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Economic Policy Review Volume 3
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CHAPTER 2
THE MACROECONOMIC IMPLICATIONS OF DEVALUATION AND IMPORT RESTRICTION
by Wynne Godley and Robert M. May*
The main purpose of this paper is to set out a framework in terms of which a rigorous discussion of alternative trade strategies can proceed. It is not concerned with the legal, or what may broadly be called administrative, implications of the alternatives, but will demonstrate that on certain assumptions about macroeconomic relationship!. the gain to employment, real wages and prices brought about by import restriction iS extremely large compared with a policy of devaluation, particularly in the first few yeart. after the policy is introduced.
Introduction Through the last few years the CEPG has suggested
that largescale and longterm restriction of imports
may be necessary if the UK is to recover full employ
ment; also that protection may well moderate the rate
of inflation compared with a strategy of exchange rate
depreciation. These suggestions have so far met with
almost universal opposition, not least from profes
sional economists. The most influential modern works on international
trade theory [for example Johnson (1971) and Carden (1974)] explicitly make and maintain the assumption
that the quantity of output (and therefore presumably
employment) is given. The core of their argument
then concerns the response to alternative policies of
the terms of trade, which alone can generate any puta
tive benefits from protection. But, however elaborate
the theoretical superstructure which is erected on this
basis, such work must of its essence beg the major
policy question with which we are concerned; for this
central question is not merely through what agency
and how quickly full employment can be achieved
without protection, but whether it can be achieved
at all. This paper aims to give a simplified, but mathemati
cally rigorous, exposition of the macroeconomic impli
cations of alternative trade strategies. The problems
addressed here are in many respects the same as those in the study 'Import controls vs. devaluation' by Messrs. Corden, Little and Scott (CLS) which con
tested the views put forward by the CEPG in its first Economic Policy Review in February 1975. The intention here is not merely to answer the main points made
by CLS, but as a matter of methodology to fill a gap
between verbal argument [such as used by CLS and
by Corden (1977)1} and the crude presentation of numbers which emerge from computer simulations.
*The order of authorship was determined by the outcome of a backgammon contest lasting two days. One of us (RMM) is indebted to the King's College Research Centre for its hospitality, and to the US National Science Foundation for its support under Grant DEB 7510464. We are grateful to Francis Cripps, Gordon Hughes and Robert Neild for reading the manuscript and making useful suggestions, but responsibility rests of course with us.
!See Chapter 2 of On how to cope with Britain's trade position, Trade Policy Research Centre, January 1977. Corden's contribution has no penetration because it is unrigorous and dogmatic; those by Hugh Corbet and Brian Hindley contain a large number of errors, particularly on the properties of the CEPG model, that are best answered by referring readers to the technical manual by Fetherston (April 1976) of which there will be a revised version in the Spring of 1977.
When assumptions are not defined by precise equations, and mathematical theorems are absent, verbal argument can degenerate into something reminiscent ofthirte∑;:nth century scholasticism; conversely, in the absenceofanalytic understanding, the behaviour of a large computer model can be mistrusted, as depending on special choices of input data which are not necessarily acceptable and as being of course conditional on the model itself.
It was as a compromise between these two extremes that Cripps and Godley ( 1976, hereafter referred to as CG) recently presented a formal analysis of a relatively simple and highly aggregated model, which incorporates the essential assumptions of the full CEPG model. They were thus able to give relatively simple, and mathematically exact, formulae for the way quantities such as imports, exports, real national output and income behave under the well defined initial economic assumptions of the model. The CG study lies squarely in the tradition of classical applied mathematics: the aggregated model is a pedagogic device, whereby the dynamical properties of the underlying model can be discussed with a rigour that is difficult in verbal exposition, and with an understanding that is difficult in large computer studies.
The present paper is complementary to CG but different in the crucial respect that, whereas CG explicitly omitted shortterm dynamics and looked only at the longterm behaviour of their model, the present paper is focussed on shortterm dynamical responses, and particularly on the shortterm dynamical differences in real national output, real national income, and real disposable wages under various policy options.
It cannot be too strongly emphasised that the purpose of this paper is to describe precisely how an economy would work under well defined assumptions. To the extent that the a.!isumptions are artificial so are the theorems and numerical results. It will only be in the final section that some tentative speculations will be made as tu the operational significance of this work; and even in this section artificial assumptions about what may broadly be termed administrative feasibility have been retained.
Aims and policy instruments We assume that the object of policy is simultaneously to achieve target values for employment and for the
32
The Macroeconomic implications ofdevaluation and import restriction
current balance of payments. The model employed combines the 'elasticity' approach to the balance of payments (in which exports and imports are determined by relative prices) with a simple 'portfolio balance' approach, in which the stock of financial assets owned by the private sector is kept in some relationship to its disposable income. The policy instruments available for the task are assumed to be tariffs on imports (at a rate tm), subsidies on exports (at a rate sx), valueaddedtaxes on personal consumption (at a rate tva1), and import quotas (amounting to an ex ante import volume reduction 'ffiq). We assume in our model that foreign countries do not retaliate against our exports if tariffs or quotas are imposed, nor do they indulge in competitive devaluation.
Although much of the formal discussion is in terms of a combination of the above policy instruments, the basic interest lies in the comparison between pure strategies of devaluation, versus two kinds of import restrictions, namely tar~ffs only or quotas only, these three strategies being special cases of the general com
bination of trr., Sx and mq. As is well known, to a close
approximation, a devaluation of x% is logically equi
valent to setting tm =Sx =x where tm is a tariff on all imports of goods and services. The main differences between a tax/subsidy scheme and devaluation arise because in the latter case there is a revaluation of foreign assets and net property income from abroad; we doubt whether such revaluation would significantly alter our results. A tariffonly policy will generally apply to selected categories of imports only.
The assumptions of our model make it unnecessary to give separate consideration to monetary policy or to the capital account of the balance of payments. This is (1) because the stock of financial assets which the private sector holds in a given relation to income is assumed to include net foreign assets, and (2) because the target for external finance is assumed to be current balance of payments. Implicitly the latter involves us in a supposition that private capital outflows on the balance of payments are either prevented or can be financed by official borrowing or reserves. 1
The accounting framework
The device we have used to display the differences
between trade strategies is to compare the conse
quences of each with some alternative evolution of
the economy in which none of them is adopted. This
technique of analysing changes compared with 'base
line' values, using linearised approximations (defined
more fully below) to treat the ensuing equations, is
widely used for dealing with dynamical syst
ems in the physical and biological sciences, and gives
relatively simple results which are accurate to within
well defined limits.
The 'baseline economy' may be written in terms of
the national income identity at current prices
Y~~XP~+G~+XjM~FCA~
(I)
IThese are probably not strong assumptions in the present
context, since we are undertaking comparisons between alternative situations in each of which the private sector's stock of
financial assets is assumed to be throughout in the same ratio to its disposable income, while in the long term the current balance of payments and also the public sector's borrowing
requirement are tending to be the same as well.
where Y~ =national income and output
XP~ =private expenditure at market prices
(consumption and investment)
G*t
Xi, M~ FCA i
=government expenditure on goods and services
=exports, imports of goods and services =net indirect taxes.
In order to focus attention on the problem of un
employment which is now assuming such importance
in the UK, it will be assumed that in the baseline
economy the current balance of payments (X*M*)
is always zero while unemployment is high and con
tinuously rising. Naturally for such an evolution to
occur it has to be assumed that the conditions for
simultaneous internal and external balance are not
fulfilled, and that the zero current balance is only
achieved by the government using fiscal and monetary
policy to keep the growth of output progressively
lower than that of productive potential.
An unrealistic assumption is now made (to which
we shall return later) that average money earnings are
the same under each alternative as in the baseline
economy.
The various trade strategies may now be explored
by analysing the differences made by each of them to
the baseline economy, these differences being repre
sented throughout by unstarred symbols. As changes
in public expenditure are excluded by assumption from
the policy instruments, differences (compared with the
baseline economy) may be written as
Y1=XP1+X1M1FCA 1
(2)
where all variables are measured at current prices and
Yt=XPt+x;iJtFCAt
(3)
where the bar denotes that the variables are all measured at the prices of the baseline economy. Thus, notwithstanding that equation (I) is entirely in current prices, Y/Y*,X/X*,M/M* etc. measure proportionate additions to output and to the components of demand at constant prices.
For exports, imports and private expenditure the relationship between equations (2) and (3) follows logically from accounting identities. Thus
Xt=X1.IIX1+X ~(11X1 1)
(4)
M 1=M1.IIM1+M ~(IIM,1)
(5)
XPt=XP1.IIXP1+XP ~(IIXP,1)
(6)
where IIX, liM and IIXP represent the ratios of the
prices of exports, imports and private expenditure to
their levels in the baseline economy. The value of the
change in net indirect taxes is
FCA 1=FCA 1+TM1+TV1SX1
(7)
where TM, TV and SX are money yields from dis
cretionary changes in tax and subsidy rates (tm∑ tvat
and sx) while FCA is the money yield from existing
indirect tax rates resulting from XP 1∑
The trade responses To a good approximation, the response of import
prices to a tariff on imports will be immediate. The
tariff may, however, not be fully passed on, so that the
import price subsequent to the introduction of tariff
r,.. takes the form
11M=1vt"'
(8)
33
Economic Policy Review
The cumtax import price will be:
JIM (cum tax)==(lvtm)(l+tm)
Or, to a good approximation:
JIM (cum tax}~ 1+(1v)tm
(9)
Similarly, the effect of subsidies on export prices is to produce in the absence of tariffs on imports:
JIX=lusre.
O<u<l
(10)
If there is a tariff on all imports imposed simultaneous
ly with the subsidy on exports, the export price dif
ference is assumed to take the form
JIX=Ius.,+w'(lv)tm
(11)
where w' is the proportion of costs (excluding profits)
taken by imports.! In the case of a tariffonly policy it
will be assumed that a 'tariff drawback' will simul
taneously be introduced, i.e., exporters can reclaim the
tariff element in their own costs so that w' =0 in such a case. The fact that tariffs entering export costs are assumed to be rebated under a tariff strategy requires that to reduce JIM (i.e. the average price of all imports) by the amount shown in equation (8) the rate of tariff must exceed trn∑ We shall assume that the import content of private expenditure is roughly equal to that of exports and that the import content of government expenditure is nil. Accordingly for the tariff strategy the rate at which the tariff has to be
calculated is given by
frn ,_f,. (XP*+X*) XP*
(12)
In future, wherever the term tm is used in an expression to describe a tariff strategy, this must be understood as the average rate of tax on all imports implied by the rate tm applied selectively. As the import prices of basic materials are for the most part determined in world markets and price 'shading' most typically occurs in the case of manufactured goods, there is reason to suppose that v will take on a greater value the more tariffs are applied selectively.
Changes in the terms of trade, according to equa
tions (9) and (11) are:
TT=IlX= 1us,.+w'(lv)tm IIM 1vt,
(13)
~ 1usx+[v+w'(lv)]tm
For a country like the UK, whose exports are predominantly manufactures and the majority of whose imports are food and materials, it may uncontroversially be assumed that u>v+w'(lv). Equation (13)
then says that devaluation Urn =Sx) worsens the terms
of trade compared with the baseline economy, and tariffs (Sx=w' =0, tm o4=0) improve them.
Jt also says that quotas (tm=Sre =0) leave the terms of trade unchanged so long as it is assumed that foreign suppliers do not raise their prices at all in response to such restrictions.
The relationship between changes in the prices and volumes of exports and imports are represented as loglog equations and are incorporated as such in
CG. We are content here with the linear approximation,
(14)
where E1 represents the price elasticity of foreign demand for exports. The subscript t has been retained,
because although price changes occur almost instan
taneously, the consequent export volume changes
involve time lags. We write E for the longterm (asymp
totic) value of E1∑ Such asymptotic values are used throughout CG, which deliberately ignores short
term effects. Note that equations (10) and (14) can be
combined_!o give X directly as a function of sre and tm
Xt=E 1[us.,w'(lv)tmJXt
(15)
The corresponding empirical relation for the change
in ex ante import volume, m1 in response to changes
in prices is
i1it='7t M':'(JIM[cum tax]1).
(16)
That is, using equation (9) to introduce tariffs explicitly,
(17)
where '7 is the price elasticity of demand for imports. Just as the value of vis likely to be higher if tariffs are applied selectively to competitive rather than complementary imports, so also is the value of '7∑
Changes in real national output
Our device for comparison of the three strategies is
first to assume that under each of them the current
balance of payments is held (as in our preferred base
line economy) to zero throughout, by whatever mani
pulation of the internal tax rate (tvat) is necessary.
Given this assumption it is easy to solve for Y and the
detailed steps are given in Appendix C. To first order
in s., and tm (i.e. neglecting terms which involve the
product of two or more such quantities), the result is
p. Y1=[us,w'(lv)t,.][E1l]X*
+ t , M * [ v + ' 7 1( l  v ) ]
(18)
Here p. is the marginal propensity to import (relative
to GOP volume). 2
This overall change in Y is a mixture of price effects,
which are expressed immediately, and volume effects,
which are lagged. In the long term, the system settles
to its asymptotic value (with E1=E and '7t='J), of which the longterm dynamics are discussed in CG.
The following theorem brings devaluation (s, =t"' =
t d∑v) and import tariffs, (s.,=O and t,.' =t1at) into
equivalence so far as the longterm value for Y is con
cerned, so long as it is assumed that X* =M* and
forgetting the complication that v and '7 will tend to
be higher (not necessarily by an equal proportionate
amount) the more tariffs are directed toward com
petitive imports.
~=
t,1"',
~+ ~
[uw'(lv)][Ei]\ v+'7(1v) /
8
(19)
where B==XP*+X* XP*
!Should devaluation be used, instead of t,. and Sz liM will equal the change in the 'dollar' price of imports, while liM (cum tax) will be the change in the sterling pnce of imports. IIX represents the fall in the dollar pnce under devaluation; the sterling price of exports rises under this assumption
IIX= I +(1u)s,+w'(lv)t,.
34
2 Strictly speaking we are postulating in ,_,a fixed relationship between an addition to output and an addition to imports beth measured at the current prices of the baseline economy in year t.
This would produce nonsense answers if the baseline economy contained significant changes in the terms of trade, so we are assuming that it does not do so.
The Macroeconomic implications ofdevaluation and import restriction
In the case of quotas it is assumed that the scheme
is operated by cutting some category of imports and
holding them. at that level subsequently, thereby re
ducing the marginal propensity to import compared
with lk∑ If we can assume that quotas can be made
instantly effective, the solution for Yis simply
P' Y=mq.
(20)
where the prime indicates a different (lower) marginal
propensity.
The following two expressions bring quotas into
equivalence, for a given long term value for •; with
devaluation and tariffs.
fflq=fdev{[uw'(lv)][El]X*
+[v+(lvh]M*} [P'IP]
(21)
Omq=ftarM*[v+(lvh][P'fP]
(22)
We now consider the short term dynamics, en route
to a common asymptotic value of Y.
For import quotas there is no dynamical behaviour
for Y under our assumption that the balance of pay
ments does not change at any stage. We may there
fore simply adopt equation (20) above and write a
time subscript under Y:
For tariffs, equation (18) becomes
fJ Y; (tariff)=tm[v+1j1(1v)]M*
(2~
Note that, even if the volume response is slow, Y1
must always be positive for all reasonable values of the
parameters.
For devaluation, equation (18) becomes
P f 1(devaluation)=tm{[uw'(lv)][E1l]X*
+ [v+77t0v)]M*} (24)
In the exportdriven term, the price response pro
vides an immediate negative effect and the volume
response provides a lagged positive effect. Although
the volume response will make Y positive in the long
run (so long as the Marshall Lerner conditions are
satisfied) there can easily be shortterm net negative
effects. Indeed as we shall see, these shortterm nega
tive effects can be sufficiently substantial to overcome
the importdriven term, leading to a net initial
decrease in Y.
Put in a more conventional way, if the terms of
trade move adversely_ quickly and the volume responses
are slow, the condition we have imposed that the current
balance is always zero may require that tvat be initially
raised on a scale which will cause Y to be negative.
Changes in the real national income
Changes compared with the baseline economy in the
real national income, YR, are determined by changes
in the real national output, Y, and in the terms of
trade, TT. To a linearised approximation, we have (so
long as X* =M*)
Y'R 1= ~+M*(TTI)
which may be approximated by
(25)
Y_!.t= Yt+{[v+w'(Iv)]tmus.,}M*
(26)
with Y1 given by equation ( 18).
f
The rom
volume
Y: by a
of real national income YR n unlagged term which is
1 then differs positive for
tariffs, zero for quotas, and negative for devaluation:
YR1(tariff)= Y 1 (tariff)+vtm M*,
(27)
YR1(quotas)= Y; (quotas),
(28)
YR1 (devaluation)
= Y1 (devaluation)[uw'(lv)v]tmM*. (29)
Thus for a given longterm value of Y, real national
income will be least with devaluation and greatest
with tariffs, while in view of the shortterm dynamical properties of Y that have just been discussed, these trends in YR under the three strategies will be (proportionately) more pronounced in the short term than in the long.
Changes in real takehome pay There are three reasons why under each strategy the proportionate change in real disposable wages will be different from that in the real national income. First, since government expenditure on goods and services is assumed to be given, the whole of YR accrues to private expenditure. Second, the three strategies imply differences in the distribution of real private disposable income between pay and other income. Third, as the initial response of the private sector to changes in disposable income is, in part, to accumulate financial assets, the level of internal taxes has to be different if all the output generated by the different strategies is to be bought.
The addition to real takehome pay has three components; that which is received by people entering employment who would otherwise be unemployed, that which derives from higher overtime pay for those already in employment and that which results from alterations to the level of consumer prices. It is this last category which is of particular interest because, apart from the importance of prices per se, what is being measured is the alteration in the posttax real purchasing power of a standard hour's work. Recall that we have so far assumed money wages given, so the differences in price behaviour are crucially important with regard to the inflationary tension they generate.
It will emerge that in each case the benefit (or loss) to average real pay is larger than that to real national income, this benefit (or loss) always being additional to the effect on employment.
Our assumption about consumer prices is that these are determined entirely by (normal) unit costs and indirect tax rates. Lags can be ignored, because indirect taxes are generally passed on immediately, while the cost of materials is passed on with a mean lag of well under half a year.
More specifically (normal unit labour costs being given), it is assumed for a tariff strategy that
llCt=[(lvtm')(l +tm')w+(lw)](l +tvat,)t
::::=I +w(lv)tm' +tvatot
(30)
where llC represents consumer prices as a ratio of∑
those in the baseline economy. For a devaluation strategy the expression is identical except that t ,, should be substituted for tm'∑ For quotas t m=tm' =0. The formula for consumer prices implies that neither foreign exporters nor domestic importers raise their prices under a quota strategy.
To obtain consumer prices we now have to find an. expression for 1vat∑ the change in the indirect tax rate which, it has been assumed, is continuously adjusted so as to keep X =M, and this is by far the most compli∑ cated part of the exercise. The main economic assumption which has to be made concerns the relationship between disposable income and the stock of financial assets held by the private sector; this relationship may alternatively be expressed in terms of the relationship between the additional disposable private income
35
Economic Policy Review
which is created and the expenditure which this,
in turn, generates.
Our assumption about the relationship between
disposable income and the stock of financial assets
takes the form
SFA =(1a)(lTd) Y
(31)
where SFA is the stock of financial assets (compared
with that in the baseline economy) and Td is the mar
ginal direct tax rate on total private factor income.
Equation (31) may alternatively be written (since
L,SFA =(1Ta) Y XP) as the aggregate expenditure
function
XPt=a(lTd) Y;+(la)( lTd) Y1_ 1 (32)
The tedious manoeuvres which, using this equation,
link Y1 with fvat∑t have been banished to Appendix C.
The expression for tvat corresponding to any long
term value for Ylinearises to
frot.OO=
where T; is the baseline marginal rate of indirect tax on private expenditure, y is the proportion ofXP*taken by personal consumption, and a1 and a2 are constants which are precisely defined in Appendix C. Thus equation (32) says so long as the Marshall Lerner condi
tions hold in the long run (i.e. Y00 is positive when X=
M) and if a1 and a2 are roughly equal, tvnt will ulti
mately be reduced under all three strategies. It will be reduced most under the tariff strategy; and more or less with quotas compared with devaluation depending on the relative size of a, and Oz.
Note that net acquisition of financial assets by the government, overseas and private sectors must sum to
nil. Therefore it fvut is set so as to achieve a zero current balance of payments, while in eguilibrium
Y(lT a) XP is roughly equal to zero, it follows that the ex post public sector financial deficit is (in the long run) unchanged under every strategy. In other words the changed yield from baseline tax rates must, under these assumptions, equal the net yield of the discretionary changes in tax and subsidy rates. Formally
+Td Y +41XP=t,.(M*+M)+s,(X*+X) yt,,ntCXP* XP)
(33)
Empirical relations and numerical results In this section we shall infer some numerical results which are appropriate for the British economy under
certain well specified assumptions. The empirical relations which are crucially impor
tant for producing illustrative numbers are the price and volume response of exports and imports to sx and
t"" the way consumer prices are determined and the ∑ relationship between private disposable income and
expenditure. It is assumed that v=O∑I, whereupon equation (8)
says that a 10% tariff on all imports of goods and services leads to a L% lowering of ex~tax import prices.
(A 10% devaluation under the counterpart assumption would lead to a 9% rise in sterling import prices.)'
It has been assumed that u=0∑6 and that w' =0∑33, so equation (II) says that with t,=s,=IO%, export
1We are writing as though the complications of the 'green' currencies do not exist.
36
prices (in both sterling and 'dollar' terms) fall by 3%. (A 10% devaluation would (under a counterpart assumption) lead to a 3% fall in 'dollar' prices and therefore a 7% rise in sterling export prices.)2
We take 2∑5 and 0∑5 as acceptable values for" and 71 in the UK, the aggregate longrun price elasticities of demand for respectively exports and imports. The low figure for 71 is consistent with an elasticity of about 2 for imports of finished manufactures.
These numbers are sufficient to evaluate equation ( 19), which brings tariffs and devaluation into equivalence with one another. The expression implies that if confined to goods not entering into export costs the rate of tariff (t,.') would have to be just over twice as large as devaluation to produce the same longterm
value for Y (ignoring once again that if tariffs are
selectively applied v and 71 would both be higher). If the tariffs were confined to finished manufactures they would have to be at a higher rate still, though probably only a little, for while the value of v might be slightly larger, the price elasticity of demand 71 would be very much higher, probably as high as 2.
So far as the temporal behaviour of the empirical coefficients "t and 'Y/t are concerned, we have assumed that it would take three years for each to obtain its asymptotic value. Thus, supposing the measures are imposed at the beginning of year I, it is assumed the volume responses would be complete after three years, giving 10 %. 25 ~;.;, 60 ~~ and 100% of the asymptotic values in the annual totals for years 1, 2, 3 and 4.
These empirical relationships enable us to evaluate for each strategy the magnitude of the gestures required to achieve some given increase in output and employment, together with its time profile, so long as we continue to assume that fiscal policy is in each case continuously adjusted so as to keep the balance of payments unchanged.
Let us suppose the baseline economy is roughly the same as the British economy in 1975, i.e., the crucial ratios are those implied by the following numbers:
X*=M*=£27b. PX*=£75b. G*=£32b. FCA*=£10b.
Y*=£97b. As personal consumption was £63b., y=0∑84.
We have already assigned values to "∑ 71, u and v (namely 2∑5, 0∑5, 0∑6 and 0∑1}. We further assume that 1'=0∑35 and 1', =0∑25, the rather large difference between the two arising because it is on finished manufactures (for which the marginal propensity for import is very large) that the main restrictions would fall. We assume finally that T;=O∑I, T,1=0∑3.
Now should the objective be to raise real output by 10%, thereby ultimately raising employment by about 5% and reducing unemployment by about 3% (or 750,000), equations (18) and (20) imply that the necessary step devaluation would be 12t %, the average rate of tariff on imports of goods and services entering
domestic expenditure would have to be 31 %, while
2We write throughout using linear approximations. In realit> simulation of a 10% devaluation would require s,=O∑IO, r,. =0∑11 =('o"o~ I). The 3% fall in dollar prices under devaluation would therefore become an 8% rise in sterling pricew (i.e. H ∑ I). Similarly the nonlinearised rise in import prices would be 10~~ (i.e. ~~I).
The Macroeconomic implications ofdevaluation and import restriction
the reduction in imports by quota restriction (compared with what otherwise would have happened) would initially have to be worth 9% of M* i.e., about £2t billion in the UK economy, rising ultimately to about £3 ~ billion (both at 1976 prices).
In calculating numerical values for the counterpart changes in consumer prices, we make the assumption that in equation (31) a=0∑6.
Now, using equations (20) (23) (24) (27) (28) (29) (30) and (32), we can write down values for all the crucial variables, assuming that the longterm addition to GDP is I 0% and that the current balance is not allowed to change.
These results must not without heavy qualification be taken as realistic estimates of what could happen under the alternative trade strategies, because of the uncertainty of some of the assumptions employed; it is important to recall nevertheless that any benefit to real takehome pay caused by lower consumer prices is additional to any benefit from higher employment and overtime.
As the assumption that the balance of payments is not allowed to change at any stage is an extreme one, involving enormous difficulties in its execution, we
have reworked the answers, using the same assumptions about trade policy instruments, but setting tvot immediately at its longterm value. Thus the consumer price change is fixed for each option and the dynamics are thrown back into output and the balance of payments; the detailed mathematical relationships are given fully in Appendix C. Assessment We first note that there are legal, institutional, diplomatic and administrative obstacles to our freedom to use trade policy instruments, including devaluation, in the way so far assumed; and that foreign countries may render any or all of these policies ineffective by retaliation. Beyond observing that as a matter of history certain countries, e.g. Germany and Japan, have maintained protection for long periods (and thrived under it) these points will not be further discussed here, although it is recognised that they may singly or together make it impossible to implement any of the strategies under review.
What we briefly discuss in this final section, having made a heroic assumption about what may broadly be called administrative feasibility, is the validity of our results as predictions conditional on such feasibility.
Numbers for crucial variables assuming Y/Y*=lO% in long term and X=M throughout. Per cent changes compared with the 'baseline economy'
Year
12 34 5
A. Devaluation (at 12! %)
f vut
Consumer prices
0∑8 1∑5 1∑0
+2∑8
+1∑0 +0∑3 2∑3
+1∑5
+5∑2 +4∑5 5∑9 2∑1
+10∑0 +9∑3 9∑2 5∑4
B. Tariffs (on goods and services entering domestic expenditure) at 30∑9 %
y
+2∑6
+3∑9
+6∑7
+101)
YR
+3∑3
+4∑5
+7∑4
+10∑6
fvat
121
12∑5
14∑9
17∑2
Consumer prices
2∑8
_:.3∑2
5∑6
7∑9
+ID0 +9∑3 7∑3 3∑4
+10∑0 +10∑6 __) 15∑8 6∑5
C. Quotas (cutting by 9% ofM*)
Y=YR
+10∑0
t∑vut 10∑5
Consumer prices
 10∑5
+10∑0 6∑3 6∑3
+10∑0 6∑3 6∑3
+10∑0 6∑3 6∑3
+10∑0 6∑3 6∑3
Numerical.results assuming Y/Y*=10%in the long term but witht.,at fixed initially at its longterm value
Year
12 34 5 6
A. 12~~;,; devaluation, 7∑3% reduction in tvat Change in consumer prices is3.4% throughout
7
Y(%) YR(%) XM(£ b.)l
+3∑0 +2∑3 1∑2
+4∑9 +4∑2 13
+7∑0 +6∑3 0∑6
+9∑2 +8∑5 +0∑3
+98 +9∑1 +0∑1
+9∑9 +9∑2
0
+10∑0 +9∑3
0
B. 30∑9% tariff, 158% cut in tva 1 Change in consumer prices is 6∑3% throughout
Y(%) YR(%) XM(£ b.)l
+4∑9 +5∑5 0∑8
+6∑5
+7l 0∑9
+7∑9 +8∑5 0∑4
+9∑5 +10∑1
+0∑2
+9∑9 LJ0∑5
0
+10∑0 +10∑6
0
+ JOo() +10∑6
0
C. Quotas at 9 /'~ of M*, a cut of 6∑3% in tvat Change in consumer prices is 6∑3% throughout
Y=YR(%) XM (£ b.)l
+7∑1 +0∑7
+9∑2 +0∑2
+9∑8 +0∑1
+9∑9 0∑1
+10∑0 0
+10∑0 0
~ 10∑0 0
I Assuming X*=M*~ £27 billion.
r 37
Economic Policy Review
So far as the price and volume responses of exports and imports are concerned, we are pretty confident that we have attributed values to these which are about right and which most people will accept. It is worth noting that none of the 'repercussions' mentioned by Corden ( 1977) are important given our assumptions. As we have assumed a baseline economy which, like the UK economy, has high and growing unemployment, it is unnecessary to take account of capacity constraints. At the same time we have assumed a very high import content for all expenditure diverted to domestic purchases. Accordingly our
answers for real national output and income if M
could really be held equal to X would appear to be correspondingly well founded.
Our view about the determination of consumer prices is more controversial. Many would say that under the 'law of one price' the response of domestic producers of all goods which are competitive with imports will be to increase prices by fully as much as import prices; indeed the 'Scandinavian' theory of inflation and its transmission is based specifically on this assumption. Here, however, we are disposed to stick to what may appear an extreme position, since the law ot one price appears to have little empirical foundation. Indeed the very elaborate study by Coutts, Godley and Nordhaus (1977), which examines the relative m0vement of domestic and competitive import prices for seven UK industries over a period of several years, finds no effect of the latter on the former whatever. And, generally speaking, pure 'mark up' models of consumer price determination, such as those in Godley and Rowe (1964) and Coutts (1975), have given good results.
A more controversial major empirical assumption is that all private disposable income gets spent within two years, for which the econometric evidence is set out in Fetherston (1976). But those who disagree with this assumption (given that they accept the hitherto conventional view that income and output are determined by exogenous variables operating through a multiplier process) will, we believe, generally suppose the 'leaks' to be larger than we have assumedi.e. that the spending relative to income will tend to be less and take longer to materialise. But this would necessarily strengthen our answers, in the sense that it would require falls larger than we have entered for fvat (and therefore lower consumer prices) in the long term and even more violent changes in the short run. A qualification to this relationship should be addedthat any very violent change in total final sales would result in abnormal destocking and supply constraints, so for a time total expenditure would be lower in relation to ,disposable income than we have assumed; in other ∑words the shortterm output responses to the quota strategy look impossibly large. There is no reason, however, why the tax cuts could not be phased in much more gradually under a quota strategy, allowing the balance of payments to improve initially, with the result that the shortterm benefits to output and real income would be smaller.
Another very questionable major empirical assumption so far made is that average money wages would be unaffected by the adoption of any of the strategies.
38
There is a clear possibility, since it is only plausible to assume that fiscal policy must be operated so as to prevent a major deterioration in the current balance at any stage, that the response of money wages to the initial loss of real wages under the devaluation strategy will make the policy largely, if not wholly, ineffective; the implication of this could in one extreme case be that devaluation ultimately adds a fully equivalent amount to the rate of price inflation and nothing at all to real output or income. No parallel gualification needs to be made for the protectionist strategies, except on the assumption which is, to us, extremely implausible, that the initially higher pressure of demand for labour would operate, under some Phillips curve mechanism, to offset the benefits to the price level achieved directly.
If we ignore (without ever forgetting) that devaluation may be ineffective, by resuming the assumption that money wages are given, there remains a very difficult problem of assessing our results, which arises from the real difficulty of how fiscal policy should be conducted. For instance, it is not generally likely that a devaluation strategy could be accompanied by a simultaneous huge tax cut, leading to the balance of
payments being about £3 billion worse in total than it
woufd otherwise be in the first three years, any more than it is conceivable that quotas could be accompanied by an even more huge tax cut with output rising
I0% in the first year.
There is no simple way of setting out the alternatives comprehensively, particularly as the strategies could be combined in changing proportions, e.g. protection might gradually be phased out and devaluation substituted for it.
As there are major difficulties about the conduct of fiscal policy under each strategy, it seems that the crucial results are best presented as comparisons of the two protectionist strategies with devaluation on the two assumptions about fiscal policy already used and which may be regarded as extremes; these assumptions are, on the one hand that the balance of payments is held to zero throughout, on the other that fvat goes at once to its longterm value. The numbers below are simple inferences from the two previous tables.
What these figures show is that, apart from the substantial permanent increase in real pay, there is an enormous advantage during a longish transitional period (i.e. one lasting for two or three years) to output, employment, prices and real incomes in adopting a protectionist strategy and that these vastly exceed tli.e gain brought about via the terms of trade (which is of negligible importance). These advantages also dwarf any loss of 'consumer surplus', at least as estimated by Batchelor and Minford (1977). They also, in our judgement, are far larger than could be counteracted by any increase in prices charged by foreign exporters or domestic importers under a quota strategy.
It has become customary to refer to a protectionist strategy as 'the siege economy'. Under our assumptions the epithet is very inappropriate, since protection generates abundance, whereas a successful siege must result ultimately in starvation.
One final qualification should, however, be added, which may influence assessment of the very longterm
The Macroeconomic implications ofdevaluation and import restriction
consequences of alternative strategies. Under our assumptions a devaluation strategy if successful will, corresponding to a given level of domestic output and a given balance of payments, generate a higher level of both exports and imports and also of profits and
investment than a successful protectionist strategy; this could ultimately mean a better longterm trend of productivity and some modification of the relatively poor performance of real income and prices following .devaluation.
Year
2
A. Fiscal policy makes X= M throughout
(I) Tariffs compared with devaluation
y
Consumer prices
+3∑4 5∑6
+2∑9 4∑7
3
+1∑5 3.5
(2) Quotas compared with devaluation
y Consumer prices
+10∑8 13∑3
+9∑0 7∑8
+4∑8 4∑2
B. Fisc:d policy puts tvat immediately to its longterm value
(I) Tariffs compared with devaluation Difference to change in prices is 3∑1% throughout
y
XM (£b.)
+1∑9 +0∑4
+1∑6 +0∑4
+0∑9 +0∑2
(2) Quotas compared with devaluation Difference to change in prices is  2∑7% throughout
y
XM(£b.)
+4∑1 +1∑9
+4∑3 +1∑5
+2∑8 +0∑7
4
0 2∑5
0 0∑9
+0∑3 0∑1
+0∑7 0∑2
5
0 3∑1
0 2∑9
+0∑1 0∑1
+0∑2 0∑1
67
0 31
0 3∑1
0 2∑9
0 2∑9
+0∑1 0 00
+0∑1 0
0 0
APPENDIX A This appendix gives a glossary for the symbols employed in the paper. The catalogue is arranged under the headings of control variables, parameters and baseline values, and endogenous variables.
Control variables:
trn rate of tariff on imports ~, rate of subsidy to exports tvat rate of discretionary indirect tax
mq ex ante decrease in import volume, due to
quotas t,' rate of tariff applied selectively to imports
entering domestic private expenditure.
Parameters and baseline values :
X* 'base' value of exports M* 'base' value of imports XP* 'base' value of private expenditure T d marginal direct tax rate
T' marginal net indirect tax rate
v coefficient of response of import prices to tariffs
u coefficient of response of export prices to, subsidies
'YJ, E price elasticity of demand for imports, exports
w weight of imports in cost of private expenditure and exports
y weight of consumption in private expenditure fL marginal propensity to import (relative to
volume of real national output) a coefficient of private expenditure function w' share of imports in costs of exports: for pure
devaluation, we take w' = w; for pure tariffs we take w' =0.
Endogenous variables:
Here and below, symbols refer to changes in values at current prices (plain symbols) and at baseline prices (symbols with bars) compared with their baseline values. Prices (against a baseline normalised to unity) are denoted by the prefix II. In the following list the word 'volume' means that the variable is measured at baseline prices.
X volume of exports
m ex ante change in volume of imports
II X price of exports JIM price of imports.
TT terms of trade X value of exports M volume of imports M value of imports
39
Economic Policy Review
B current balance of payments (value) XP private expenditure (value) XP volume of private expenditure IIXP price of private expenditure Y value of real rtational output (GOP at factor
cost)
y volume GOP
yp value of private disposable income
YR volume of real national income FCA value of factor cost adjustment FCA volume of factor cost adjustment
sx value of export subsidy
TM value of tariff receipts TV value of receipts from discretionary indirect
tax TD value of direct tax receipts.
APPENDIX B
The equations for the endogenous variables are presented here without discussion. The first nine equations are simple definitions. These are followed by expressions for the values of various tax receipts, and then by nontrivial relations among the remaining endogenous variables. The economic assumptions underlying these equations are discussed in CG and elsewhere.
Y=B+XPFCA Y=X+XPMFCA YR= Y+M*(TTI) YP=YTD X=X. IIX+X*(IIXI) M=M. IIM+M*(IIMI) B=XM TT=IlXjiiM XP=[XPXP*(IIXP1)]/IIXP SX=sx(X*+X) TM=tm(M*+M)
(AI) (A2) (A3) (A4) (AS) (A6) (A7) (AS) (A9) (AIO) (All)
TV=tvatCXP*+XP)y
(Al2)
TD=Ta Y
(Al3)
FCA =T;XP
(Al4)
FCA=FCA+TM+TVSX
(Al5)
M=m+p.Y
(Al6)
XP1=a. YP1+(la). YP1_ 1 IIM=ivtm
(Al7) (AIS)
llX= 1us.,+w'(lv)tm
(Al9)
m1 =7J 1M*[IIM(I +tm)1] Xt=EtX*(IIX1)
(A20) (A21)
IIXP1=[(IIM)(I +t,)w+(Iw)] [I +Ytvat.t] (A22)
To a linearised approximation, (A22) becomes
IIXPt= I+w(lv)tm+Ytvat∑t
(A23)'
The price of private consumption (IIC) is the same as equation (A23) without yin the final term, so long as we assume the import content of private consumption is the same as that of total private expenditure.
APPENDIX C Here we use the basic relations catalogued in Appendix B to derive the equations discussed in the main text.
This is done in two parts. In Part/, we treat the policy variables tm, s., and ifiq as being set to those constant, predetermined values which in the long run produce the desired change in output volume; a general indirect tax on all consumption fvat.t. is finetuned so that the balance of payments remains unchanged at each time step, that is Bt =0. for all t>O. We thus derive expressions for the short
term dynamical behaviour of Y'1 and of tvd't∑t en route
to their long term goals.
In Part II ali the policy vm:iables tm, s.,, mq and t," 1
are set to their constant final values in one step; their values are such as eventually to produce the desired
value of Y00 in conjunction with B 00 =0. In this case
we give explicit expressions for the dynamical be
haviour of Y1 and of B1∑
Throughout, we linearise in the policy variables; all terms involving the product of two or more of the
quantities tm, s.,, ifiq, fvat are discarded. On the other
40
hand the direct and indirect tax rates T a and T 1 are treated exactly.
Note that once we have expressions for Y1 and for
the associated values of the policy variables (with fvat
itself being timedependent in Part 1), expressions for
YR1 and for the price of private consumption follow. From equations (A3) (AS) (A IS) and (A 19), the linear
ised approximation for the volume of real national
income is
YR1= Y1+(vtmUsx+w'[Iv]tm)M*
(A24)
Part I: B1=0
Throughout this first part, we take B1=0 (i.e. X =M at each time step), with this constraint being main
tained by appropriate controi of fvat.t∑
Substituting from equation (A5) for X, we can re
write equation (A6) as
M =[X∑IlX+ X*(IlX I)M*(IIM I )]/IIM (A25)
Thence equation (Al6) reads
p.Y1 =mt+X~ ∑ TT+X*(IIXI)/IIM
M*(IIM1)/IIM
(A26)
The Macroeconomic implications of devaluation and import restriction
We now substitute equations (Al8) (Al9) (A20) and
(A21) for m1, X~o JIX and JIM, to obtain (given the
constraint B1=0)
+fL 'Y;=tmM*["7t0v)+v/(lvtm)] [usxw'(Iv)tm]
X*[ e 1( 1  [ u s x  w ' ( I  v ) t m ] )  l ] / (1vtm). (A27)
Here Q is given by equation (A32), and the super
script 'dagger' on Y1_ 1 is to denote the definition that
Yt0 =fJ
(A39)
(which .makes for notational simplicity in equation
(A38}). Likewise for notational convenience we have
introduced
Under the linearised approximation discussed above this becomes
(A40) In the long run, we can use the asymptotic value
fL Y1=tmM*[v+1)1(1v)]
+X*[o; 1  l ] [ u s x  w ' ( I  v ) t m ]
(A28)
Y00 in equation (A38), to get the indirect tax rate
needed to keep B=O once the system has settled to
In the long run, once time delays in the volume
equilibrium:
responses of exports and imports have worked their way through the system, this gives
[yXP*(lT;)]tvat.XJ = [ 1T] Y oo +(a,sxa2tm)(IT;)yXP* (A41)
fLY00 =tmM*[v+1)(1v)] +X*[o;l][us.,w'(lv)tm]
(A29)
Here " and "7 are the asymptotic values of "t and 7Jt∑ This important formula gives the basic relationship
Here Y 00 is given by equation (A29), and the constant coefficients a 1 and a2 are defined to be
(IT1)yXP*a1=[u+( 1u)T]X*
(A42)
between the longterm cnange in volume of real
(1T;)yXP'"a2 =[v+(lv)T]M*
national output, and the associated values of the
+ wXP*(lv)(I Ti)Ta+w'X*(lv)(lT) (A43)
. export subsidy and import tariff rates. It remains to determine the value of lvat∑t required, at each time step, to maintain B1=0. As a first step, subtract equation (A2) from equation (A I) to get
Tis given by equation (A40). Using this equation (A41) for the asymptotic in
direct tax rate, we can express equation (A38) in a simpler form as
I
Y Y=(XX)(MM)+(XP XP)
fvat.t=fvat.oo+Z[(lT) Y00
(FCAFCA)
(A30)
(1aT) Y1+(la)TY/_i]
(A44)
Using the linearised versions of equations
Here z is the quantity
(A5) (A6) and (A9), this gives
i'. = 1/[yXP*( lT1)]
(A45)
Y Y=X*(JIX1)M*(JIMl) +XP*(JIXPl)(TM +TVSX) (A31)
In conjunction with the explicit expressions given earlier for JIX, JIM, JIXP, TM, TV and SX, this leads to the conclusion that the righthand side in equation (A31) is a constant:
(A32)
Here the constant Q is defined to be
fJ=[(lu)s,,+w'(lv)t m]X*+(lv)tm(wXP*M*) (A33)
Next we note that, from equation (A23), the linearised version of equation (A9) is
XP=XPXP*[w(lv)t,+ytvat]
(A34)
Then from equations (AI), (AI5) and (Al4), it
follows for B1=0 (as throughout Part I) that
Y=XP~XPT 1 TMTV+SX
(A35)
That is
Yt=XPI(IT;)yXP*(lT;)fvat.tf mM*
+s,X*+T1wXP*(lv)t.,.
(A36)
Finally, we combine equations (A 17), (A4) and
(Al3) to get
(A37)
Equation (A36) can now be expressed as a relation
between tvat∑t and Y1∑ Alternatively, using equation (A32), the relation is between the desired value of
tvnt∑t and Yt. the latter being known from equation
(A28). Thus at last we have
yXP*( 1T,)fvat∑t=(1aT) Yt+(la)TY't1 +sxX*tmM*+T1wXP*(Iv)t,.(l __:___T)Q (A38)
This derivation has perforce been a bit of a mess. Nevertheless, the essential results are clear. The longterm relations between the targeted values of Y and B, and the policy variables needed to attain those tar
gets, are given by equation (A29) for Y00 and equa
tion (A41) for the concomitant VAT rate needed to
maintain B=O. The shortterm dynamics of Y 1 are described by
equation (A28), and the corresponding shortterm
behaviour of the VAT rate (finetuned to keep B1 =oO at each time step) follows from equation (A44).
Part If: tw 1 is constant
We now turn to the case where all policy variables,
including the VAT rate, are set to constant values,
chosen to produce a given longterm change in Y
accompanied "by no longterm change in the balance
of payments, B 00 =0. The relations between the targeted asymptotic
values of
s.., m,l and
Y00 and B 00 , and
t vat are of course as
the policy variables t "" described above by equa
tion (A29) for Y00 and equation (A41) for the
indirect tax rate corresponding to Boc, =0.
Part II differs from Part I in that tvat is held con
stant, and consequently B1 manifests shortterm dynamical behaviour on its way to its asymptotic value of
zero: this contrasts with Part I, where B1 is held constant at zero, and the indirect tax rate exhibits time
dependence.
It is worth emphasising that the shortterm be
haviour of Y1 referred to throughout Part II is slightly
different from that in Part I (by virtue of the different
policy constraints); that is, the equations for Y1 are different. But the h1gterm value Y00 is common to
the two parts.
41
Economic Policy Review
For an equation connecting Y1 and Bt. we begin by
returning to equation (A3S), and noting that an addi
+tional term B1 sbould be inserted on the righthand
side (RHS) if B1 =F 0. The subsequent manipulations, which use equations (A34) and (A37) to replace XP and XP with Yin equation (A3S), and then use equa
tion (A32) to replace Y with Y, may be carried out ∑as above, mutatis mutandis. The result, as before, is equation (A38), but with two alterations: first, there
is an additional term +B1 on the RHS; second, the
indirect tax rate is not timedependent, but is constant, equal to the asymptotic value given by equation (A4D.
Substituting from equation (A41) into the altered
equation (A38), and rearranging, we get
(1aT)Yt=(la)TY1t_I +Bt+(lT) Y00 (A46)
Here Tis as defined by equation (A40), Y00 is giv~n
by equation (A29), and, as before, the dagger on yt
denotes that fto= .Q(as specified by equation (A39));
this convention.is motivated by the desire for compact
notation in equations (A38) and (A46))..
In order to obtain an explicit expression for the
dynamical behaviour of Y1 under a constant indirect
tax rate, we need to eliminate B1 in equation (A46).
To do this, note that from the definition (A7)
B t = X t  M1∑
(A47)
From the linearised versions of equations (AS) and
(A6), this becomes
B1=X1M1+X*(IIXl)M*(IIMl), (A48)
Or, using equations (A 16) (A 18) and (A 19)
B1=JJ Yt+(•1m1(USxw'[!v]tm)X*
+ v t mM*]
~A49)
The term in square brackets is immediately recognisable as the expression for the timedependent changes
in volume of real national output in Part I, equation
(A28). To avoid confusion between this expression for
volume output with the VAT rate finetuned to keep
B1=0, and the present Part II expression for Y1 with
constant indirect tax rate, we rechristen the former
as r?t: ftrp 1=mq+X*[E11][us.,w'(1v)tm]
+M*tm[v+1Jt(lv)]
(ASO)
(cf. equation (A28)). Then equation (A49) reads
B1=JJ(rp 1 Yt)
(AS!)
Notice that of course rp00 = Y00 (cf. equation (A29)), and thus B 00 =0, as it should.
Substituting equation (AS!) into equation (A46),
and rearranging, we finally obtain an expression for
the short term dynamical behaviour of Y1 under a
constant indirect tax rate:
~=
(1T) Yoo +( 1a)TYtt1 + JJrpt
(1aT+JJ)
(AS2)
This expression is to be read in conjunction with the
definitions (A29), (A39), (A40) and (ASO).
With the value of Y1 determined by equation (AS2), the short term dynamical behaviour of the balance of
payments under a constant indirect tax rate is given
by equation (A'il). In short, under a policy of a ∑constant ind:rect tax
rate, the longterm relationship between Y and B ( =0),
and the policy instruments lm, sx, mQ and tva.~> are as
before given by equations (A29) and (A41 ). The
shortterm dynamical response of Y1 is described by
equation (AS2), and of B1 by equatio11 (AS1).
BIBLIOGRAPHY Corbet, H. (1977) 'Britain's predicament in the struggle for an
open world economy', in On how to tope with Britain's trade position, by H. Corbet et a/. Trade Policy Research Centre, Thames Essay No. 8. Corden, W. M. (1974) Trade policy and economic welfare. Oxford, Clarendon Press. Corden, W. M., Little, I. M. D. and Scott, M. F. G. (1975) Import controls versus devaluation and Britain's economic prospects. Trade Policy Research Centre, Guest Paper No. 2. Corden, W. M. (1977) 'General analysis of import controls for balance of payments purposes', in On how to cope with Britain's trade position, by H. Corbet et al. Trade Policy Research Centre, Thames Essay No.8. Coutts, K. (1975) 'The outlook for retail prices during 1975'. Economic Policy Review, No. I, 1975. Coutts, K., Godley, W. and Nordhaus, W. D. Industrial pricing in the U.K. Department of Applied Economics Monograph 26 (forthcoming). Cambridge University Press. Cripps, F. and Godley, W. (1976), 'A formaL analysis of the Cambridge Economic Policy Group Model'. Economica, 43, pp. 335348.
42
Fetherston, M. J. (1975) 'Estimation of simultaneous relationships: a UK private expenditure function'. Department of Applied Economics, Cambridge (unpublished paper).
Fetherston, M. J. (1976) Technical manual of the CEPG model. Department of Applied Economics, Cambridge.
Godley, W. A. H. and Rowe, D. A. (1964) 'Retail and consumer
prices 19551963', National Institute Economic Review, No. 30, pp. 4457, November 1964. Hindley, B. (1977) 'Britain's economy as ~een by the Cambridge
group', in On how to cope with Britain's trade position, by H.
Corbet et a/. Trade Policy Research Centre, Thames E;say No.8.
Johnson, H. G. (1971) Aspects of the theory of tariffs. London,
Allen and Unwin. Kemeny, J. and Snell, J. L. (1972) Mathematical models in the
social sciences. Massachusetts lns:itute of Technology Press,
Cambndge, Mass. Maynard Smith, J. (1968) Mathematical ideos in biology. Cam
bridge University Press.
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Chapter 2
The Macroeconomic Implications of Devaluation and Import Restrictions
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Wynne Godley
Robert M May
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Economic Policy Review Volume 3, pages 32  42
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March 1977