OPEC, rationality, and the macroeconomy

JON HARKNESS Queen’s University

OPEC, Rationality, and the Macroeconom y* This paper builds a simple two-nation macro-model which includes a large manufacturing economy, such as the OECD and OPEC. Its distinguishing feature is that OPEC is a revenue-maximizing cartel who exploits the imperfectly elastic oil demand curve emerging from the rest of the world’s use of imported oil as an intermediate good. Unlike the case of a small open economy facing OPEC, the large open economy is found to have a vertical aggregate supply curve. Consequently, anticipated macro-policies have no effect on real GNP. Moreover, micro-policies which induce the adoption of oil-saving technologies are also found to be neutral.

By now, the macroeconomic implications of exogenous oil shocks well understood [see, for example, Bhandari and Turnovsky (1982), Bruno and Sachs (1979), Djajic (1980), Dornbusch (1979), Findlay and Rodriguez (1977), Harkness (1982), and Schmid (1976; 1980)]. Less well understood is how OPEC’s willingness to exercise her market power has fundamentally altered the macro-structure of the oil-using countries. Presumably, OPEC’s pricing policies are neither arbitrary nor capricious but, rather, derive from her rational exploitation of market power. Clearly, OPEC’s economically rational price is not independent of the oil demand she faces nor, therefore, of the state of the oil-importing economies. In short, the world economy should no longer be modeled as though oil’s price were exogenous. This must have implications for the structure of the oil-importing economies and, therefore, for their conduct of macro-policy. Of course, regardless of OPEC’s pricing policy, oil’s price will still be exogenous to a small open economy. It will not, however, for large economies such as the U.S., EEC, or OECD. This paper builds a simple two-nation macro-model which includes a large manufacturing economy and OPEC. Its distinguishing feature is that OPEC is a revenue-maximizing cartel who exploits the imperfectly elastic oil demand curve emerging from the

are

*I

thank

Journal Copyright

two

anonymous

of Macroeconomics, 0

1986

by Wayne

referees.

Fall 1985, Vol. State University

7, No. 4, pp. Press.

567-576

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Jon Harkness rest of the worlds use of imported oil as an intermediate good. Section 1 presents the basic model and its solution for world and OPEC real GNP. Unlike the case of a small open economy facing OPEC, the large open economy is found to have a vertical aggregate supply curve. Consequently, anticipated macro-policies have no effect on real GNP. Moreover, micro-policies which induce the adoption of oil-saving technologies are also found to be neutral. Section 2 determines equilibrium prices. Conclusions follow in Section 3.

1. The Model Consider a simple two-good, two-nation world with complete specialization in production. For concreteness, call the two economies OECD and OPEC. OECD is competitively organized and produces only manufactures, using nontraded labor and oil as variable inputs. In fact, OECD is a composite economy comprising all oil-using nations, among whom purchasing power parity is assumed to hold. On the other hand, OPEC is organized as a revenue-maximizing cartel which produces only oil. Everywhere, oil is strictly an intermediate good so that the world’s only final good is manufactures. Define the following OECD magnitudes: 9 = manufacturing output; Q = real GNP; N (H) = employment of labor (oil); P (R) = price of manufactures (oil); T = R/P = oil’s real price; w = real wage rate. Where necessary, an asterisk (*) denotes the corresponding OPEC magnitude. A “real” variable is one valued in terms of manufactures (i.e., final goods). Manufactures are produced using well-behaved aggregate technology, where the productivity of inputs is subject to random shocks. Thus. 9 = f(aN, PW,

fi, Jj, - fii > 0,

for all i, but i # j,

where, (Y and p are shift parameters representing, respectively, bor-augmenting and oil-augmenting productivity shocks. Given competitive firms, input demands are determined 568

(1) laby

OPEC, Rationality the usual marginal

productivity

and the Macroeconomy

conditions:

In addition, for the usual reasons, let labor supply related to the real (consumption) wage so that N” = N”(w),

N; > 0.

be positively

(3)

Lastly, consider OECD’s real GNP. This is simply her real value-added or, equivalently, gross manufacturing output net of her real oil-import bill. Of course, since OPEC produces only oil, all of which she exports to OECD, her real GNP, Q*, and OECD’s real import bill are identical. Thus, Q=q-TH=q-Q*

(4)

This implies that world real GNP is gross manufacturing output, q. Letting the labor market clear, the above expressions can be solved for world, OECD and OPEC real GNPs as well as for oil demand. The Appendix shows that such solutions take the form:

4 = qb, t),

H = Ma, t)/P, Q* = Q*(a, t),

41,

-92

’

0;

hl, -h, > 0; QT>O,Q$=?;

(5)

where, t = T/p is oil’s efficiency-adjusted real price. Of course, the function hp)/P corresponds to the usual notion of a factor demand when there are two variable inputs. It gives the profit-maximizing use of oil given that labor has been optimally chosen. Explanation of these functions is straightforward once it is noted that: (a) with well-behaved technology (i.e., fie > 0), labor and oil must be gross complements, and (b) t = T/P is the real price of oil’s services where, clearly, H barrels of oil yield an oil input of PH efficiency (or service) units. First, for the usual reasons, a hike

Jon Harkness in oil’s real price, T or t, reduces oil use and, via gross complementarity, employment. Hence, both world and OECD real GNP fall. But OPEC’s real GNP, Q * = TH, will also fall if and only if oil demand is own-price elastic. Second, via gross complementarity, a labor-augmenting productivity shock, cy, raises oil use and, thereby, OPEC real GNP. More productive labor and higher oil use together imply a rise in both world and OECD real GNP. Lastly, for much the same reasons, an oil-augmenting productivity shock, B, also raises world and OECD real GNP. It does so by essentially lowering the efficiency-adjusted real price of oil, t = T/P. But such a productivity shock has an ambiguous impact on oil use and therefore on OPEC real GNP. On the one hand, H tends to fall because a barrel of oil is now more productive while its real price, T, is fixed. On the other hand, gross complementarity implies an accompanying rise in labor’s marginal product and thereby in labor demand which drives up the real wage. This wage hike may then cause sufficient (net) substitution in favor of oil that, on balance, oil use rises rather than falls.’ The usual textbook notion of aggregate supply considers the own-price response of real GNP when all input markets clear. Then, since t = T/j3 = R/P/3, one might view the function Qt) as the OECD aggregate supply curve. For a given nominal oil price, R, this curve is upward-sloping. Clearly, a hike in R (P) would lower (raise) real GNP. This is the source of the stagflationary effect of an oil shock in most models. It also implies that the OECD authorities could “inflate away” the recessionary effect of an exogenous oil-price hike. This view of aggregate supply would be appropriate, however, only when oil’s price can legitimately be treated as exogenous to OECD. Nevertheless, suppose OPEC were a revenue-maximizer. Then, oil’s price would not be exogenous. It would depend on world (i.e., OECD) oil demand. This fact must be considered when constructing the OECD aggregate supply function. To maximize her revenue, OPEC would choose that price at which oil demand is unit-price-elastic. Clearly, this elasticity will be a function with arguments identical to those entering oil demand. For simplicity, assume technology has constant elasticity of substitution while labor supply has constant wage elasticity. With

‘Note, however, unequivocally falls

570

that demand for oil measured with a rise in oil’s efficiency-adjusted

in efficiency price,

units, PH t = T/p.

=

hc),

OPEC, Rationality

and the Macroeconomy

this additional simplifying structure, the Appendix own-price elasticity of oil demand is

rl = Tb> t),

rll

=

?,

12

>

0,

shows that the

(6)

where, -q = -(R/H)(dH/dR) = -(t/PH)h,.2 Now, let 9 be unity and invert Equation (6). Then, if OPEC is maximizing her revenue (i.e., GNP), oil’s efficiency-adjusted real price will be

t = g(d

g’ = ?,

(7)

where, g’ = -qi/q2, and t = T/B. OPEC’s strategy would be simply to set oil’s nominal price (or its quantity) so as to produce the efficiency-adjusted real price indicated by expression (7). Moreover, because oil demand depends only on real magnitudes, such a strategy turns out to maximize OPEC’s nominal and her real GNP.3 Combining Equations (5) and (7) produces

Q = Gb),

G’ > 0,

Q* = F(4,

F’ > 0,

(8)

as shown in the Appendix. The first expression in system (8) is the OECD aggregate supply curve. It is vertical. Further, given purchasing power parity among all nations, each member of OECD must also have a vertical aggregate supply curve. OPEC acts so as fully to index oil’s price to final prices. Thus, no nation’s authority could, by manipulating domestic (i.e., own-currency) manufacturing prices, alter oil’s worldwide real price.4 In short, demand management policies would be neutral in every nation. Both for OECD and for OPEC, real GNP simply depends on the productivity of labor in manufacturing. An improvement in la‘When OECD also produces oil (or some substitute energy source), the price elasticity faced by OPEC will depend on the total elasticity, q, and on OPEC’s share of total oil production, as shown by Ott and Tatom (1982). My model does not consider this complication. ?hus, although OPEC was assumed to maximize nominal revenue, I could just as easily begin by assuming she maximizes her real GNP. ‘Clearly, in the absence of purchasing power parity among nations, no economy’s aggregate supply curve would necessarily be vertical.

571

Jon Harkness bor productivity, (Y, would raise OECD real GNP, essentially for the reasons noted above. This improvement in real GNP could be moderated but not reversed, since, according to expression (7), OPEC night also be induced to raise oil’s real price. On the other hand, a hike in oil’s productivity, p, does not &ect OECD (or OPEC or world) real GNP. This is a somewhat curious result.’ Of course, ceteris paribus, such a productivity improvement would, by lowering t, raise OECD real GNP. But, according to Equation (7), it would also induce OPEC to jack up oil’s real price. This oil-price hike will be sufficient that, on balance, OECD real GNP is unaltered. Thus, OECD’s attempts to shield herself from OPEC by adopting oil-saving technologies are self-defeating. Presumably, this would also be true for a sufficiently large individual member of OECD, such as the U.S.

2. Equilibrium

Prices

The demand side of OECD is simply a Fleming-Mundell model of a large open economy. First, financial capital is perfectly mobile among nations with the world nominal interest rate being determined in the large OECD capital market. Second, expectations are rational. Along with prior results, this implies identity between the ex ante real and the nominal interest rates in all nations, including OPEC.” The OECD IS and LM curves would then be, respectively,

Q = D(Q, i) + X(Q*, i) - Q*> M/P = L(q, i),

D1,

x,

>

0,

D21

L1 > 0, L2 < 0,

x2

<

0,

(9)

where, i is the interest rate and q = Q + Q* is world real GNP. Since OECD comprises many nations, all linked by purchasing power parity, her nominal money stock, M, and price level, P, may be denominated in any arbitrarily chosen currency. The IS curve is just demand for OECD value-added, where D (X) is OECD (OPEC) d emand for manufactures. Such demands ‘Of course, this “curious result” stems from the fact that, in Equation (l), ef ficiency units are assumed to be the simple product, f3H. qhis follows from the fact that the model is static and deterministic. Moreover while real and nominal interest rates would differ, the monetary growth rate cqd be nonzero without materially altering my results.

572

OPEC, Rationality

and the Macroeconomy

depend, conventionally, upon the relevant nation’s real GNP and interest rate. Clearly, X - Q* is the real trade balance, since OPEC’s demand for manufactures is OECD exports while OPEC’s GNP is OECD imports. The LM curve is conventional except that money demand depends on world, not on OECD, GNP to allow the possibility that OECD currencies are held in OPEC portfolios.’ Solving IS and LM yields the aggregate demand function

Q = E(MIP, Q*, 4,

El, -Es

Es > 0,

(10)

where d is a shift parameter capturing the effects of exogenous elements of aggregate demand, such as fiscal policy. Conventionally, the aggregate demand curve is negatively-sloped and is raised by expansionary monetary or fiscal policy. But, aggregate demand falls with a hike in OPEC’s real GNP. This can be seen from the IS curve where the impact of Q* on the trade balance and, therefore, on aggregate demand is (X, - 1) = -MPS* < 0, where MPS* is, essentially, OPEC’s marginal propensity to save. Letting the goods market clear, the Appendix uses the vertical aggregate supply curve and the negatively-sloped aggregate demand curve to derive the OECD price level as P = P(M, d, u),

PI, Ps, -Ps > 0.

(11)

First, expansionary monetary or fiscal policies raise aggregate demand and, thereby, prices; otherwise, they are neutral.’ Second, a hike in labor productivity, (Y, raises aggregate supply and, by raising OPEC’s real GNP, reduces aggregate demand. Consequently, it raises real GNP while lowering prices. Third, a hike in oil productivity, B, has no effect either on real GNP nor, thereby, on prices.

3. Conclusions My model has nothing to say about oil shocks. When OPEC is a revenue-maximizer, such shocks will not occur except from ‘This specification of money demand is used solely for the sake of generality and is immaterial here. However, as Scarth (1979) shows, it would not be immaterial if OECD were small. *I am not suggesting that policies are coordinated among nations. Any individual large nation would, by using domestic monetary or fiscal policy, alter the OECDwide value of M or d.

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Jon Harkness noneconomic causes. Observed oil-price changes would merely be endogenous responses to shocks originating in the oil-using nations. For a large economy, monetary and fiscal policies are neutral. Further, a micro-policy to stimulate oil-saving technology is also neutral. Lastly, with purchasing power parity, it has been appropriate to infer that results derived for the oil-using group of nations also obtain in a suillciently large individual open economy. But, this would not necessarily be the case in a more general model where the manufacturers of various oil-using nations are not perfectly substitutable one for the other.’ Received: August 198.3 Final version received: April

1985

References Bhandari, J.S., and S. J. Turnovsky. “Materials Price Increases and Aggregate Adjustment in an Open Economy.” Mimeo (February 1980). Bruno, M. and J. Sachs. “Macroeconomic Adjustment with Import Shocks: Real and Monetary Aspects.” Working Paper 340, National Bureau of Economic Research (April 1979). Djajic, S. “Intermediate Inputs and International Trade: An Analysis of the Real and Monetary Aspects of an Oil Price Shock.” Working Paper 394, Queen’s University (June 1980). Dornbusch, It. “Relative Prices, Employment and the Trade Balance in a Model with Intermediate Goods.” Mimeo, IPEA/INPES, Rio de Janiero (1979). Findlay, R., and C.A. Rodriguez. “Intermediate Imports and Macroeconomic Policy Under Flexible Exchange Rates.” Canadian Journal of Economics 10 (May 1977): 208-217. Harkness, J. “Intermediate Imports, Expectations and Stochastic Equilibrium under Flexible Exchange Rates.” Canadian Journal of Economics 15 (February 1982): 118-42. Ott, M., and J.A. Tatom. “Are There Adverse Inflation Effects Associated with Natural Gas Decontrol?’ Contemporary Policy Issues 1 (October 1982): 36-44. ‘Nevertheless, even effectiveness of demand ficiently large economy

574

without purchasing power parity, my results suggest the management policies might be severely limited in a sufsuch as, say, the U.S.

OPEC, Rationality

and the Macroeconomy

Scarth, W.M. “Real Disturbances, Perfect Capital Mobility and Exchange Rate Policy.” Canadian Journal of Economics 12 (February 1979): 93-100. Schmid, M. “A Model of Trade in Money, Goods and Factors.” Journal of International Economics 6 (November 1976): 347-61. -. “Keynesian and Monetarist Analysis of Oil Price Shocks.” Paper presented at the Konstanz Seminar on Monetary Theory and Monetary Policy, June 1979.

Appendix For simplicity, assume technology exhibits constant returns in N and H and define the positive magnitudes: k = wN/q = labor’s share; h = PH = quantity of oil measured in efficiency units; t = T/R = efficiency-adjusted real oil price; E = wage-elasticity of labor supply; q = own-price-elasticity of oil demand; and u = elasticity of substitution.” Then, in system (5), 9 = [(l - k) E + al/k; h, = -qH/T Q2 = -h(l

< 0;

Q1 =

+ E) < 0;

Q*2 = h(1 - q) = ?;

h, = h[k(l Q(1

f

+ E) + al/k

E) >

> 0;

0;

Q*l = th, > 0; and qj = Qj + QS.

Oil Pricing The first- and second-order conditions for revenue-maximization imply: rt = 1; cr < 1; and C$ = (1 - k)e(E - 1) + (1 - a) (1 + E) > 0. Then, in Equation (6): ql = (1 - k)[E(l - E) + a(1 + E)]/k = ?; and 712 = (1 - k)+/tk’ > 0. Setting q to unity and inverting it gives the oil-pricing function, Equation (7). As noted in the text, the oil-pricing and elasticity functions are based on the assumption that u and E are both constant.

“Letting y = q/N and b = II/N, written in intensive form as: y = y(b). stitution is: CT = -y’w/byy” = -ky’/by”.

the aggregate production Th en, by definition, the

function elasticity

can be of sub-

575

Jon Harkness Aggregate Supply The above results imply that, with q = 1 and u < 1, the derivatives of Equation (8) are: G’ = Q1 + Qzg’ = (1 - ka)Q(l k)(l + e)2/tk2-q2 > 0; and F’ = Q*l + Q*zg’ = th, > 0. Prices Let 2 = p/ME, > 0. Then, in Equation = ZE3 > 0; and P3 = Z(F’E2 - G’) < 0.

576

(11): PI = P/M;

P2