Oil Prices, Industrial Prices and Outputs: A General Equilibrium Macro Analysis

NOT FOR QUOTATION WlTHOUT PERMISSION OF THE AUTHOR

OIL PRICES, INDUSI'RIAL PRICES

AND

OUTPUTS:

A GENERAL

EQUILIBRIUM MACRO ANALYSIS

Graciela Chichilnisky*

December 1983 WP-83-126

Working Papers a r e interim reports on work of t h e international Institute for Applied Systems Analysis and have received only limited review. Views o r opinions expressed herein do not necessarily represent those of the Institute o r of its National Member Organiza- tions.

INTERNATIONAL INSTITUTE FOR APPLIED SYS'IXMS ANALYSIS 2361 Laxenburg, Austria

This is one of t h r e e papers derived from research on N o r t h S o u t h trade performed i n the System and Decision Sciences Area during the summer of 1982. The aim of this research was, first. t o construct a model of N o r t h S o u t h resource trade and then to use i t as a framework for further work in gaming, negotiations, and interactive decision making.

In this paper, a two-region general equilibrium macro model is con- structed t o explore t h e impacts of oil prices on output, employment and t h e prices of goods in industrial economies. It is shown t h a t the effects of an increase in the price of oil depend considerably on the initial prices. The author examines different regimes, looking a t their policy implications and in particular t h e possibility of cooperative pricing policies.

ANDRZEJ WTERZBICKI Chairman

System and Decision Sciences

A two-region general equilibrium macro model is constructed to explore the impacts of oil prices on output, employment and prices of goods in indus- trial economies.

The industrial region is a competitive m a r k e t economy t h a t produces two goods (consumer and industrial) with three inputs (capital, labor and oil). It trades industrial goods for oil with another region. The oil-exporting region is a monopoly which s e t s t h e price of oil. The general equilibrium of the model determines endogenously the price and level of output of industrial goods, t h e volume of exports and imports, and the utilization and prices of factors in t h e industrial economy.

The results show t h a t an increase in oil prices can have a number of out- comes. Depending on t h e initial oil price, the real revenues of t h e oil exporter may e i t h e r increase or decrease. The r a t e of profit and net value of output in t h e industrial economy may also either decrease or i n c r e a s e , depending on initial prices. This paper examines different regimes, looking a t their policy implications, and in particular t h e possibility of the importer and exporter adopting cooperative pricing policies.

A computer program (in BASIC) describing t h e model together with a n u m b e r of r u n s a r e given in the Appendix.

OIL PRICES.

INDUSTRIAL

PRICES AND

OUTPUTS:

A GENERAL EQUILIBRIUM MACRO ANALYSIS

Graciela Chichilnisky*

1. INTRODUCTION

The increased activity of OPEC i n t h e early seventies produced s o m e of t h e m o s t significant c h a n g e s in t h e international economy i n t h e post-war p e r i o d These c h a n g e s coincided with a renewed awareness of t h e problems produced by t h e exhaustibility of n a t u r a l resources. An extensive l i t e r a t u r e on t h e economics of exhaustible resources developed, based on t h e s t u d y of intertemporal optimality a n d efficiency of depletion p a t h s i n one-sector growth models, a n d looking a t t h e effects of m a r k e t s t r u c t u r e on price a n d depletion paths, e.g., Stiglitz (1974, 1976). Sweeney (1977) a n d Dasgupta a n d Heal (1979).

*Professor of Economics, Columbia University.

Research support from NSF Grant SES 7914050, UNITAR, and the Rockefeller Foundation is grateful- ly achowledged. I thank T. Agbeyegbe, L. Bergman, Z. Fortuna, 0 . Hart, G. Heal, D. Horwell, S.

Kojima, K Mino, L. Mathiessen, 0 . Galor, H. Ryder, H. Soederstrom, K. Smith, J. Stein, A. Ulph, and A. Wierabicki for comments and suggestions.

While i t is t r u e t h a t t h e intertemporal issues relating to depletion rates a r e t h e ones t h a t most readily spring to mind when considering extractable resources, there a r e in fact a n u m b e r of issues related to t h e pricing of such resources t h a t can be analyzed in a static general equilibrium context.

Amongst these a r e t h e effects of resource prices on t h e relative prices of dif- ferent goods and services, their effects on international t e r m s of trade, and t h e i r effects on the macroeconomic equilibria of t h e consuming countries.

The prices of extractable resources a r e of course not unique in having such m a r k e t effects, b u t i t is nevertheless t h e case t h a t these effects include some of the m o s t widely-debated impacts of resource pricing policies. There is prob- ably a t least a s much concern about t h e effects of oil prices on t h e macroeconomic equilibria of t h e consuming countries, on international t e r m s of trade, and on the international distribution of wealth,* a s t h e r e is about t h e i r effects on depletion rates. This paper emphasizes t h e behavior of inter- national resource m a r k e t s and t h e limitations this imposes on t h e plans of both exporters a n d importers.

Recent work in international economic theory has dealt with some aspects of these problems, e.g., Corden (1971) studied t h e short-run impact of oil prices within a one-sector (IS-LM) analysis of t h e world economy in which t h e redistribution of world income in favor of OPEC is seen as raising overall propensities t o save. However, i t is not possible t o study t h e specific effects of oil policies on t h e importing c o u n t r i e s using t h i s model. Findlay a n d Rodri- guez (1977) and Buiter (1978) studied a Fleming-Mundell model incorporating imports of intermediate goods, where t h e nominal price of oil is an exogenous variable to which a particular small open economy has t o adjust. In a m o r e

*The Rariloche model (see Chichilniaky, 1978) explored the long-run effects of self-sufficient growth patterns on output and distribution in the different regions, but no conclusions were drawn about the functioning of international markets, or about the main effects on employment, output and pricee within the industrial oil-importing economies.

recent piece. findlay (1983) studies t h e relation between t h e volume of oil exported by a cartel and t h e levels of output and employment within an oil- importing country, using a model in which t h e nominal price of one aggregate good is determined endogenously.* Other recent pieces of work in t.his a r e a a r e due t o Dixit (1981), Harkness (1980), Sachs (1983) and Djajic (1981).

In c o n t r a s t with these works, this paper is an attempt t o c o n s t r u c t a model t h a t is able t o explain t h e domestic general equilibrium responses of a n oil-importing country, a c o m p e t i t i v e m a r k e t economy, t o t h e pricing policies of a monopolistic exporter. The model fcrmalizes t h e notion t h a t t h e demand faced by t h e exporter shifts as a consequence of his own actions, through t h e impact of oil prices on t h e general equilibrium of t h e importing region. OPEC is one example of a monopolistic organization which should be i n t e r e s t e d in t h e general equilibrium implications of its own actions. Similar eFfects have already been formalized by Pearce (1953, 1956), Hahn (1977) a n d m o r e recently by Hart (1982), t h e latter two in a general equilibrium context.**

I t

will be shown h e r e t h a t consideration by the monopoly of these general equili- brium effects leads t o policy implications r a t h e r different from those obtained using partial equilibrium analysis or standard general equilibrium models.

*However, the assumptions of Findlay's model rule out the study of certain important relationships between oil supplies, output and prices when the cartel's actions affect both the demand and the supply of the importing region, an issue which is a t the core of much of the present N o r t h S o u t h debate. For instance, in Findlay's model, the nominal wage in t h e importing region is assumed to be fixed, and, furthermore, real wages and rates of interest have no feedback on employment, ex- cept through real balance effects. Furthermore, the importing region produces one aggregate good, with the result that an increase in oil supplies unequivocally increases output and employ- ment. and reduces the price level in this region. In the long run, through the assumption of a posi- tive effect on demand of an increase in employment, the oil cartel is seen not t o affect t h e level of employment, but to decrease the returns t o factors instead.

**These publications relate to our model in the sense that they study the general equilibrium responses of demand to monopolistic policies. Pearce (1853, 18%) studied a closed economy in which total demand responds in a general equilibrium fashion t o the actions of a monopoly and ex- plored the implications of this response. More recently, Hahn (1877) studied the 'conjectural equlibria' of a closed economy, in which a firm attempts t o consider the general equilibrium re- percussions of i t s o m actions. It appears that these works are quite closely related t o the ap- proach we follow here, and, indeed to the approach that seems most appropriate in the case of OPEC. In a recent piece, Hart (1882) examines in a general equilibrium framework the case of a monopolistic producer that can affect its o m market. His approach contrasts with that adopted here in that the eKects of the firm's policies are on other firms, rather than on the demand the firm itself faces.

I t is clear t h a t t h e optimal pricing policy for OPEC will depend upon t h e elasticity of demand for oil in the oil-importing countries and t h a t t h i s elasti- city m u s t be a total one, taking into account t h e effect of oil prices on output and employment in these countries. But, as mentioned in Dasgupta a n d Heal (1979, Chapter l l ) , this elasticity is likely to change because t h e equilibrium s t a t e of t h e industrial economy varies with different oil prices. Hence t h e total demand function facing t h e exporter may be very complex a n d have an elasticity t h a t varies significantly with t h e price, reflecting overall changes in output, employment and prices within the industrial economy. A b e t t e r understanding of t h e behavior of this elasticity would be of g r e a t value in predicting t h e consequences of alternative pricing policies. The p r e s e n t model provides a first s t e p towards s u c h an understanding. Moreover, when t h e general equilibrium effects of t h e monopoly's policies a r e taken i n t o account, i t is readily perceived t h a t oil prices m a y have a non-trivial effect on t h e prices of goods imported by t h e oil exporter a n d t h u s on t h e "real" elasti- city of demand for oil, measured in t e r m s of t h e power of the oil exporter t o purchase industrial goods. These ideas are formalized in this paper: t h e effects of oil price changes are t r a c e d across t h e equilibria of t h e model through t h e functioning of all m a r k e t s in t h e importing region ( m a r k e t s for consumer and industrial goods, a n d for t h e t h r e e factors of production).

We prove h e r e t h a t if oil prices a r e initially low. a n increase in t h e price of oil leads t o a n increase in t h e real revenues of t h e oil exporter in t e r m s of industrial goods imported. Thus t h e r e a l elasticity of demand for oil is g r e a t e r than -1 in this case, and t h e optimal policy of t h e oil exporter is t o i n c r e a s e prices.

However, after a n oil price level

%

has been reached, f u r t h e r i n c r e a s e s in price produce t h e opposite result: t h e real revenues of t h e oil exporter

decrease. This is b e c a u s e i n c r e a s e s in p S above jiS m a y in fact r e d u c e total exports of industrial goods, e i t h e r b e c a u s e of a fall in t h e r a t e of profit a n d t h e o u t p u t of industrial goods, or because of income effects within t h e industrial c o u n t r i e s . In t h e l a t t e r case, i n c r e a s e s in domestic demand exceed t h e i n c r e a s e in t h e supply of industrial goods as the price of oil increases. There- fore t h e g e n e r a l equilibrium effect of higher oil prices is to reduce t h e volume of industrial goods exported.

A similar non-linear response t a k e s place in t h e revenues of t h e indus- t r i a l country: a t low oil prices a n increase in t h e price of oil leads to h i g h e r r e t u r n s on domestic capital, a n d

tb

higher levels of oveiall output, while t h e opposite occurs when oil prices s t a r t from a high level. The specific condi- t i o n s u n d e r which t h e s e different "regimes" prevail, a n d t h e i r effect on o u t p u t a n d employment within t h e i n d u s t r i a l economy, provide t h e s u b j e c t of t h i s paper. Computer simulations of t h e situations obtained by varying t h e (exo- genous) price of oil a r e given in t h e Appendix.

A f u r t h e r i s s u e which h a s been extensively discussed, a n d on which t h i s p a p e r m a y throw s o m e light, is w h e t h e r t h e relationship between capital a n d e n e r g y is one of c o m p l e m e n t a r i t y o r substitutability. Empirical evidence on t h i s i s ambiguous (see Berndt a n d Wood, 1979), suggesting t h a t in s o m e coun- t r i e s t h e f o r m e r is t r u e a n d in o t h e r s t h e l a t t e r . In t h e following analysis, we shall show t h a t i n s o m e c i r c u m s t a n c e s a n increase i n t h e price of oil will lead t o a n increase in t h e g e n e r a l equilibrium r e t u r n on capital, whereas in o t h e r s a decrease is observed. An i n c r e a s e in t h e r e t u r n on capital c a n be i n t e r - p r e t e d a s implying t h a t , a t t h e aggregate level, capital a n d oil a r e behaving a s s u b s t i t u t e s ( a n i n c r e a s e i n t h e price of a factor will raise t h e d e m a n d for, a n d p r i c e s of, s u b s t i t u t e factors), while a decrease can be i n t e r p r e t e d a s showing c o m p l e m e n t a r i t y between t h e s e factors. Hence t h e aggregate cross-

equilibrium relationship between capital and energy prices may display e i t h e r complementarity or substitutability, depending on t h e values of parameters and endogenous variables. This point is developed f u r t h e r in Chichilnisky and Heal (1982).

2. A GENERAL EQUILIBRIUM

MACRO

_MODEL

The model used h e r e is based on Chichilnisky (1981), but has been extended t o include oil as an imported input which is t r a d e d for industrial goods. There a r e a n u m b e r of features which have been introduced primarily to keep t h e comparative static analysis tractable, and which a r e not essential to t h e results. These a r e t h e assumption of fixed-coefficient production processes, a n d t h e assumption t h a t all wages a r e consumed in good B. The first (Leontief) assumption yields simple price equations, while t h e assump- tion concerning consumption simplifies certain cross-equilibrium relation- ships. Both can be relaxed without changing t h e basic qualitative features of t h e r e s u l t s - for example. similar results c a n be obtained from Cobb-Douglas production functions and from more general savings behavior. However, t h e increase in complexity is considerable.

The industrial economy is represented by a competitive general equili- brium model with two produced goods and t h r e e factors of production. In addition t o t h e production and savings assumptions mentioned above, i t is assumed t h a t factor supplies in t h e industrial economy a r e sensitive t o r e a l factor prices. The supply of labor is t h u s an increasing function of t h e real wage, a n d t h e supply of capital an increasing function of t h e real r e t u r n on capital. The assumption about labor supply is routine, b u t t h a t concerning capital supply perhaps merits some comment. What we have in mind is a situation in which t h e economy h a s a capital stock composed of machinery of differing vintages and t h u s differing efficiencies. The fraction of this t h a t is

actually used a t equilibrium will therefore depend on t h e f a c t o r prices, a n d will i n c r e a s e with t h e price of capital.' .4lternatively this assumption could r e p r e s e n t a f o r m of factor mobility i n t o or out of t h e region. The dependence of factor supplies upon t h e i r real rewards is a s s u m e d t o be linear. I t should be noted t h a t in spite of t h e linearity of t h e factor supply equations a n d produc- tion functions, t h e supply, d e m a n d and production a s p e c t s of t h e model i n t e r a c t in s u c h a way t h a t i t s equilibrium relationships a n d comparative static p r o p e r t i e s a r e highly non-linear: t h e y a r e in s o m e c a s e s of t h e fourth order.

The i n d u s t r i a l c o u n t r y produces a basic c o n s u m e r good a n d a n industrial good, d e n o t e d by

B

a n d / respectively. There a r e t h r e e i n p u t s t o production:

labor (L), capital (K) a n d oil ( I9 ). Oil is not produced domestically. In o r d e r t o simplify t h e analysis, t h e production functions of t h i s c o u n t r y a r e of t h e fixed-proportion type

where L B , 1 9 ~ a n d KB denote i n p u t s of labor, oil a n d capital i n t o t h e produc- tion of t h e c o n s u m e r good, a n d a l . b l a n d c l a r e t h e inverses of factor/output coefficients. Similarly. t h e production f u n c t i o n for t h e indus- trial good is

rS =

m i n (LZ/ a2

.

^{dl/ b 2}

.

^{Ki/ c2)}

.

₍₂₎

The a s s o c i a t e d or 'dual' p r i c e equations (assuming competitive behavior) a r e t h e n

*Aa an example, one could think of oil-consuming power plants of differing vintages and thus costs.

The higher-cost plants are commonly brought into and out of production as relative prices change.

where w denotes wages, pd denotes t h e price of oil, ^T the quasi-rent of capital, pz t h e price of t h e industrial good, a n d pg the price of t h e c o n s u m e r good.

The factor rpz is a proxy for t h e u s e r ' s cost of capital, which e n t e r s as a cost.

Although t h e two production functions both specify factor use in fixed propor- tions, t h e y a r e assumed below to have very h f f e r e n t oil u s e / o u t p u t coeffi- cients. In addition, i t is shown t h a t t h e patterns of demand imply s u b s t i t u t a - bility between B and I. These two properties of t h e model imply t h a t t h e r e is a considerable a m o u n t of s u b s t i t u t i o n in t h e use of factors in t h e economy a s a whole. In certain cases s t u d i e d below this also implies significant c h a n g e s in t h e elasticity of demand for oil a s a n input. We assume t h a t factor supplies a r e sensitive to prices. If t h e price of t h e consumer good is t a k e n a s t h e unit of m e a s u r e m e n t , t h e n labor supply is responsive to real wages:+

and capital is a function of t h e r a t e of profit T , i.e.,

Next we formulate t h e d e m a n d behavior, postulating t h a t a t equilibrium t h e value of basic goods c o n s u m e d equals wage income, i.e.,

p B ~ D

=

W L S

.**

The m a r k e t equilibrium conditions a r e L D = L B + L Z

p~ ~ -

*Although a is taken t o be positive here, it may in general be either positive or negative depending on whether labor supplies respond positively or negatively to wage increases. The response may be negative when leisure has a high level of utility, i . e . , there is a "backward bending" labor supply.

**Demand behavior outside equilibrium is not considered here.

where

X?

denotes exports of I.

X :

denotes imports of oil and t h e superscripts

D

a n d S indicate domestic demand and supply. The last equation is a balance of payments condition. We assume t h a t t h e industrial country produces no oil, s o t h a t all of t h e oil used must be imported ( d D

= xi).

The national income identity (national demand equals national income) for this model

p B ~ D

+

pIID

=

ZUL'

+

T I ~ S (9)

is always satisfied a t equilibrium, when all m a r k e t s a r e cleared.*

To summarize, t h e model's exogenous variables a r e t h e coefficients a l

,

a 2 , b l , b 2 , c 1 , c2, and t h e p a r a m e t e r s a and

19

representing t h e

*This is eesily verified by substitutmg for p ~ and pl from ( 3 ) and (4) in the left-hand side of (9):

pB B~ + pl ID = (alw + b ~p,, + c 1rpl)BD + ( a 2 w + b g , , + c 2771)(P

-

^@)

= w ( a l B S

+

a21s)

+

(c ,Bs+ c ,IS)

+

_{l ~}

+

_Sb

ZP) -

^{Xfla2w +} c ~ r p ~ + b z~,,)

= w ~ S + r p ~ K S + p , , x ~ - ~ , x -

.

Since P,& = we obtain (8).

responses of domestic factor supplies to prices.

The model c a n be formalized m o r e concisely a s a system of five behavioral equations, ( I ) , (2), (5), ( 6 ) , (7), a n d nine equilibrium conditions, (8a--8i). The endogenous variables are: supply O F I,

' ; 1

demand for

I , I D ;

exports of I ,

: X

supply of B

.

^B'; d e m a n d for

B

, g D : supply of labor, L ~ ; demand for labor,

L ~ ;

capital supplied,

KS;

capital demanded.

K D ;

oil supplied, 29'; oil demanded,

g D ;

oil imported,

x:;

a n d t h e prices in all five m a r k e t s , i.e., r a t e of profit, r ; wages, w ; price of

B

, p g ; price of I , pl; a n d t h e price of oil pb-

We t h e r e f o r e have 14 equations in 16 unknowns: i n t h e usual g e n e r a l equilibrium fashion, t h e s y s t e m c a n be solved up t o o n e p a r a m e t e r value, tak- ing one good a s a n u m e r a i r e . We choose t h e price of oil t o be t h e exogenous p a r a m e t e r . The prices t h a t emerge for t h e o t h e r goods a r e therefore relative prices. Because t h e t e r m s of t r a d e between oil a n d industrial goods r e p r e s e n t a significant endogenous variable i n t h e model, a n d in order t o facilitate possi- ble empirical i n t e r p r e t a t i o n of t h e results, we choose

B

t o be t h e n u m e r a i r e , i.e., p~

=

1. The oil exporter is therefore a s s u m e d to adopt a pricing policy by which he s e t s t h e price of oil relative t o t h a t of

B.

3.

OIL

PRICES. INDUSTRIAL PRICES

AND

EXPORT REVENUES

We now s t u d y t h e g e n e r a l equilibrium responses of t h e industrial econ- omy t o c h a n g e s i n t h e exogenously d e t e r m i n e d price of oil. This is very m u c h a comparative s t a t i c s exercise, a n d involves a c e r t a i n a m o u n t of computation (see t h e Appendix for details). The basic point is t h a t as t h e price of oil varies, t h e equilibria of t h e model will in g e n e r a l form a one-parameter family, i.e., t h e y will describe a curve in t h e space of endogenous variables. Along t h i s curve, t h e prices of goods, wage a n d i n t e r e s t r a t e s , o u t p u t levels, relative

prices of imports a n d exports (i.e., t h e t e r m s of t r a d e ) a n d t h e q u a n t i t y of exports a r e all endogenously related. We now study t h e behavior of t h e s e vari- ables across different equilibria. In o r d e r t o do t h i s , we m a k e c e r t a i n a s s u m p - tions about t h e production of c o n s u m e r a n d industrial goods t h a t simplify t h e computations. These are:

1.

M =

a l b z - a z b l

>

0, i.e., t h e c o n s u m e r good is relatively labor- intensive and the industrial good relatively oil-intensive.

2. c

=

0 , so t h a t t h e c o n s u m e r good requires no capital inputs.

3. b i s small, so t h a t t h e c o n s u m e r good requires little in t h e way of oil inputs.

Assumption 2 i s not strictly n e c e s s a r y t o obtain t h e results: all t h a t i s r e q u i r e d is t h a t

B

be significantly l e s s capital-intensive t h a n I, s o t h a t t h e r e c a n be substitution in t h e aggregate u s e of factors. One could t h i n k of

B

a s a non-traded relatively labor-intensive commodity, s u c h a s services. C o m p u t e r r u n s of t h i s model with c l small, b u t n o t zero, give similar r e s u l t s ( s e e t h e Appendix).

I t is also shown in t h e Appendix t h a t t h e cross-equilibrium r e l a t i o n s h i p between t h e price of t h e industrial good relative t o t h a t of t h e c o n s u m e r good ( p I ) a n d t h e price of oil relative t o t h a t of t h e c o n s u m e r good (pd) is:

where

Equation (10) implies t h a t when condition 3 is satisfied ( b l is small), a n d a c z

<

^2@alaZ (this i s c a s e A of Theorem 1

-

s e e l a t e r ) , t h e price of t h e indus-

trial good relative to t h a t of the basic good

(PI)

increases as t h e relative price of oil increases. Intuitively it is not surprising t h a t a small b has this result;

the industrial good is more oil-intensive than t h e basic good, so t h a t its price should increase with the price of oil. When b l is not small, so t h a t neither good is clearly more oil-intensive, t h e relative prices of the two goods may move in a more complex way in response to changes in t h e price of oil p d .

We next study how t h e r a t e of profit T varies with t h e price of oil. The relevant expressions are:

so t h a t T is a quadratic function of pd , r is zero when pd is zero or 1/ b and T

attains its maximum a t pd

=

^1/ 2b

These relationships a r e displayed in Figure 1. Their interpretation is related to t h e point made in the introduction about t h e complementarity or substitutability relationships between capital and oil emerging from t h e model. An increase in t h e price of oil always h a s two effects on t h e demand for capital: a substitution effect and a n income effect. The substitution effect causes substitution of capital for oil. This occurs in t h e present model, not because of a shift along isoquants ( t h e r e a r e fixed factor proportions in each firm), but because t h e relative prices of oil- a n d capital-intensive goods change. causing a change in demand patterns, production p a t t e r n s and t h u s relative levels of employment of factors. The income effect simply reflects the fact t h a t an increase in the price of oil reduces income and t h u s demand in t h e industrial economy. This will t e n d t o depress t h e r e t u r n on capital.

What Figure 1 shows is t h a t t h e substitution effect of an oil price increase

dominates a t low oil prices, and t h e income effect a t higher prices. The c u r r e n t conventional wisdom t h a t increases in oil prices depress t h e r e t u r n on capital in industrial economies can thus be interpreted in t e r m s of this model as showing t h a t c u r r e n t oil prices must be in t h e range 1/ 2 b t o 1/ b

The dependence of r on p g is also related to the issue of whether oil and capital a r e complements or substitutes. This point is developed further in Chichilnisky and Heal (1982). Here we just note t h a t (6) shows t h a t t h e supply of capital increases with r , so t h a t t h e amount of capital used a t equilibrium m u s t increase and then decrease with the price of oil. This m e a n s t h a t , across equilibria, t h e cross-price elasticity of demand between oil and capital is first positive and t h e n negative, implying a switch from substitutability t o com- plementarity. Note t h a t t h e elasticity referred to here is defined in Chichilni- sky and Heal (1982) a s a total cross-price elasticity.

It is shown in t h e Appendix t h a t exports from t h e industrial t o t h e oil- producing country satisfy

and

Two cases can be distinguished here. The first is when T is bounded below a l / 2 0 , in which case

~ X P

^{@ a} h a s t h e same sign as a ~ / apd. Alternatively, if

T can exceed a l / 2 0 , then ax?/ 3% will vary from negative t o positive a s pa increases, while a r / apd varies from positive to negative. The first case is easy to interpret: as t h e price of oil and t h e interest r a t e rise, t h e supply of capital increases, a n d with it t h e supply of capital-intensive industrial goods.

This facilitates an increase in t h e export of industrial goods. Conversely, when

t h e i n t e r e s t r a t e falls, capital employed, production of industrial goods and t h e volume of exports all decrease. This is shown in Figure 1. The second case is more complex, and is portrayed in Figure 2. As p+ increases, and r with it, exports rise as long as r

<

a 2 0 . .4t this point exports fall as r continues t o rise, then rise as ^T falls, until ^T once more reaches a l / 2 D , a t which point both

X :

a n d r move down as pd rises. What is happening in this case is t h a t a s pfl rises, ^T increases and with i t t h e supply of capital and t h e output of indus- trial goods, as before. However, in this case t h e parameters of the system a r e such t h a t an increase in profits, all of which a r e spei~k on industrial goods (equations (9) and (7)), leads t o an increase in t h e demand for these goods which exceeds t h e supply. The difference between supply and demand, which is exports, therefore falls. We can confirm this by noting t h a t this occurs when

which can happen if and only if

c 2 is t h e inverse of t h e capital/output ratio in t h e industrial goods sector: t h e higher t h e value of c 2 and t h e lower t h e value of

B

(the responsiveness of capi- tal t o i n t e r e s t rates), t h e smaller t h e response of industrial output t o t h e sup- ply of capital and hence t o r a n d p d . And i t is obvious t h a t t h e smaller t h e response of industrial output to capital supply, t h e more likely it is t h a t out- put will fall s h o r t of t h e increase in demand, leading t o a drop in exports.

We have now prepared t h e ground for t h e main results of this section.

Theorem

1 .

If

t h e initial p r i c e of oil pd .is l o w , an i n c r e a s e in this p r i c e w i l l i n c r e a s e t h e v o l u m e of i n d u s t r i a l g o o d s e z p o r t e d

x?.

H o w e v e r , o n c e t h e p r i c e

o f oil has r e a c h e d a c e r t a - h u a l u e jid, f u r t h e r i n c r e a s e s in this p r i c e w i l l l e a d t o a d e c r e a s e in t h e v o l u m e of i n d u s t r i a l g o o d s e x p o r t e d

x,?.

m e r e a r e t h e n t w o p o s s i b i l i t i e s :

A. a c i I Z p a l a 2 . En. this c a s e , i n c r e a s e s in t h e p r i c e of oil t o a b o v e

pd =

1/ 2 b d e c r z a s e t h e r a t e o f p r o f i t r in t h e i n d u s t r i a l e c o n o m y . ^This d e c r e a s e s t h e t o t a l c a p z t d a v a i l a b l e , a n d thus d e c r e a s e s t h e d o m e s t i c s u p - p l y o f i n d u s t r i a l g o o d s a n d t h e v o l u m e a v a i l a b l e f o r e z p o r t (see f i g u r e I ) .

Figure 1. Case A: acg C 2/3ala2, i.e..

r

is always bounded below a l / 2 0 . In t h i s c a s e t h e volume of industrial exports initially increases with t h e price of oil. For p 4

>

1/ 2 b l , however,

X?

d e c r e a s e s with f u r t h e r increases in p4. This is due t o t h e effect of oil prices on t h e r a t e of profit in t h e industrial economy.

1

B.

_{a c z}

>

2 a a l a g . N o w

pd =

(*I - (-

- a

I ) ) B e t w e e n

%

a n d I/ 2 b l ,

2b 1 Y

i n c r e a s e s

in

t h e p r i c e of oil r a i s e t h e r a t e o f p r o f i t b u t l o w e r t h e e z p o r t s 1 1

o f i m d m t r i a L g o o d s . Fbr -

c

p4

c

+I+(-

y4a1 )?i),

a n i n c r e a s e in o i l

2b 1 2b ¹ Y

p r i c e s l o w e r s t h e r a t e o f p r o f i t a n d r a i s e s e x p o r t s , a n d f o r h i g h e r o i l p r i c e s b o t h e z p o r t s a n d t h e r a t e of p r o f i t f a l l as p* i n c r e a s e (see F i g u r e

2).

K g u r e 2. Case B: ac;

>

^2#lala2. s o t h a t r exceeds a l / 2D for ( 11

-

^[(7-2a1)/ 7 _p 1 2 b 1 ( 1

+

[(7-2a1)/ 7 ) . These Limits a r e indicated a s Q a n d R, respectively, i n t h e figure. This r e s u l t is d u e t o cross-equilibria income effects: increases in t h e price of oil i n c r e a s e t h e r a t e of profit r , b u t t h i s produces increases in d e m a n d t h a t exceed i n c r e a s e s in t h e supply of industrial goods within t h e industrial economy. This also happens in Case A, but since r decreases with p,, in this l a t t e r case, t h e total effect i s t h a t t h e volume of exports i n c r e a s e s with p,,.

The proof of t h i s t h e o r e m is given in t h e Appendix.

The final issue t h a t we shall discuss in t h i s section is t h e relationship between t h e price of oil a n d t h e elasticity of d e m a n d faced by t h e oil exporter.

We a r e i n t e r e s t e d in t h e real elasticity of demand: t h e real revenue of t h e oil exporter i s p,,~$/pl (as only industrial goods a r e imported), a n d it is t h e n n a t u r a l t o define t h e r e a l elasticity a s

It is shown in the Appendix t h a t

q >

¹ if a n d only if -

aqs >

0

ap ^T9

ax?

1

q

<

-1 if a n d only if - < O

.

apd

The behavior of t h e elasticity of demand with r e s p e c t t o t h e price of oil is t h e n as shown in Figures 3 and 4 for cases A and B of Theorem 1.

Figure 3. Elasticity of demand a s a function of

p~

when

acg

1 2@ala2 (Case A)

-

These r e s u l t s confirm our expectation t h a t t h e elasticity of demand fac- ing the oil exporter will change a s t h e equilibrium of t h e oil-consuming coun- t r y changes.' A demand relationship a s complex a s t h a t shown in Figure 4 h a s

*The nominal elasticity of the demand for oil c can also be computed directly from its definition

I

^a

^-

^{2b. 1 I4 Price of} 0 i 1 . p ~

Figure 4. Elasticity of demand as a function of po when a c

>

2/3ala2 (Case

El).

Here

Q

and R a r e given by po

=

( I / 26 1)(1

+

[(7-2al)/ 7]1W).

-

significant implications for t h e optimal long-run monopoly pricing policy, which involves prices increasing a t t h e s a m e r a t e a s t h e demand elasticity changes (Dasgupta a n d Heal, 1979, Chapter 12).

4. INDUSl'RlAL

OUTPUT AND

EMPLOYMENT

We study now t h e effect of variations in t h e price of oil on t h e overall lev- els of output and employment in t h e industrial country, across equilibria.

We shall denote by Y t h e total value of ( n e t ) domestic output, i.e., t h e value of total o u t p u t m i n u s t h e value of t h e imported input:

Y = ~ ~ B ~ +

.

~ ~ I ~ - ~ ~ x ~

C = 2 b l ~ a ( a l b z + a z b l)(r

-

b a d ) (1

-

b ~ d ) ( a 1 b 2 b lPd + a z b 1 0 - b lPd)) where

and is therefore also seen to vary with the price of oil p*.

Y is t h e overall domestic value-added in the industrial economy. Since a t e q u i l i b r i u m p + ~ : = plx?and

B ' =

gD, it follows t h a t

Y = p B ~ D +plrD

.

(13)

Our next aim is t o compute changes in the equilibrium values of Y and of total overall employment L a s the price of oil p g varies. We first study t h e effect on employment.

Note t h a t by (3), when c

=

0

Therefore, since L

=

a w , increases in pd a l w a y s decrease overall e m p l o y m e n t when a

>

^0. When c # 0, a w / apd can be e i t h e r positive o r negative.

Next we study t h e effect of oil prices on consumption. From (5), (6). (?), (9) a n d (13)

so t h a t

Note t h a t because p B ~ D

=

aw 2 a n d p B

=

1, a n d c l

=

0

Therefore, when a

>

⁰ and 0 I p d < 1/ b l , domestic consumption of B ( g D ) decreases as the price of oil increases. This does not necessarily happen w h e n

C l # 0.

Finally, we use t h e above analysis t o study how o u t p u t

Y

responds t o changes in

p d .

Since

r

= 0 when

p+

= 0, (14) and (15) imply t h a t overall out- put is a decreasing function of

p g

for small values of

p+.

However, since

d r / apg

2 0 for

p g <

1/ 2 b a n d b

-

^{0 , Y} is an increasing function of t h e price of oil when

p g

is g r e a t e r t h a n some small value (denoted by

p;).

This is due t o t h e fact t h a t , as

pd

increases, t h e value of t h e d e m a n d for

I

,

p l ~ D = p[@r2,

also increases, since

a r / a p g > 0

a n d

a p [ / a p g 2 0

when

1/ 2

, s e e Figure 2. Since b is r a t h e r small, t h e increase in p l ~ D in (13) will exceed t h e decrease in the value of d e m a n d for

B , B ~ ,

so t h a t

Y

increases with t h e price of oil.

Finally, note t h a t when

p,,

exceeds a certain value

p$

,

a Y / a p d

becomes negative again, because r

=

0 when

p,, = 1/ b

,

ar/ ap,, <

⁰ for

pg > 1/ 26

l ,

and

a ~ ^ap,, ~ <

0 ,

/

a n d ^T

(apl/ apd)

is bounded above by

-(h!ac2b

l /

pa l a 2 ) p d ,

f r o m

( 1 0 )

a n d

(11).

We therefore have the following s i t u a t i o n (see Figure 5):

Theorem

2.

When the initial price of oil p,,

is

close t o zero, a n increase

in

this price lowers the level of n e t overall domestic output

in

the industrial econ- omy. m e n

o i l

reaches a price pz, however, f u r t h e r price increases will increase overall output

in

the industrial economy. When pd reaches a value

p$ > p $ , increasing the price

o f o i l

still further will reverse the situation

once again, overall output n o w decreasing

with

increasing p d . The overall level of employment in the economy decreases as the price of

o i l

rises, as does the level of consumption 01 basic consumer goods.

The fact t h a t domestic employment and consumption of basic goods decrease monotonically with i n c r e a s e s i n t h e price of oil will occasion little surprise.

What is less obvious is t h a t t h e r e is a range of oil prices for which value-added increases with increases in t h e price of oil p d . As indicated above, this occurs because, over a certain range of values, increases in p S lead t o t h e substitu- tion of capital for oil, and hence t o increases in both profits and demand.

Figure 5. The behavior of overall output Y and employment

L

with increases in t h e price of oil, across equilibria.

5. CONCLUSIONS

In t h e previous sections we presented a simple general equilibrium model of an oil-consuming country, a n d used this t o analyze t h e macroeconomic responses of s u c h a country t o changes in t h e price of oil. We studied t h e responses of outputs, prices, profits a n d consumption levels in the oil- consuming country, and showed how t h e s e depend on p a r a m e t e r values and t h e price of oil. A number of conclusions were relatively straightforward -for example, if c

=

⁰ employment a n d consumption of

B

decrease a s t h e price of

oil rises. Others, however, were less obvious, suggesting t h a t t h e full impact of an oil price increase is very complex. I t was shown t h a t profitability first rises and then falls with an increase in the price of oil. The switch reflects t h e changing importance of income and substitution effects. Substitution of oil by capital bids up the r e t u r n on capital, athough beyond a certain point this is outweighed by t h e demand-reducing effects of higher oil prices. Also n o t immediately apparent is t h e fact t h a t in certain regions an increase in t h e price of oil may increase total value-added in t h e oil-using economy. This is because in some cases i t leads t o an increase in profitability, as noted above, and h e n c e t o increased demand.

I t emerges from this analysis t h a t t h e r e a r e certain situations in which an i n c r e a s e in oil prices may c a u s e profitability and output in t h e industrial economy t o rise, even though employment and consumption of basic goods will fall. In other situations, all four variables will decrease as t h e oil price rises. In t h e former case, one c a n n o t say t h a t t h e increase in oil prices is unambiguously harmful: indeed, taking GNP as a welfare index, i t could be judged beneficial. Another issue t h a t we examined was t h e effect of oil price changes on t h e export of industrial goods t o t h e oil producing country. This can be r a t h e r complex: t h e plot of real exports aganst oil prices may have e i t h e r one or two maxima, which implies t h a t t h e cross-equilibrium d e m a n d function facing t h e oil exporter m a y be far removed from t h e simple functions often u s e d in dynamic studies. We also characterized precisely how t h e elasti- city varies with t h e price of oil.

One interesting implication of these results is t h a t t h e r e may be situa- tions where an increase in t h e price of oil will benefit both oil exporters (by raising their real revenues) and oil importers (by raising t h e i r profits a n d GNP). These two groups a r e therefore not always playing a zero-sum game.

APPENDIX

The Relationships Between P* and the Equilibrium Values of Endogenous Variables

First note t h a t t h e production functions ( 1 ) and ( 2 ) yield equations for the demand for factors

L ,

K, and 19 a t each level of output, assuming that the factors a r e used efaciently:

L~ =

BSal

+

p a z ( A 1 )

Equations ( A 1) a n d ( k 2 ) imply t h a t when factors are used efficiently B'

=

(c2LS

-

a , ~ ~ ) /

D

where

D

is the determinant of the matrix

The price equations (3) and (4) can be regarded as a system of two equa- tions in two variables, w and r , when p g is a constant. From these equations we obtain

Substituting

LS

a n d

K S

from (5) and (6), and w and T from (A.6) and (A.7) into ( k 4 ) , we obtain t h e equilibrium values of t h e supply of consumer goods

B S

as a function only of t h e price of industrial goods pl:

where

N = c l b 2 - c 2 b 1

.

Similarly, substituting t h e expressions for

K S , L ~ , W

and T into (A.5) leads t o

Now, from t h e demand relation ( 7 ) and t h e accounting identity (9), we have a t equilibrium

~ D = T K ~

.

(A 10)

Therefore, when pg

=

1, t h e equilibrium relation

B S = B D

can be rewritten,

using (5), (A.6) and (A.8), as follows:

while from ( 6 ) , ( A . 9 ) and (A.10), jS = ^jD

+

^{X? is}

(A. 11)

(A. 12)

From equation (9), equations ( A l l ) and (A12) a r e not independent a t e'quili- brium. The implicit function t h e o r e m implies t h a t one c a n obtain, a t least locally, a function pI

= ~ ~ ( p , , )

from ( A l l ) . Therefore, since p9 is given, t h e value of pI a t equilibrium c a n be obtained. This, with (A8) a n d (A.9), yields t h e equilibrium supply of B and I, B' and

I S .

Equilibrium values of wages and profits w and T c a n be deduced from (A6) and (A?), and t h e equilibrium use of inputs

' K

and

' L

from (5) a n d (6). This allows ID t o be calculated from ( A ~ o ) , so t h a t t h e volume of i n d u s t r i a l exports

qS

c a n be found; t h e volume of oil i m p o r t e d c a n t h e n be c o m p u t e d from (8i). The model is therefore 'closed', i.e., i t s equilibria a r e predetermined (and locally unique) for given pd. When

p,,

is changed, t h e equilibrium values of all endogenous variables will change.

In particular, t h e volume of industrial exports

X?

and t h e i r price pI will change, a n d o u r next goal is t o compute how they change in relation t o each o t h e r across equilibria. We now make some assumptions which simplify t h e computations, and which a r e discussed in more detail earlier in t h e text.

1.

M =

a l b

-

a 2 b

>

0, i.e., B is m o r e labor-intensive and I m o r e oil- intensive.

2 . c

=

0, i.e., B requires no capital inputs.

3. b is small, i.e., B requires only a small input of oil.

From ( A l l ) , using assumption 2 , one can obtain an explicit expression for PI

= P I ( P * ) ~

(A. 13)

where

and

M =

a l b 2 - a 2 b 1

Consider now t h e possible range in which p g c a n vary. From t h e price equa- tion ( 3 ) , w

r

0 implies l / b l 2 p g

r

0, since c l

=

0. From ( A 13) we have, when p d

=

0.

and when pd

=

-, 1 b 1

(A. 1 4 )

Note t h a t since

M >

^{0 ,} a z / a l

<

b 2 / b We can now study t h e change in t h e price of t h e industrial goodpI a s t h e price of oil increases:

The sign of ( A . 1 6 ) is therefore t h a t of t h e quadratic function f (J+) = - ( M y b : ) p i - ( 2 a z y b : ) p d t a l M

+

a 2 y b l , which is i l l u s t r a t e d in Fig- u r e Al.

f i g u r e A l . Plot of t h e quadratic function f ( p g ) = - ( ~ ~ b

f)Pz

-

( 2 a z 7 b

1 2 ) ~ ~

^{+ a 1M + az7b 1 .}

I t is e a s y t o s e e t h a t f ( J I ~ ) = ⁰ h a s only one positive root

p G .

In o r d e r t h a t a p I / 8 p d b e positive for all p d between 0 a n d I/ b i t is n e c e s s a r y a n d suf- ficient t h a t f ( I / b

>

0. But f ( l / b

=

-My

-

y a Z b

+

Ma1

>

⁰ a n d so

Therefore 8 p I / 8 p d

>

0 if a n d only if

@ l a z > I a n d b l < b z ( g a l a 2 - a c :

a c

22 g.2"

^I

i.e., if we have c a s e A discussed in t h e t e x t ( a c g I g a l a z ) a n d b l i s small.

Now, f r o m (3)

(A. 17)

and t h u s (4) implies

Substituting for pI from (A. 13) we obtain

(A. 18)

(A. 19)

Therefore T

=

0 both when p B is zero and when i t assumes its maximum value 1/ b l . The change in t h e r a t e of profit as t h e price of oil varies i s

Since

(A. 20)

a n d T is quadratic in p d , it follows t h a t t h e r a t e of profit is an increasing func- tion of pd for p,?

<

^1/ Zb and a decreasing function for pd

>

^1/ Zb l. Since T

attains its maximum value when p,?

=

1/ 2 b ^l, t h e maximum value of T is

Note t h a t t h e conclusion in fact requires only condition 2 above, i.e., t h a t C 1 = o .

We shall next analyze t h e response of t h e volume of industrial goods exported to changes in t h e price of oil. Since

X?

₌

lS -ID,

we deduce from ( 6 ) , (A.5) and ( k 1 0 ) t h a t

Therefore

(A. 2 4 )

Note t h a t r I E W

>

a l / 2 0 if and only if

(A. 2 5 ) a c ; > 2 p a l a 2 .

Proof of Theorem 1

Consider first t h e case where a c i

<

2 @ a l a 2 . Then

r

is always bounded above by a 1 / 2 D . In t h i s case t h e si;. f ax?/apd is t h e same as t h a t of a r / a p d , from ( k 2 4 ) . F u r t h e r m o r e ,

ar/

^apd

>

0 for p+

s

1/ 2b a n d

ar/

^apd

<

0 for pd

>

1 / 2 b l from (A.19)--(A.22). Here as the r a t e of profit increases, t h e supply of industrial goods increases more than does t h e domestic demand for these goods, since IS

=

a l p r / D and I D

=pr2

(from (6), (A.5) a n d ( A l O ) ) , a n d a l / 2 D

>

r , s o t h a t a ( I S - I D ) /

ar =

p [ ( a l / D ) - 2 r ]

>

0.

Therefore, since

x?=

^I

^-I

^{and by} ( ~ 2 4 )

ax?/apd

=

p [ ( a 0 ) - 2 ~ ] ( a r / ap*), t h e volume of industrial goods exported a t equili- brium

@

will increase with increases in the price of oil for p*

<

1/ 2b For

p* >

1/ 2b however, this relation is reversed: increases in t h e price of oil will

now decrease t h e volume of industrial goods exported across equilibria. In both cases considered h e r e this change in the reaction of industrial exports

X?

t o increases in t h e price of oil

p*

is related t o t h e change i n t h e response of the r a t e of profit t o i n c r e a s e s in t h e price of oil p*, a s illustrated in Figure 1.

Consider now t h e c a s e where acg

>

2/3alaz. In this case

r >

a l / 2 D for values of

p,,

n e a r 1/ 2b l . When

r > a l /

2D

.

^{aIs/ &}

^<

^{a I D /}

^ar .

s o t h a t t h e increase in t h e supply of industrial goods is exceeded by t h e i n c r e a s e in t h e domestic demand a s t h e r a t e of profit rises, i.e., t h e cross-equilibrium income

effect dominates t h e price (or substitution) effect. In this case, t h e reaction of t h e volume of industrial exports t o changes in t h e price of oil,

aqS/ap4.

depends both on t h e sign of t h e change in the r a t e of profit T ,

a r /

^{apd, a n d on}

t h e s i g n o f ( a l / D ) - 2 r . I n f a c t f J ~ F / a ~ ~ = ~ a r / a p 4 = 0 , 0 r a l / D = 2 r . This occurs when pa

=

(1/ 2b ,)(lk[(y-2a 1)/ yI1"). It follows t h a t we have a succession of different situations as pg increases from 0 t o 1/ b

a T

I. - _{2 0 and T}

_<

_-, ^{a1 .} _{1.e.- -}

ax?

2D ^{2 0}

ap

a

ap 79

a~

^{a I}

ax?

11. - 2 0 and r

>-,

i.e., -

2D

<

0

a~

d

a~

d

ar <

0 and r

<

- 1.e. -

ax?

IV.

- 1 0 .

*d 2 0

a~

^d

This is illustrated in Figure 2, a n d completes t h e proof of t h e t h e o r e m . Behavior of the Demand Elasticity Facing the Oil Exporter

Firstly, note t h a t t h e "real" revenue of t h e oil exporter is p d ~ $ / p I , which in a n international m a r k e t equilibrium equals

~ r ,

^where

~ r

is t h e a m o u n t of industrial goods i m p o r t e d a n d

$

is t h e a m o u n t of oil exported.

Now by definition t h e r e a l elasticity of d e m a n d for oil is given by

since t h e d e m a n d is basically t h e export demand.

If R denotes r e a l revenues, t h e n across equilibria we have for t h e oil e x p o r t e r

It follows t h a t

-

a(x$/

P I )

xi

ap,

^{' + +} -

ap

I9

PI

= - - - + , + I )

x2 . PI

Therefore

a R / ap, >

⁰ if a n d only if q

>

-1, or

1

^q

1 <

1 for q

<

0, a n d

aR/++ <

0 if a n d only if q

<

- 1 o r ) r ]

1 >

1, for q

<

^0. Since R

= p , ~ i / p I

⁼

xY,

i t follows t h a t r ]

>

-1 when p ,

< p,

a n d q

<

-1 when

P, > P,.

Computer Simulations for the Industrial Country

fin 1. The following p a r a m e t e r a n d f a c t o r response values were used:

Table A l . Results of t h e first r u n , with c

=

0. These r e s u l t s a r e i l l u s t r a t e d in Figure A2.

Exogenously set price of oil (pd)

Values of endogenous variables

Valun of

Figure A2. Behavior of t h e endogenous variables as t h e price of oil increases ( r u n 1).

Run 2.

The following p a r a m e t e r a n d factor response values were used:

Table A2. Results of t h e s e c o n d r u n , with c l # 0. These results a r e i l l u s t r a t e d in Figure A3.

Exogenously Values of endogenous variables

s e t price of oil (pd)

Pz

^{7 w PZXS}

Y

0.0 0.66890 0 . 5 5 7 4 ~ 1 0 ~ 3.33332 0 . 3 3 7 1 5 0 ~ 1 0 ~ ~ ~ 11.111 1 0.5 0.85861 0.243452 3.16597 0.580648 10.1251 1.0 1.10132 0.456505 2.99832 1.20033 9.44897 1.5 1.41239 0.644688 2.83030 1.84227 9.18463 2.0 1.80953 1.807918 2.66179 2.48953 9.44742 2.5 2.30945 0.946045 2.49272 3.12497 10.3476 3.0 2.91912 1.05883 2.32303 3.7312 1 11.9419 3.5 3.61864 1.14595 2.15284 4.29064 14.1388 4.0 4.33894 1.20707 1.98254 4.78579 16.5742 4.5 4.95548 1.24203 1 .81282 5.20000 18.5754 5.0 5.33000 1.25113 1.64444 5.5180 1 19.3906 5.5 5.38881 1.23504 1.47782 5.72565 18.6234 6.0 5.16262 1.19450 1.31278 5.80860 16.4559 6.5 4.75047 1.12996 1.14877 5.75144 13.4507 7.0 4.25777 1.04152 0.98521 5.5376 1 10.2080 7.5 3.76058 0.929042 0.82168 5.14990 7.16683 8.0 3.30079 0.792336 0.65794 4.57096 4.57735 8.5 2.89531 0.631209 0.49390 3.7835 1 2.55107 9.0 2.54664 0.445510 0.32955 2.77048 1.11951 9.5 2.25047 0.235131 0.16490 1.5149 1 0.276035

10.0 2.00000 0.385923~10-' 0. 0.257568~10-'~ 0 . 5 9 5 7 4 6 ~ 1 0 ~ ~ ~

V a l u a of wramatars

20

I

Figure A3. Behavior of t h e endogenous variables a s t h e price of oil increases ( r u n 2 )

Listing of the computer program (in BASIC)

The c o m p u t e r p r o g r a m u s e d t o obtain t h e r e s u l t s given in t h e previous s e c t i o n is listed below. I t was designed t o r u n on a S h a r p m i c r o c o m p u t e r . The p a r a m - e t e r s a n d variables h s c u s s e d in t h e t e x t a r e r e l a t e d t o t h e variables u s e d in t h e c o m p u t e r p r o g r a m as follows:

Text P r o g r a m Text P r o g r a m

I

^Text P r o g r a m

1

s o l u t i o n s S

P r o g r a m Listing

10 LF2 11 TEXT 12 CSIZE 1

20 INPUT "ENTER ALPHA AND BETAV;AL, BE 30 INPUT "ENTER Al,Bl,Cl";Al,Bl,Cl 40 INPUT "ENTER A2,BZ,CZ";AZ,B2,C2 45 INPUT "PRICE OF 0IL";PO

48 LPRINT "(";AL; ".";BE;")"

47 LPRINT "(";~1;",";Bl;",";Cl;")"

48 LPRINT

"(";a;

",";BZ;",";CZ;")":LFZ 60 H

=

1 - B l * P O

7 0

M

= A l * B 2 - M * B 1

9 0 GA = A L * C Z * C ~ / ( B E * A ~ ) 9 0 N

=

C l * B 2 - B l * C 2

1 0 0 D

=

A l * C 2 - A2*C1 1 1 0 A5

=

AL*C l * C 1

1 2 0 B 5

=

A L * c ~ * ( C ~ - 2 * C l * B 2 * P O - 2*C2*H)

130 C 5

=

AL*(CZ*C2*H*H+C1*C 1*B2*B2*PO*PO+2*Cl*C2*B2*PO*H-C2*C2-C2*POXN) +BE*Al *A2

1 4 0 D 5 =-A~*BE*(PO*M+M) 150 I F A 5

=

0 THEN G O T 0 4 0 0

160 P5

=

B5/A5:Q5

=

C5/A5:R5

=

D5/A5 170 A6

=

(1/3)*(3*Q5-P5-2)

1 0 0 B 6

=

(1/27)*(2*P5-3-9*P5*Q5+27*R5) 190 J 5

=

(BE-2/4) + ( ~ 6 - 3 / 2 7 )

2 0 0 I F J 5

>=

⁰ THEN GOT0 250

210 Z 5

=

ACS ((-B6/2)/SQR(-A6-3/27))):A9

=

SQR(-A6/3) 220 S l

=

2 * ~ 9 * C o S ( Z 5 / 3 ) - P 5 / 3

230 S2

=

2*A9*COS(Z5/3+ 1 2 0 ) - P 5 / 3 240 53 =2*A9*COS(Z5/3+ 2 4 0 ) - P 5 / 3 245 GOT0 420

250 A7

=

- B ~ / z + s ~ R ( J ~ ) : B ~

=

-BG/z-SQR(J~) 260 A0

=

SGN(A7)*(ABS(A7))-(1/3)

270 BS

=

SGN(B7)*(ABS(B7))-(1/3) 280 I F J 5

=

0 THEN GOT0 300