Download NOTES ON EXCHANGE RATES AND COMMODITY PRICES

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NOTES ON EXCHANGE RATES AND COMMODITY PRICES
by
Kenneth W Clements
and
Meber Manzur
DISCUSSION PAPER 01.25
DEPARTMENT OF ECONOMICS
THE UNIVERSITY OF WESTERN AUSTRALIA
CRAWLEY, WESTERN AUSTRALIA 6009
NOTES ON EXCHANGE RATES AND COMMODITY PRICES
by
Kenneth W Clements
Department of Economics
The University of Western Australia
and
MeherManzur
Curtin Business School
Curtin University of Technology
DISCUSSION PAPER 01.25
DEPARTMENT OF ECONOMICS
THE UNNERSITY OF WESTERN AUSTRALIA
CRAWLEY, WESTERN AUSTRALIA 6009
NOTES ON EXCHANGE RATES AND COMMODITY PRICES
Prices of internationally traded connnodities have been markedly volatile over the
last two decades. As Maizels (1992) demonstrates, the world market price of sugar, for
example, varied between 2.5 and 41 U.S. cents per pound in the 1980s, and coffee ranged
between 60 and 303 U.S. cents per pound over the same period. 'Hard' connnodities
were similar, with aluminium prices swinging between 42 and 162 cents and copper
between 58 and 159 cents (see, for more illustrations, Maizels 1992). Note that
connnodity price volatility is even sharper and more pronounced in well-organised
markets like the Chicago Board of Trade. Why are connnodity prices so volatile?
The conventional approach is to explain this volatility in terms of demand-supply
characteristics inherent in agricultural, energy and mineral connnodities (variable supply,
inelastic demand, and so on) and, in some cases, business cycles (see, for an overview,
Sapsford and Morgan, 1994). Interestingly, a stylised fact is that connnodity-price
volatility echoes variability in exchange rates since the switch to floating by major
currencies in the early 1970s. Whilst it is true that connnodityprices and exchange rates
are both asset prices that respond to news instantaneously, can something stronger be said
about causation? Is exchange rate volatility responsible for the wide swings in
connnodityprices? Interestingly, this is the exact opposite to the question considered by
Freebairn (in Chapter 9 of this volume), whereby the values of connnodity currencies
(such as, the Australian dollar) respond to changes in world connnodity prices. In this
chapter, we demonstrate that under the condition of purchasing power parity (PPP)
holding for traded goods only, variations in exchange rates of dominant countries can be
said to cause changes in the world connnodity prices.
What follows are brief analytical notes on the interactions between exchange rates
and commodity prices. The objective is to set the stage for further rigorous analysis on
this topic to follow in subsequent chapters. The material in this chapter is largely based
on an approach first used by Ridler and Yandle (1972), and subsequently further
developed by Sjaastad (1985). A similar approach was also developed by Dornbusch
(1987). The chapter is organised as follows. In the next section, we provide some
illustrations of the issues using gold and iron-ore prices as examples. Section 2 presents
a stylised model to determine the effects of exchange-rate changes on the internal and
external prices of commodities. This is followed in Section 3 with a simple geometric
exposition of the issues. Concluding comments are contained in the last section.
I. SOME ILLUSTRATIONS
We assume that PPP holds for individual commodities, but not for all goods (see
Chapter 2 of this volume for more details on PPP). For illustration purposes, we first use
the price gold as an example. Let
p
be the price of an ounce of gold in $US, p" be the
DM price and s be the spot exchange rate, the $US cost of 1 DM. Then, under PPP, we
have
p = (l+x)sp',
where x represents transportation costs and the effects of any other barriers to trade in
gold which cause a spread between the $US price,
p,
and the DM price converted to
$US, sp'. Let x be approximately constant, so that the PPP condition in change form is:
... "* = s~
p-p
(1)
where a "'"' indicates percentage change. In words, equation (1) states that the change in
the $US price of gold relative to its DM price equals the change in $US/DM exchange
rate (note that s > o if the DM appreciates or the $US depreciates). Now, consider a 10
percent depreciation of the $US relative to the DM, so that
s=10%. How is this
I0
percent relative-price change divided up between p and p"? The possibilities are:
(i)
p = 10%, p' = 0;
(ii)
p = o, p' =-10%; and
(iii)
p>O, p'<o with p+ [i3'[=10%.
These possibilities of internal and external price changes can be shown graphically in
Figure I. As will b.e shown later, if the US is a small country with respect to the world
gold market and Germany large, we are more likely to get case (i), and vice versa for
case (ii). When both countries have some market power (when they are able to change
the foreign currency price of gold), case (iii) pertains.
We now turn to iron ore prices as another example. Australia produces about 12
percent of the world's iron ore; and iron-ore exports from Australia represent almost 30
percent of the total world trade in iron ore. Thus,primafacie Australia can be considered
2
p
lO
{p, j).}
must lie along
this line
\
Rise in US
prices
..
45 11
-lO
p
0
Fall in
German prices
Figure 1. Internal and External Prices
as a large producer of iron ore in the world so that it can affect world prices. In other
words, Australian iron-ore producers as a whole face a downward-sloping demand curve.
Consider the effects of a 10 percent depreciation of the $A. This increases returns to
Australian iron ore producers in terms of $A, thereby increasing the profitability and
production ofiron ore as long as costs do not also increase equi-proportionally. Iron-ore
exports now go up and this increase in export volumes decreases the world price of iron
ore as Australia is a large producer. Hence, from equation (1), the $A price of iron ore,
p,
increases by less than 10 percent; j) < 10 percent as
s= 10 percent by assumption,
and j)' < 0 by the large-country effect.
The above examples illustrate a general principle. Suppose the Europeans
dominate the world gold market, so that an appreciation of the DM (=depreciation of the
$US) by 10 percent generates case (i) above. That is,
p($US) = 10%,
jl' (DM) = 0.
Here gold producers as a whole gain from the increase in the $US price of gold. By a
similar argument but now in reverse, iron ore producers as a whole are hurt by the
depreciation of the $A as that depresses world iron ore prices (in terms of foreign
currency). Thus, we obtain the general principle that producers of a commodity
3
dominated by a count1y whose currency appreciates will be better off. and producers of
a commodity dominated by a count1y whose currency depreciates will be worse off
2. A FORMAL MODEL
For simplicity, consider a commodity (any internationally-traded commodity, not
just gold or iron ore) produced only by one country and this country exports all of its
production. For this commodity, the domestic supply function is an increasing function of
the internal relative price:
q' =q' (
~)'
(2)
where p is the internal price of the commodity; Pis the general price index internally;
and pl P is the internal relative price. The corresponding foreign demand decreases with
the external relative price:
(3)
where p' / p' is the external relative price. Market clearing requires
(4)
As before, let PPP hold for this commodity, so that
(5)
•
p=sp.
We now use this model to determine the effect of a change in the exchange rate
on internal and external prices of the commodity. In change form, equations (2) and (3)
are
iJ'=e(fJ-fa)
qd = T/ ( j;' - fa') '
where e > o is the supply elasticity and T/ < o is the demand elasticity. Using equation (4)
in percentage change form, q·' = qd, and combining this with equation (5), we obtain
j;' = -a s+a fa+ (1-a)
fa', where a
= e / (e - T/)
is a positive fraction, or
f;'-P'=a(fa-fa' -s).
(6)
Equation (6) tells us the determinants of the relative price of the commodity in terms of
the foreign currency. That is, the change in this price is a positive fraction, a , of the
4
appreciation of the home country currency, adjusted for inflation. Note that the term in
the bracket on the right-hand side of equation (6) is the change in the real exchange rate.
When (fa-fa' -s) > O, there is a real appreciation of the domestic currency, and vice versa
for a real depreciation. It is obvious that if PPP holds for all goods, the real exchange rate
is constant: fa-fa' =s .
Next, we consider the relative price in terms of the home currency, (p-PJ. From
the PPP condition, this can be expressed as p-fa = p' + s-fa. From equation (6), this can
be expressed as
ft-fa =[-as+ a fa+ (1-aJfa'J+ s-fa.
Collecting the terms, we have
fi- fa= (I-a)( s-P +fa').
(7)
Note that the second bracketed term on the right-hand side of equation (7) is the same as
that in equation (6), except for the sign. We now consider equation (7) in conjunction
with equation (6). These two equations reveal that a given change in the real exchange
rate, fa- fa' -s, is divided up between a change in the external relative price, p' -fa', and
the internal relative price, p- P. The fraction of the real exchange rate change that "goes
to" the external price is a, while the remainder,
l-a,
goes to the internal price. If the
currency depreciates, then the world price falls by a times the depreciation, and the
domestic price rises by I- a times the depreciation. For example, suppose that the supply
elasticity B =I, and demand elasticity 77 = -1 so that a= B /(s-77) =I/ 2. Then ifthe homecountry' s currency depreciates by 10 percent in real terms, the world relative price of the
commodity decreases by 5 percent, while the internal price increases by 5 per cent.
It is to be emphasised that a =sl(s-77) is the key parameter in this framework.
The value of a determines if a country is considered large or small in a given
commodity market. A country is considered small if a = o, which occurs when
B
= 0 or j 77 I = ~.From our illustrations in the previous section, for example, the US is a
small country in the world gold market with a= O, as it faces a close-to-horizontal
demand curve at the world price for its gold output. On the other hand, a country is
considered large if a = I (when
B
= ~ or 77 = O). When the supply of the commodity is
highly elastic (relative to demand), a real depreciation stimulates exports to such an
extent that the world price falls by the full amount of the depreciation. Similarly, when
5
demand is completely inelastic, an increase in exports causes the world price to fall by a
large amount.
Since the share a is expressed in terms of the two parameters, its role can be
highlighted more elegantly in terms of equi-value contours. For this purpose, we rewrite
a= e/(E-T/)
as e=[a/(a-l)]T/ or, as T/ < 0,
l_!!__l
e = a-I 1T/I .
The above expression can be used to plot e against IT/ I for a given value of a, as in
Figure 2. As can be seen, for a fixed value of e, a falls as IT/ I rises. And as e rises with
IT/ I fixed,
a also rises. When a large country devalues, then from equation (6), it
depresses the world price of the commodity in question by a large amount. In the limit
when a=!,
j)'-i" = (fa-P'-s)
Similarly for small countries a= o and
.
(;J' - p• )= o. In this case, from equation (7), the
entire real depreciation is translated into an equi-proportional increase in the domestic
relative price of the commodity.
a= I
I
ll'=-
2
Supply
elasticity
0
Iq I
Demand
elasticity
Figure 2. Equi-Value Contours
3. A GEOMETRIC ANALYSIS
In this section, we provide a geometric exposition of the above ideas. We first consider
the relationship between relative prices at home (that is, in terms of domestic currency)
6
and those abroad (in terms of foreign currency). From PPP, we have p=sp' ,or dividing
through by the price level, P,
p_
p
=
p*
p*
p
p' .
s-.-
This equation states that, under PPP, the relative price at home equals that abroad
after adjusting for the real exchange rate, sP' ! P. We thus write the above equation as,
(8)
where R is the real exchange rate. From equation (8), if we hold the real exchange rate
constant atR
0
,
we can graph the internal relative price against the external, as in Figure 3.
In this figure, the ray from the origin, OX, is the real exchange rate schedule whose slope
is the real exchange rate. A real depreciation causes the ray to get steeper and to shift
from OX to OX' in Figure 3.
p_
x'
p
x
•
0
}!_
p'
Slope= R,,
Figure 3. Internal and External Relative Prices
Next, we consider the world market for the commodity. Recall the supply and
demand function for the commodity in question and the market clearing condition:
q'=q'(~} q'=q'(~}
q'=l·
If we increase the internal relative price pf P and hold p •/ p' constant, then supply rises
with demand unchanged, so that there is excess supply. That excess supply can be
7
eliminated by decreasing the external relative price
as this stimulates demand for
p • / p',
the commodity. This can be seen from Figure 4. Here the downward-sloping schedule
WW is the locus of relative prices for which the world market clears. Overall equilibrium
requires that the prices be such that we are located on ox and the WW schedule
simultaneously. The point E in Figure 5 is such an overall equilibrium, with (p/ P), and
(p•/ p'),
the associated relative prices. A real depreciation of the home currency causes
w
p_
p
B
excess
supply
w
A
•
p'
0
Figure 4. World-Market Clearing
the real exchange rate schedule to get steeper, which results in the new equilibrium point
E' in Figure 5. The real depreciations thus causes external prices of the commodity to
fall, and internal prices to rise.
p_
p
w
X'
x
E'
w
}!_
p'
0
Figure 5. Overall Equilibrium
8
As shown earlier, a small country (a= O) cannot affect world prices by a
depreciation of its currency, and in this case the WW schedule is vertical, as in Figure 6.
In this case, the internal relative price p / P rises by the full amount of the depreciation
and the world price is unchanged. On the other hand, the WW schedule is horizontal for a
large country (a=l), as in Figure 7. In this case, the world price falls by the full amount
of the depreciation, while the internal price remains constant.
w
p_
X'
p
/
x
w
a
p'
Figure 6.The Small-Country Case
p_
X'
p
x
E'
E
w
w
L
p•
a
Figure 7. The Large-Country Case
9
•
4. CONCLUSION
In this chapter we provided brief analytical notes on the interactions between exchange
rates and commodity prices. Using PPP as the building block, we introduced a stylised
model in which PPP holds for traded goods only. This model determines the impact of
real exchange rate changes on the relative prices of commodities. The model illustrates
the general principle that producers of a commodity dominated by a country whose
currency appreciates will be better off, and producers of a commodity dominated by a
country whose currency depreciates will be worse off. While the model is very simple
and stylised (the commodity is produced in one country only and sales of this commodity
are on the world market only), the above result holds in a more general setting, as is
shown by Sjaastad (1985).
10
REFERENCES
Dornbusch, R. (1987), Exchange rates economics: 1986. Economic Joumal, 97,
1-18.
Maizels, A. (1992), Commodities in crisis, Oxford: Clarendon Press.
Ridler, D. and Yandle, C. A. (1972), A simplified method for analysing the
effects of exchange rate changes on exports of a primary commodity, IMF Staff
Papers 19.
Sjaastad, L.A. (1985), Exchange rate regimes and the real rate of interest, in The
economics of the Carribbean Basin, eds. M. Connolly and J. McDermott, New
Yark: Praeger.
Sapsford, D. and Morgan, W., eds (1994), The economics of primmy
commodities: models, analysis and policy, London: Edward Elgar Publishing.
11
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