:

gtatyy?, ntsc/otycamtyay'y, etzcp.jmtycamisap.),
Jj J J J Ij J J

2 i_yi : :
F'SOF/OK°, £'=9£/aK~, gay /y* for s,i=d,o,& and j=p,o,m.
An explicit solution to the equation system (18) requires inversion of the
matrix [, a task that is considerably simplified if this matrix is

partitioned as


-30-

Figure 1

Stabilization Policies and Optimal Oil Prices

t t + dt time

log(P%)

Poem 6 PS, = 68 Se =8

t t+ dt time

The top panel shows the time path of the probability of a restrictive policy
reaction to an oil price increase, p. The bottom panel shows the effect of
an increase in this probability on the optimal oil price path (expressed in
logs for simplicity). The actual price path depends on the relative
magnitudes of 6 and %; three paths are possible:

Path I: 6>6-%<O; Path II: 6>8-Z=0; Path III: §>8-2>0.


-29-

Table 3

Effect of a Permanent Increase in p on
the Optimal Growth Rate of Oil Prices

Probability
of Restrictive Optimal 0i1
Fiscal Policy Price Growth Rate Optimal 011 Price
Period e Po Ps
. Py 6
~ yk =p*
t-2 % 6 Po t-2 PS t-3o7TMP6 8)
tel . * =p*
%o 8 Po.t-1 Pot 2e7PC 8)
~> ~
- k= pk -
t P1* Py +dp 6> 6 Ge 0 pe PS tn1emcé t)
+! a =p*
tel at $ rote PeeorPC 8)

Optimal oil prices could increase, remain constant, or decline following an
increase in p. The effect of an increase in p on optimal oil prices depends
on the relationship between the discount rate, 6, and the rate of change of

the total price elasticity, t

B20 ae 6 2 (1/6 0)" )(ae/ 99)/ (141/ eC 0) )-


countries on optimal pricing strategies. Our main result is that optimal
oil prices decline in response to a restrictive policy stance. Finally, the

last section contains our conclusions.

A Theoretical Model Of Oil Price Effects

The world economy is divided into three country blocs: developed economies;
oil-producing countries, OPEC; and non-OPEC developing countries. These
country blocs export manufactures, oil, and primary products respectively.
Financial asset holdings and nominal exchange rates are not modeled.
Income is determined by demand in developed countries and by supply in both

: : 6 :
developing countries and OPEC. The structure of the model appears in

Table 1.

Developed Economies

The real income of developed countries, y4, is determined from the demand
side in equation (1), implying a situation of excess capacity in these’
countries. There are three demand components: private absorption, c4cy4);
an exogenously given level of government purchases, of; and the trade
account, 34 from equation (2), Without financial assets the trade account
equals the balance of payments; capital movements compensate for the flow of
goods (Dornbusch and Fischer 1980 determine capital movements in a similar
way). The trade balance is expressed in terms of manufactures, and thus the
model incorporates the terms-of-trade effect of changes in oil prices,
because oil imports are valued in terms of the manufactured goods needed to

pay for them.


-18-

Since marginal revenue is defined as

m= Py (1 + 1/2¢)),

logarithmic differentiation results in

8 =m, = P+ (d(141/6(0))/dt )/(141/ 600) ),

ae
which yields the optimal growth rate of oil prices, Pot?

BY = § - {a(141/e( 0) )/dt }/ (141/ eC p) )s (28)

Pot

As equation (28) reveals, the optimal growth rate for oil prices
is anchored to the discount rate, but departures from this rate are allowed
as a response to changing market conditions arising from income effects and
stabilization policies in oil importers. Specifically, if the total price
elasticity is constant over time--that is, there are no feedback effects——
then om = §, which is Hotelling's r-percent rule. In addition, declines in
oil prices are consistent with Hotelling's analysis of nonrenewable
resources, provided changes in the price elasticity exceed the discount
rate?! Intuitively, oil prices could decline if favorable market conditions,
such as strong growth in oil importers, were no longer present. Finally,
optimal oil prices depend on stabilization policies in developed countries
because of the association between ¢ and p, ¢(p)

To examine this dependence further, assume that all parameters
remain constant over time except p, which experiences a once-and-for-all
increase at time t. The resulting impact on the optimal growth rate of oil

prices is


-26-
Table 1

Theoretical Model of a Three Region World Economy

Developed Countries

vis cfcxty + ott Bf ql)
d_ id d d

Be= Xo - ((2,/PMGt (2 /P OM) (2)
d_ id d

Mo Mi(Po/P ae Y) (3)
d_ yd d

My 4 (P/F Y) (4)
rt TP ot mW, (5)

Non-OPEC Developing Countries

y's ex’, 2) (6)
Kes x, +t @)
& &

I= ig + iM) (8)
& 2 g

Mo (R + POX - POMS) /P a (9)
2 8 &

Mo My (PQ/Pa» Y’) (10)
OPEC

¥°= F(K°) q.)

R= KO, + 1° (12)
1° bo +b ” a3)
oO. Oo

Mo BP OX/P a (14)

Equilibrium Conditions

d_.o 2
xn Mat My (15)
Oo 4d, ik
Xo Mot MS (16)
xis re (17)


THE INTERNATIONAL TRANSMISSION OF OIL-PRICE EFFECTS AND
OPEC'S PRICING POLICY

Jaime Marquez

International Finance Division
Federal Reserve Board
Washington DC 20551

February 1985 .
(revised)

Analyses of oil-price effects generally maintain. the assumption that oil-
importers can be treated as small economies, which allows oil-price changes
to be treated as exogenously set by OPEC. Analyses of oil-price
determination rely on the assumption that the demand for oil is a stable
function, which implies that real income of oil-importers is unaffected by
oil-price changes. Our analysis treats oil prices and economic activity as
jointly determined. The effects of exogenous oil-price changes are studied
in a simple theoretical world model. Hotelling's analysis is generalized to
allow for both oil-price feedback effects and stabilization policies.

This paper is based on my dissertation at the University of Pennsylvania. T
am grateful to F. Gerard Adams, Lawrence Klein, Peter Pauly, Wilfred Ethier,
Geoffrey Heal, Albert Ando, Kenneth Rogoff, Peter Hooper, Thomas Glaessner,
Brian Pinto, Erling Vardal, and David Germany for their comments and
criticisms. This paper was presented at the Fifth World Congress of The
Econometric Society. Two anonymous referees and the editor made a number of
useful comments and suggested several extensions on several drafts of this
paper. I am also grateful to Mendelle Berenson, whose editing made this
Paper more readable. Any remaining errors are my own. This paper
represents the views of the author and should not he interpreted as
reflecting the views of the Board of Governors of the Federal Reserve System
or other members of its staff.


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income to OPEC——could be offset by the associated indirect effects--namely,
increases in the price of manufactures and the recycling activities of OPEC.
For developing countries, the strong and adverse direct effect--the increase
in the real ofl bill--could be aggravated by the associated increases in the
price of manufactures, despite the beneficial effects associated with OPEC's
recycling activities. In practice, whether the direct effects dominate the
indirect effects depends on the relative magnitudes of key parameters such
as the markup on oil prices, OPEC's recycling coefficient, demand price
elasticities, and economic policy reactions.

Consequently, we examine the sensitivity of the comparative-static
results for equations (22) and (23) with respect to changes in the values of
1%) and 8. The results are summarized in Table 2. For developed economies,
an increase in oil prices reduces real income if there is no markup in oil
prices (1,0) and if the value of the recycling coefficient is less than one
(B<1). In this case, the transfer of resources to OPEC is not fully
recycled back to developed countries, and the value of this transfer is not
deflated away since the price of manufactures does not change. If OPEC
recycles all of its export revenues by importing manufactures from developed
countries (8=1), then oil-price increases do not affect the real income of
the latter countries. In this case, the increase in the value of oil
imports of developed countries (expressed in manufactures) is exactly
matched by an increase in their exports of manufactures to OPEC, and thus
the trade account is unaffected.

If the markup 1% is positive, then an increase in oil prices
raises the export price of manufactures with an ambiguous impact on the GDP

of developed countries:


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the consequences of relaxing such an assumption, suppose that fiscal policy

responds to oil price shocks inasmuch as these shocks affect P 16
m

xd + xd ~ ~ SN
G/P = (G /P_)(P /P_),
° mo mo
If the fiscal policy response to changes in P is equal to vo,
m

. d .
then the impact on Y of a change in in is equal to
oe
Y/PQ= (Cv2211> Yizw21) + Ya2buiam, )/det(l)
ad x xd
= (Y IP) G=0) + Ya2vujam/det(T). (24)

Thus the overall impact of a change in oil prices on the real income of
developed countries can be decomposed into two terms. The first term--
derived earlier as equation (22)--represents the impact of an oil-price
change on real income assuming that fiscal policy does not respond to such
a price change. The second term captures the direct and indirect effects on
domestic output of the fiscal-policy response. The direct effect is the
recessionary impact of a reduction in government purchases in a closed
economy. The indirect effects stem from the impact of fiscal-policy changes
on the imports of developed countries from both OPEC and developing
countries with the subsequent feedback to exports and income of developed
countries,

Equation (24) indicates that a restrictive fiscal policy could
offset any positive impact of oil price increases on the income of developed
countries (if the first term of the equation were positive). In particular,

if


TO THE MEMORY OF

RAY LUBITZ


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statistical and theoretical evidence points to a relationship between .
relative price changes (a change in 011 prices) and the overall inflation
rate (Cukierman 1983).

7 Fiscal policy may try to stabilize output instead of mitigating

increases in prices. If this is the case, then one possible policy reaction
would be

o=((y22wi1 - yiawai) + y2zwi2(c4/P,)), or

(64/P,)= ~ (yzzwin - yi2w21)/Cy22012).

For an empirical implementation of policy reactions using optimal control,
see Marquez (1983).

18 This result has been verified empirically (in a dynamic context)
by applying optimal control to a 3x3 medium size econometric model for the
world economy; see Marquez (1983).

19 The values of K and a are

K

dd 2k
(eeS(1-m,) + @e5) +

+

-1
(e4nd¢y22wii ~ yi2w21) + oene (yi iw2i- y2iwil)}det(T) , and

-1
az(e’n?(y22wi2 - yi2w22) + ene (yi1w22 - y2lwi2))det(T) ,
oO oo .

20 There are many other factors that influence OPEC's pricing
decisions. First, the structure of the international oil market as
reflected in the internal structure of OPEC and the appearance of non-OPEC
oil suppliers clearly complicate the derivation of a single path for oil
prices as indicated by Salant(1982), Newberry (1981), and Hnyilicza and
Pindyck (1976). A second consideration influencing oil prices is the cost
of extraction. As pointed out by Pindyck (1978), this cost is affected by
the returns to scale, which have an impact on the rate of extraction and
thus on oil prices. However, all these analyses presume the existence of
either a stable demand function or one that shifts at an exogenously given
rate. In other words, OPEC is assumed to ignore the possibility of a shift
in the demand for oil induced by the oil-price change.

21 One of the first analyses showing that optimal oil prices could
actually decline is that of Pindyck (1978). His empirical findings are
supported by our analysis. In addition to the factors mentioned above, the
total price elasticity is likely to increase over time in response to oil-
price hikes because of supply-and-demand adjustments. These dynamic
adjustments have been omitted from the paper because of the complexity
involved in incorporating them in this analysis (for example one would need
to couple a dynamic optimization model for oil consumers and a limit pricing
model for OPEC with the model of table 1, which is already highly

stylized). Increases in the total price elasticity arising from these
dynamic adjustments clearly limit OPEC's ability to increase oil prices in
the long run. What the results in the paper indicate is that even if these
long run adjustments were not possible, the scope for oil price increases by


Abstract

Analysis of oil-price effects generally maintain the assumption
that oil-importers can be treated as small economies, which allows oil-
price changes to be treated as exogenously set by OPEC. Analyses of oil-
price determination rely on the assumption that the demand for oil is a
stable function, which implies that real income of oil importers is
unaffected by oil-price changes. Our analysis treats oil prices and
economic activity as jointly determined. The effects of exogenous oil-
price changes are studied in a simple theoretical world model.
Hotelling's analysis is generalized to allow for both oil-price feedback

effects and stabilization policies.


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Marion, N., and Svensson, L. 1983. Structural differences and macroeconomic
adjustment to oil price increases. National Bureau of Economic
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Philadelphia: University of Pennsylvania.

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Table 1 (cont.)

Notation
Variables Superscripts Subscripts
M= imports 2= Non-OPEC LDCs o= oil
K= capital o= OPEC p= vaw materials
L= labor d= DCs m= manufactures.
Y= GDP
P= prices

I= investment

B= trade account

G= government purchases
X= exports

R= Resource transfers
C= absorption

Parameters

He GDP share of imports of commodity i in country j.
Lie
8"

oil import share of country i in total world oil trade.

nis income elasticity of imports by country j of commodity i.

= ratio of country i's income to country j's income.
B = OPEC's recycling coefficient
i

ej price elasticity of imports by country j of commodity i.
1
8

= sensitivity of developing countries' investment to manufacture
imports.
b = sensitivity of OPEC's investment to manufacture imports.
a,= markup on the price of commodity i.

cfs marginal propensity to spend.

Exogenous Variables
Oil prices, PB primary product prices, P_; government purchases by
developed countries, G ; aid to developing countries, R; employment in
developing countries, L.

Endogenous Variables a 2
Real income in each of the three reetege (vY, y°, Y); imports of oil by

developed and developing countries, (4, > My ); imports of manufactures by
OPEC and developing countries, oe > a's imports of primary products by
developed countries, M3; capital “accumulation in OPEC and developing
countries, (1° r- 4, trade account of developed countries, B ; export price
of manufactures, Py


if oil imports are price inelastic, then the income effect of an increase in

the price of oil is

Pt: Bad + - + = \, >

Y/Po= (rezmi1- vizwei)/det(T) 20 , . (22)
and

ah o~ + > -

¥/Po= (yirw2i7 Yarwii)/det(T) < 0. (23)

Thus, as equations (22) and (23) indicate, in the absence of a fiscal-policy
response by developed countries, an increase in oil prices lowers the real
income of developing countries, but a definite conclusion cannot be obtained

for developed countries.

The International Transmission of Oil Price Effects
The ambiguity of the income effects of oil-price changes, as indicated by
equations (20) and (21), is due to the existence of direct and indirect
effects that tend to offset each other. Specifically, the direct effect of
an oil price hike is the transfer of real income fron oil importing
countries to OPEC. In the case of the developed countries, this direct
effect takes the form of a deterioration of the real balance of Payments,
given the increased cost of oil imports in terms of manufactured goods. In
the case of developing countries, the transfer takes the form of reduced
availability of foreign exchange, with subsequent indirect dynamic effects
on output growth through the influence on imports of capital goods and
investment.

The indirect effects of oil-price changes stem from both recycling
by OPEC and changes in the price of manufactures. An increase in oil prices

raises the oil revenues of OPEC, which in turn recycles a fraction 8 to


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~ >
(aci4/B )/an, ) = (8) (0.

This outcome arises because increases in Pa have an ambiguous impact on the
trade account of developed countries. If, however, OPEC recycles all of
its export revenues, then an increase in the markup on oil prices does
reduce exports and real income of developed countries and of their real
income--that is, 0( 8=1)<0.

In contrast to the case of developed economies, oil price
increases reduce the GDP of developing countries for all values of 8 and TM
between zero and one. Furthermore, increases in the markup

parameter 1%, aggravate the already adverse effects of an oil-price

increase:
(a@/8 y/ an, ) <0 for B € [0,1].

This result is reasonable because a higher aarkup means that higher oil
prices will be associated with even greater increases in the price of
manufactures, reducing further the real foreign exchange reserves of
developing countries and dampening their capital accumulation and output
growth. These adverse effects could be partly offset by an increase in
OPEC's recycling coefficient, 8. A higher 8 raises the real income of
developed countries and stimulates exports of developing countries,
allowing faster capital accumulation and output growth in the latter.
However, as the negative entries in Table 2 indicate, any export gains of
developing countries arising from an increase in OPEC's recycling are more

than offset by the increase in their real oil bill.

O11 Price Effects And Stabilization Policies
The preceding analysis is simplified by the assumption that government

purchases (6) do not respond to changes in oil prices. In order to examine