Movie Industry: Protection and the Size of the
Market
Eduardo C. Andrade
Ibmec/ SP
Rua Maestro Cardim 1170/ 11o. andar
Paraíso - São Paulo - SP
01323-001 Brasil
e-mail: eduardo.andrade@ibmec.br
tel: 11-3175-2311
fax: 11-3175-2315
First Version: July 30th, 2002
This Version: July 30th, 2002
JEL Classi…cation: F13; L82
A bst r act
I st udy t he e¤ect s on economic welfare of an import tari¤ on foreign movies wit h t he revenues eit her t o subsidize out put or project s of home producers. T he analysis indicates t hat t he degree of t he optimum int er-vention reduces t he greater is t he market for home movies outside t he count ry.
Title: “ Movie Industry: Protecion and
the Size of the Market”
1
I nt r oduct ion
T he Amer ican movie industry dominates the world cinema. Although it does not make most feat ure movies, it isthe only one that reaches ever y market in the world. For example, the market shar e of the American motion pict ures in the European Union was about 70% in 1996. In Canada, 96% of all movies shown in t he theaters are foreign, primarily American. Even in Japan, America accounts for more than half the …lm industry. In contrast , foreign movies repr esents only a t iny fraction of the American market , with a share of less t han 3%.
It is no surprise t hat t he supremacy of t he American movie industry triggers movements in the rest of the wor ld to protect their local producers. In France, t here is a consumption tax on all movie tickets and the revenues are used to …nance t he French movie makers. T he Brazilian gover nment provide tax exemp-t ion, up exemp-to a cerexemp-tain limiexemp-t , exemp-to privaexemp-te companies exemp-thaexemp-t …nance culexemp-tural projecexemp-ts, including obviously new movies. There is pressure from many countries to ex-empt cult ural goods from internat ional agreementslowering trade barriers, with t he justi…cation that free tr ade can threat national cultur es.1
From a theoretical point of view, there is just i…cation for government inter-vention t o protect and/ or pr ovide …nancial support for local industr ies char ac-t er ized by incr easing r eac-turns ac-t o scale, such as ac-t he movie indusac-try.2 The
advan-t age of advan-the Amer ican producer s is exacadvan-tly advan-the facadvan-t advan-thaadvan-t advan-they can exploiadvan-t a big market at home. They can dillute t he high …xed costs in their own market and sell abroad at low marginal cost. Instead of r elying or demanding protection, one can argue that pr oducers from other countries should be more aggressive in t he international mar ket and not restrict t heir focus on the domestic market. However, the possibility of exploiting t he global mar ket scale is limited to these producers for one particular reason. Di¤erently fr om other goods traded in the internat ional market, movies have some characteristics that ar e ver y speci…c to some markets. One obvious example is the language. American consumer s do not enj oy watching movies in French, whereas this is a feature demanded by French consumers. As a result, ther e may exist an additional reason, beyond t he traditional one, to protect an industry charact erized by increasing returns t o scale as the outside market is restricted. T his possibility is analyzed here.
In this paper, I develop a model of a small countr y that pr oduces a ho-mogenous good and home movies, t he lat ter character ized by scale economies
1For more det ai ls on this pressur e, see T he Economist (1998).
2See Helpman and Kr ugman (1989) for a r eview of the t heor etical models wit h increasing
and product di¤erentiation, standar d feat ures in the literature.3 As there is
monopolistic competition in the movie industr y, there is room for government intervention. I consider two types of policies. First , t he government imposes an import tax on for eign movies to …nance the output subsidy to the home pr oduc-ers. Second, t he gover nment imposes the same tax to subsidize the home movie projects. Bot h interventions are welfare improving. The major conclusion that emerges fr om the analysis is that the optimal import tari¤ is lower, under both types of intervention, the greater is t he mar ket for home movies outside the countr y. In other words, the degree of the opt imal intervent ion r educes if the home movie industr y can exploit a greater market abroad. There are two papers close related t o this one, Flam and Helpman ( 1987) and Francois and Ypersele ( 2002). However, neither one considers the impact of the size of the market abr oad on the degree of intervention.4
T he model is developed in section 2. T hen, in section 3, I characterize t he equilibrium conditions. Welfare implicat ions are discussed in section 4 and conclusions ar e dr awn in the last section.
2
M odel
T here ar e assumed to be a lar ge number of potential home and foreign movies. T here are two types of individuals living in the home count ry. Type 1 individuals get ut ility only from consuming home movies. Type 2 individuals care only about consumption of foreign movies. T her e are “ f L ” individuals of the former type and “ (1 ¡ f )L ” individuals of the last type, where 0 < f < 1 and L > 0.
T ype 1’s and type 2’s economic problems ar e, respectively, the following:
max ln(X
i
cµi)1=µ;
such that ,
X
i
pici = w;
and,
max ln(X
i
c¤iµ)1=µ;
3For examples, see K rugman ( 1980) and K rugman ( 1981) .
4Flam and Helpman (1987) has a si milar fr amewor k to the one developed here. T hey
such that ,
(1 + t) p¤X
i
c¤i = w
where ci and pi are, respectively, the consumption and price of t he i th home
movie, c¤
i and p¤are, respectively, the consumption and pr ice of the ith foreign
movie, t is t he import tax on foreign movies, and w is the wage rate.5 The
par ameter µ is t he same for bot h groups and 0 < µ < 1.6 The number of home
movies actually pr oduced, n, will be assumed to be large, although smaller than t he potential r ange.7
T here will be assumed to be only one factor of product ion, labor . Total labor is equal to the home populat ion, L . T he home country produces two types of goods, the home di¤erentiat ed movies (xi) and an homogenous good (T) .
In the movie sector, I assume that every movie i is pr oduced with the same cost structure:
li = ® + ¯ xi
where li is labor used in pr oducing the it h movie, and xi is t he number of units
of t his movie, with ®; ¯ > 0. T he t er m ® can be seen as the project cost of the motion picture, wher eas ¯ is the constant production cost per unit of output. T herefore, average cost declines at all levels of output, but at a diminishing r ate. T his sector is characterized by monopolistic competit ion, with each …rm producing a di¤erent movie and having some monopoly power, but with entry of new …rms driving monopoly pr o…tst o zero. Let ¼i be the pro…ts of t he producer
of movie i. It can bewritten as:
¼i = (1 + z) pixi ¡ (®(1 ¡ s) + ¯ xi) w;
where z is the output subsidy, and s is the project subsidy. Output and project subsidy are two alternative ways of suppor ting the home movie industry.
In the homogenous good sector, which is characterized by perfect compet i-t ion, I assume i-t hai-t i-the cosi-t si-truci-ture is such i-thai-t i-ther e is consi-t ani-t mar ginal cost and no …xed cost. Therefore, tot al labor used in the production of T units of t he homogenous good is equal to:
lT = ¯TT, with ¯T > 0.
5Wit hout loss of gener al ity, I assume that p¤
i = p¤, for all i .
6As in K rugman ( 1981) , I use the l n uti lity function because of t wo useful proper ties. Fir st ,
it implies t hat every pr oducer faces a demand curve wit h elast icity 1
( 1¡ µ). Second, it simpli…es
t he welfare analysis per formed below.
7An alter native approach would be to have all people alike, with a t aste for bot h types
It is assumed that home individualsdo not obtain utility fr om consuming the homogenous good. T herefore, this good is only sold in the foreign mar ket. In order to have an equilibr ium in t he trade balance, total expenditures in foreign movies by type 2 individuals have t o be equal to tot al expenditures in home movies by foreign individuals (w¤) plus the total sales of the homogenous good
in the for eign mar ket. Hence, the trade balance equilibr ium condition is:
pTT + w¤= p¤
X
i
x¤ i;
where the exchange rate is set to be equal to one (the numeraire), pT is the
foreign price of the homogenous product, and x¤
i is the number of units of
t he foreign movie i imported by the home country. As home individuals do not consume the homogenousgood, it will be only produced in the home country asa way of obtaining resourcest o purchase foreign movies. I will impose some limits on the size of w¤and r estrain my analysis to the case in which total expenditures
on for eign movies (p¤P
i x¤i) is always greater than total expenditur es in home
movies by for eign individuals ( w¤). In other words, it is always necessary to
produce some amount of the homogenous good in order to …nance t otal impor ts, t hat is, pTT > 0.
T he home country is considered to be small. This assumption implies that it faces a given number of for eign movies, n¤, a given pr ice of the di¤erentiated
foreign movies, p¤, a given for eign spending on di¤erentiated home movies, w¤,
and a given foreign price of t he homogenous product, pT.
In order to complete the basic model, I need to spell the government’s prob-lem. It s objective function is to maximize the home country’s welfare function, which can be wr itt en as:
max f ln(X
i
cµi)1=µ+ (1 ¡ f ) ln(
X
i
c¤iµ)1=µ
I mentioned above that the gover nment can implement two types of policies. It can either provide an output or a project subsidy to the movie industry. Resources to …nance either policy is obtained only t hrough the int roduct ion of import t ax (t) on foreign movies. T he government budget constraint has to be in equilibrium, which implies that:
tp¤X
i
x¤i = sn®w + zX
i
pixi.
3
Equilibr ium Condit ions
D e…nit ion 1 Given w¤, n¤, p
T, and p¤, an equilibrium is character ized by
f cigni = 1, f c¤ign ¤
i = 1, f pigni= 1, f xigni = 1, w, T , n, t, s, z, , such that: ( i) given
f pigni = 1, n and w, f cigni= 1 solves the type 1 individual’s problem; (ii) given p¤,
and w, f c¤
i gni = 1 solves the type 2 individual’s problem; (iii) given pT, and w, T
solves the problem of the …rms in the homogenous sector; (iv) given f pjgj 6= i,
and w, pi solves the problem of the …rm that produces home movie i ; (v) the
zero pro…t condition holds in the movie sector , that is, ¼i = 0, for all i; (vi)
the labor market is in equilibrium, that is, L = lT + P i li; (vi i) given f cigni= 1,
f c¤ ign
¤
i = 1, and n, t, s, and z solve the government’s problem; and (viii) the trade
balance is in equilibr ium.
In order to …nd the competitive equilibrium, I will pr oceed in the following way. First, I will obtain the demand functions for home movies from the con-sumer’s problem. Second, the pr o…t-maximizing behavior by …rms is derived and the zero-pro…t condition indicates total output of each home movie. Thir d, t he t rade balance equilibr ium condit ion indicates the amount of homogenous good to be produced. Finally, t he labor market equilibrium condition indicates t he equilibrium number of di¤erentiated home movie.
T he …rst-order condit ion with respect to ci of the type 1 individual’sproblem
is equal to:
cµ¡ 1
i = ¸1pi
X
i
cµ i
where ¸1isthe marginal utility of income. Since all individuals type 1 are equal,
t hen xi = f L ci. Hence, the above equat ion can be rearranged in order to obtain
t he following demand curve facing the …rm that produces home movie i :
pi =
³
xi f L
´µ¡ 1
¸1
P
i
³
xi f L
´µ:
Using t his demand curve in the …rm’s …rst -order condition, I obtain the familiar r esult t hat the pr o…t-maximizing price is equal t o the mark-up pr ice8:
pi = µ¡ 1¯ w( 1 + z)¡ 1: (1)
Using the mark-up pr ice, the pr o…t function becomes:
8For si mpli city, I omitt here the foreign consumer’s problem. However , it is assumed that
each …rm faces t he same demand curve of home and for eign consumer s wi th an el asticity of
1
( 1¡ µ). In this case, each …rm char ges the same price at home and abroad. Al ternat ively, it
¼i = µ¡ 1¯ wxi ¡ (®(1 ¡ s) + ¯ xi) w:
T he zer o pro…t condition implies that :
xi = (1 ¡ s) ®µ¯ (1 ¡ µ) : (2)
T he implication isthat the price and the quantity produced of each di¤erentiated home movie are the same.
Wage is determined from the …rst-order condition of the …rms operating in t he homogenous good sector:
w = pT
¯T : (3)
From the trade balance condition and assuming wit hout loss of generality t hat p¤= p
T, one can get the t otal output of good T :
T = X
i
x¤i ¡ w ¤
pT :
From type 2 individual’s problem, one can show that he consumes the same amount of each of t he n¤foreign movies available. Asa result, the represent ative
type 2 agent buys c¤ = w
n¤p¤(1+ t ) units of each for eign movie. Since there are
( 1 ¡ f )L type 2 individuals, total units of for eign movies imported are equal to n¤x¤= n¤(1 ¡ f )L c¤= (1¡ f )L w
( 1+ t )p¤ . Using this result and equation (3), the t rade
balance condition becomes:
T = (1 ¡ f ) L (1 + t)¯T ¡
w¤
pT : (4)
In order to …nd the number of home movies pr oduced, I t urn now to the labor mar ket equilibr ium condition:
L = lT +
X
i
li = ¯TT +
X
i
(® + ¯ xi) :
Using equat ion ( 2) and (4) in the above equation, the number of di¤er ent local movies produced is equal to:
n = (1 ¡ µ) ®(1 ¡ µs)
·
L ¡ (1 ¡ f )L (1 + t) +
¯Tw¤
pT
¸
As a result of t he steps followed in this section, I obtain all variables of the model as a function of the policy variables under the control of the government ( t, z, and s). Hence, it is now possible to analyze the impact of the di¤er ent government policies on the economic welfare. Befor e turning to this analysis in the following section, it is convenient t o rewrite the government’s budget constraint, using the expressions obt ained in this section for n¤x¤, p and x.
T hen, it becomes equal to:
t(1 ¡ f )L (1 + t) = n®
·
s + z(1 ¡ s) (1 ¡ µ)(1 + z)
¸
: (6)
4
Welfar e A naly sis
I consider two typesof policiesand analyze their e¤ects on the economic welfare. First, the government imposes an import tax on foreign movies to …nance the out put subsidy to t he home producer s. Second, the government imposes the same tax to subsidize the home movie pr ojects.
In order to proceed wit h the analysis, it is necessary t o follow two steps. First, I …nd the expressions for n, c, and c¤ as a funct ion of t, the import tax,
which is the choice variable for the gover nment. Second, using these expressions in the welfar e function, I obt ain the optimal import t ax. Next subsections analyze each one of these policies.
4.1 I mpor t Tax and Out put Subsidy
Under the scheme in which t he government provides out put subsidy …nanced t hrough import t ax, s is set equal to zero. T hen, the government budget con-straint (equation (6))becomes:
z = t(1 ¡ f )L ( 1 ¡ µ)
n(1 + t)® ¡ t(1 ¡ f )L (1 ¡ µ): (7)
Using (3) and the assumption that pT = p¤ in individual type 2’s budget
constraint, I obtain c¤as a funct ion of t:
c¤(t) = 1 n¤(1 + t)¯
T
: (8)
Tot al imports of foreign movies decline with the import tax, as it should be. Government inter vention does not a¤ect individual’s wages9and p¤ is …xed
and exogenously given. W ith greater tax r ate, home individuals who cares only about foreign movies consume less goods. Obviously, they ar e made worst o¤ with the import t ax.
Using ( 7) in (5) , I obtain the number of di¤erentiat ed home movies (n) as a function of t:
n(t) = (1 ¡ µ) ®
·
L ¡ (1 ¡ f )L (1 + t) +
¯Tw¤
pT
¸
: (9)
Output subsidy …nanced t hrough import taxes allows each …rm that pr o-duces home movies to charge a lower price and still have posit ive pro…ts. As a consequence, more …rms are attracted to this market and it increases the number of di¤erentiated home movies (n) available in the new equilibrium.
From equation ( 9), one can see that the greater is the import tax, the great er is the number of di¤erent iated home movies produced. As less goods are im-ported, it is necessary a lower production of the homogenous good T in order t o be reached a trade balance. T herefore, more resources can be devoted to the production of home movies, which increases n.
Using (3), (1), (7), and (9) in individual type 1’s budget constraint, one can obt ain the expression of c as a function of t:
c(t) = ®µpT
(1 ¡ µ) ¯ [f pTL + ¯Tw¤]: (10)
Under this policy, note that c does not depend on t. The intuition behind t his result runs as follows. On the one hand, wit h t he reduction in the price of home movies, each consumer would be willing to consume more units of each home movie. On the other hand, as a greater number of home movies is available, each consumer would be inclined to reduce the consumption of the old home movies in or der to consume positive units of the new home movies. The net e¤ect, with the log utility function, is to maintain unaltered the number of units consumed of each home movie (c).10
Note that the individuals who care only about the consumption of home movies are better o¤ with the imposition of import t ax: c does not change but n increases.
T he number of di¤erent for eign movies pr oduced does not change with the local government inter vention. As the home country is small, this number is …xed and equal to n¤.
Government’s problem is to choose t he import t ax that maximizes t he wel-fare function W . On the one hand, import tax bene…ts individualswho consume home movies. On t he ot her hand, it hur ts individuals who cares only about for-eign movies. Its problem is the following:
max
t W = f ln[n( t)c(t)
µ]1=µ+ (1 ¡ f ) ln[n¤c¤(t)µ]1=µ;
subject to equations (7), (8), ( 9), and (10).
T he solution to the gover nment’s problem leads t o the following results.
10Kr ugman (1980) di scuss this issue and not es that in order to get an increase in scale,
P r op osi ti on 2 Under a policy regime with impor t tax and output subsidy, the optimum tax is equal to topt = (µ¡ 1¡ 1)pTf L ¡ ¯
Tw¤
pTL + ¯Tw¤ . Hence: (i ) if w
¤ = 0, then
topt = ¡1¡ µ µ
¢
f , (i i) if w¤> (1¡ µ)
µ f L w, then topt < 0; (i ii) if w¤< (1¡ µ)µ f L w,
then topt > 0.
P r op osi ti on 3 Under a policy regime with impor t tax and output subsidy, dto p t dw¤ <
0.
T he main point is what just i…es the potential gain in welfare due t o the introduction of the combination of import t ari¤ and output subsidy. Consider …rst the simplest case in which w¤ is equal to zero. W ith this assumption, the
opt imal import t ari¤ is positive. W ith a posit ive import tax, t otal imports is lower . As a consequence, the pr oduction of the homogenous good T , which is character ized by constant returns to scale, becomes less important. It oc-curs because homogenous good is only used to …nance t he purchase of foreign movies, the only impor ted good in this model. At t he same time, it becomes more lucrative to produce home movies, a sector char acterized by increasing r et urns to scale, wit h the boost received by t he output subsidy provided by the government . As a r esult of the government intervention, t he gains to consumers of home movies (type 1 consumer s) sur pass the losses of consumer s of foreigns movies ( type 2 consumers), increasing t he economic welfare. T he di¤er ence in t he nature of the production process in the home movies sect or vis-à-vis the homogenous good sector explains this result.
Pr oposit ion 2 indicates that the opt imal import t ari¤ is negatively related with the size of the market for home movies abr oad, that is, with w¤. A great er
w¤ works exactly in the same way as the introduction of t he import tax
men-t ioned above. When imen-t increases, men-there is a change in men-t he producmen-tion mix in favor of the sect or char acterized by increasing returns to scale. In other words, t here is a shift in the home production from the homogenous good to the home movies. As expor ts increase, it is less necessary to produce the homogenous good to exchange for foreign movies. As a result, t he optimal import tari¤ is lower .
Moreover, proposition 1 indicatest hat the opt imal import tari¤ is negative as w¤becomes greater than a critical value. T he intuition behind t his result is the
following. As discussed above, w¤plays the same role as t. As w¤incr eases, the
addit ional bene…ts to type 1 consumer s diminish and they do not compensate t he losses incurred by type 2 consumers of a greater import tax, due t o the concavity of the utility funct ion. It reaches a point, when w¤ is beyond the
critical value, that an increase in the welfare function can only be obtained by subsidizing the consumption (import of foreign movies) of type 2 consumers, t hat is, t < 0.
4.2 I mpor t Tax and Pr oject Subsidy
government ’s budget constr aint, becomes:
s = t(1 ¡ f )L
n(1 + t)®: (11)
As in t he previous subsect ion, using (3) and the assumption that pT = p¤ in
individual type 2’s budget constraint, I obtain c¤ as a function of t:
c¤(t) = 1 n¤(1 + t)¯
T
: (12)
As under the another type of government int ervention discussed in the pre-vious subsection, those individuals who consume only foreign movies are made worst o¤ wit h this new policy too. T he explanation is the same.
Using (11) in (5), the expr ession for n as a function of t is the following:
n(t) = ·
L + µ
µt(1 ¡ f )L ¡ (1 ¡ µ)(1 ¡ f )L ( 1 + t)( 1 ¡ µ)
¶
+ ¯ Tw¤ pT
¸ ( 1 ¡ µ)
® : (13)
Pr oject subsidy gives an incentive for …rms to invest in new pr ojects. It can be shown that the number of home movies (n) increases with the import tax, t hat is, the derivat ive of n with respect to t is positive. Hence, when an import t ax is imposed to …nance the project subsidy, it increases t he number of home movies.
Using ( 1) in individual type 1’s budget const raint, I obt ain t he expr ession for c as a function of t:
c(t) = µ
n(t)¯ : (14)
Note that the number of units of each home movie consumed reduces with t he import tax, as n increases. T he explanation behind this r esult is the follow-ing. As the pr ice char ged by each …rm does not change with the introduction of project subsidy11, and t here is a great er variety of home movies, the
consump-t ion of each home movie available is necessarily lower.
Note that , with the government intervention through import tax plus project subsidy, the individuals who care only about the consumption of home movies choose to consume less unit s of each movie but they take advantage of a great er variety of those movies. In other words, c decreases and n increases. T hey are necessarily bett er o¤ with this change ast hey could have opt ed t o keep the same pat tern of consumpt ion without the government intervention but they choose not to do that.
T he number of di¤erent for eign movies produced does not change with this new type of home government intervention. This number is …xed and given exogenously by n¤.
Government’s problem is to choose t he import t ax that maximizes t he wel-fare function W . It s problem is the following:
max
t W = f ln[n(t)c( t)
µ)1=µ+ (1 ¡ f ) ln[n¤c¤(t)µ]1=µ;
subject to equations (11), (12) , (13), and (14).
T he solution to the gover nment’s problem leads t o the following results.
P r op osi ti on 4 Under a poli cy regime with import tax and proj ect subsidy, the optimum impor t tax is equal to topt = (1¡ µ)[(1¡ µ)f L pT¡ µ¯Tw¤]
µ[(1¡ µf )L pT+ (1¡ µ)¯Tw¤]. Hence: ( i) i f
w¤ = 0, then topt = f (1¡ µ)2
µ(1¡ µf ) (ii) if w¤ > (1¡ µ)
µ f L w, then topt < 0; (i ii) i f
w¤< (1¡ µ)
µ f L w, then topt > 0.
P r op osi ti on 5 Under a policy regime with import tax and project subsidy,
dto p t dw¤ < 0:
T he result s obtained above are similar to the ones found in the previous subsect ion with t he same explanations. Hence, both types of gover nment inter-vention have exactly the same impact in t erms of economic welfare.
5
Conclusion
It is well known in the economic lit er ature that there is r oom for government t o intervene in industries character ized by increasing returns to scale. However, when one deals with t he movie industry, there is one additional complication. T he possibility of exploiting the global market scale is limited to pr oducers fr om a small count ry. Di¤erently fr om other goods traded in the internat ional market, movies have some character ist ics that ar e very speci…c t o some markets. One obvious example is the language.
T he analysis above indicates that the size of external markets to home movie producers a¤ects the degr ee of the optimal gover nment intervent ion to corr ect t he ine¢ ciencies of a market charact er ized by increasing returns to scale or monopolistic competition. T he optimal import tar i¤, with the revenues used either to subsidize product ion or projects, is lower the gr eater is the external market to the home movies pr oduced. A gr eater external mar ket induces a shift in the home pr oduction from t he homogenous good, characterized by constant r et urns to scale, to the home movies.
t he …lm industr y produced under incr easing retur ns to scale such as radio and t elevision pr ogramming, literature or print media.
It is important to add that, in spite of the above result s, one should be cau-t ious in adopcau-t ing policies cau-to pr ocau-teccau-t culcau-tural induscau-tr ies. Fir scau-t, cau-the incau-troduccau-tion of import t ari¤ may lead to r et aliation from other countries. Second, the gains associated with the economies of scale may not be lar ge enough from an empir-ical point of view to justify intervention. T hird, it is not an easy task to de…ne t he pr oducers who should r eceive the subsidies. It is not di¢ cult to …nd stories of public money being directed to producer s who do not need it or would have developed their projects anyway wit hout any aid. Finally, the misuse of public money is always a possibility.
6
A ppendix
P r op osi ti on 2: Under a policy regime with import tax and output subsidy, the opt imum t ax is equal to topt = (µ¡ 1¡ 1)p
Tf L ¡ ¯Tw¤
pTL + ¯Tw¤ . Hence: (i) if w
¤ = 0, then
topt = ¡1¡ µ µ
¢
f , (ii) if w¤ > (1¡ µ)
µ f L w, then topt < 0; ( iii) if w¤ < (1¡ µ)µ f L w,
t hen topt > 0.
P r oof. Using equations (9), and ( 8), I obtain, respect ively, the following expressions:
ln( n) = ln((1 ¡ µ) ®pT ) + ln
£
(1 + t)pTL ¡ pT(1 ¡ f )L + (1 + t) ¯Twf
¤
¡ ln(1 + t);
and
ln( c¤) = ln( 1) ¡ ln(n¤¯
T) ¡ ln(1 + t):
Using the above expressions in the welfare function, taking the derivative with r espect to t, and making some arrangements, the following result is obt ained:
topt = (µ¡ 1¡ 1)pTf L ¡ ¯Tw¤
pTL + ¯Tw¤
P r op osit i on 3: Under a policy regime with impor t t ax and output subsidy,
dto p t dw¤ < 0.
P r oof. From the expression for the optimal impor t tax obtained in the previous proposition, it is straightforward to show that dto p t
dw¤ < 0:
P r op osit i on 4: Under a policy regime with import tax and project subsidy, t he optimum import tax is equal to topt = (1¡ µ)[(1¡ µ)f L pT¡ µ¯Tw¤]
µ[(1¡ µf ) L pT+ (1¡ µ)¯Tw¤]. Hence: (i)
if w¤ = 0, then topt = f (1¡ µ)2
µ(1¡ µf ) ( ii) if w¤ > (1¡ µ)µ f L w, then topt < 0; (iii) if
w¤< (1¡ µ)
P r oof. Using equations (13) , (14), and (12) , I obt ain, respectively, the following expressions:
ln( n) = ln£( 1 + t)( 1 ¡ µ)pTL ¡ (1 ¡ f )L (1 ¡ µ) pT + ¯Twf(1 + t)(1 ¡ µ) + µt(1 ¡ f )L pT
¤ ¡ ¡ ln(1 + t) ¡ ln(pT®);
ln( c) = ¡ ln£(1 + t)(1 ¡ µ) pTL ¡ (1 ¡ f )L (1 ¡ µ)pT + ¯Twf(1 + t) (1 ¡ µ) + µt(1 ¡ f )L pT¤+
+ ln(1 + t) + ln(pT®µ ¯ );
and
ln( c¤) = ln( 1) ¡ ln(n¤¯
T) ¡ ln(1 + t):
Using the above expressions in the welfar e function, taking t he derivative with respect to t, and making some arrangements, the following r esult is obtained:
topt = (1 ¡ µ)
£
(1 ¡ µ) f L pT ¡ µ¯ Twf
¤
µ [( 1 ¡ µf )L pT + ( 1 ¡ µ)¯ Twf].
P r op osit i on 5: Under a policy regime with import tax and project subsidy,
dto p t dw¤ < 0:
P r oof. From the expression for the optimal impor t tax obtained in the previous proposition, it is straightforward to show that dto p t
dw¤ < 0:
7
R efer ences
Bhagwati, J. (2002). “ Free Trade Today” , Princet on University Press.
Flam, H., and Helpman, E. ( 1987). “ Indust rial Policy Under Monopolistic Competition” , Journal of International Economics 22, pp. 79-102.
Francois, P. and Ypersele, T . (2002). “ On the Protection of Cultural Goods” , Journal of Int ernational Economics 56, pp. 359-369.
Helpman, E. and Krugman, P. (1989). “ Tr ade Policy and Market Structure” , T he MIT Press.
K rugman, P. (1980). “ Scale Economies, Product Di¤erentiation, and the Pattern of Trade” , Amer ican Economic Review, vol. 70, no. 5, pp. 950-959.
K rugman, P. (1981). “ Intraindustry Specializat ion and the Gains from Trade” , Journal of Political Economy, vol. 89, no.5, pp. 959-973.
