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The effects of import quotas on national welfare: does money matter?

I. Introduction

Recent evidence shows that there is an increasing use of non-tariff barriers to trade Non-tariff barriers to trade are trade barriers that restrict imports but are not in the usual form of a tariff.

They are criticized as a means to evade free trade rules such as those of the World Trade Organization (WTO), the European Union (EU), or North American Free
 (NTBs), and especially of quantitative restrictions, such as import quotas Import quotas are a form of protectionism. An import quota fixes the quantity of a particular good that foreign producers may bring into a country over a specific period, usually a year. The U.S. government imposes quotas to protect domestic industries from foreign competition. , in the world economy to protect import-competing industries (see Table I).(1) International trade theory, however, has traditionally focused on the welfare effects of tariffs as well as on the equivalence between tariffs and quotas, with little attention paid to the welfare implications of quotas. The latter have basically been restricted within the traditional Heckscher-Ohlin trade model, where, for the case of a small open economy, import quotas always reduce welfare.

A few recent studies have attempted to fill in this gap in the literature. For instance, Young [19] compares optimal tariffs and quotas for a large country in a stochastic By guesswork; by chance; using or containing random values.

stochastic - probabilistic
 environment. Neary [14], on the other hand, investigates the welfare implications of tariffs, quotas and voluntary export restraints A voluntary export restraint (VER) is a restriction set by a government on the quantity of goods that can be exported out of a country during a specified period of time. Often the word voluntary is placed in quotes because these restraints are typically implemented upon the  under different assumptions on capital mobility. Finally, Chao, Hwang and Yu [3; 4] examine the welfare effects of import quotas under variable returns to scale.

Although the existing literature has generated important policy implications, most of the analysis has been conducted within a barter-exchange framework. It is well known, however, that the introduction of money can alter results obtained within a non-monetary environment.(2) Accordingly, this paper attempts to re-examine re·ex·am·ine also re-ex·am·ine  
tr.v. re·ex·am·ined, re·ex·am·in·ing, re·ex·am·ines
1. To examine again or anew; review.

2. Law To question (a witness) again after cross-examination.
 the welfare effects of import quotas for a small monetary economy. We develop a two-sector trade model in which money enters the economy [TABULAR tab·u·lar
1. Having a plane surface; flat.

2. Organized as a table or list.

3. Calculated by means of a table.


resembling a table.
 DATA FOR TABLE I OMITTED] through a generalized gen·er·al·ized
1. Involving an entire organ, as when an epileptic seizure involves all parts of the brain.

2. Not specifically adapted to a particular environment or function; not specialized.

 cash-in-advance constraint The cash-in-advance constraint is an idea used in economic modelling to demonstrate how equilibrium affects purchases. This is sometimes used to demonstrate Pareto efficiencies. . Building on previous work, we allow for non-uniform monetization Monetization

The securitization of the gross revenues of a contract.
 across sectors. Put differently Adv. 1. put differently - otherwise stated; "in other words, we are broke"
in other words
, the share of purchases which must be made using cash varies across goods (markets). Interestingly, we find that if the consumption of the exportable commodity requires larger cash balances than the consumption of the importable, then contrary to standard results, an import quota Import Quota

Puts limits on the quantity of certain products that can be legally imported into a particular country during a particular time frame. There is a Fixed quota, which is a maximum quantity not to be exceeded, and tariff rate surcharge, which permits additional quantities
 may promote national welfare. Moreover, we characterize the optimal level of import quotas by deriving a formula for the computation Computation is a general term for any type of information processing that can be represented mathematically. This includes phenomena ranging from simple calculations to human thinking.  of the optimal domestic-price ratio.

We then extend our basic framework to allow for economic growth, induced by technical progress, to explore the possibility of immiserizing growth Immiserizing growth is a situation first proposed by Jagdish Bhagwati, in 1958[1], where economic growth could result in a country being worse off than they were before growth.  in the presence of import quotas. Johnson [10] has shown that growth can be welfare-reducing in a small open economy with a tariff distortion. Bhagwati [2] generalizes this theory of immiserizing growth to the case of alternative types of distortions. Nevertheless, as shown in Alam [1], an important exception to this generalization gen·er·al·i·za·tion
1. The act or an instance of generalizing.

2. A principle, a statement, or an idea having general application.
 is the case of a quota quota

In international trade, a government-imposed limit on the quantity of goods and services that may be exported or imported over a specified period of time. Quotas are more effective than tariffs in restricting trade, since they limit the availability of goods rather
, where growth is always welfare-enhancing. Chao and Yu [5] elaborate further on this important exception, by examining the welfare implications of growth for a quota-distorted small economy under variable returns to scale. This paper continues this line of research by studying the issue of immiserizing growth in the context of a small monetary economy with quota distortions. We find that growth always improves welfare if the growing industry displays a higher degree of monetization than the static one. If the converse (logic) converse - The truth of a proposition of the form A => B and its converse B => A are shown in the following truth table:

A B | A => B B => A ------+---------------- f f | t t f t | t f t f | f t t t | t t
 is true then, contrary to Alam's results (obtained for a barter barter: see exchange.

Direct exchange of goods or services without the use of money or any other intervening medium of exchange. Barter is conducted either according to established rates of exchange or by bargaining.
 economy), growth can be immiserizing.

The organization of the paper is as follows. The next section develops the analytical framework and section III examines the welfare implications of quotas. Section IV characterizes the optimal quota level and section V investigates the issue of immiserizing growth. Section VI concludes the paper.

II. The Analytical Framework

Consider a standard two-sector trade model of a small open economy. The representative agent's preferences are described by a strictly quasi-concave utility function

U = U([D.sub.1], [D.sub.2]) (1)

where [D.sub.1] and [D.sub.2] denote de·note  
tr.v. de·not·ed, de·not·ing, de·notes
1. To mark; indicate: a frown that denoted increasing impatience.

, respectively, the consumption of the exportable and importable commodities. In trying to maximize this utility function, the agent faces a standard private budget constraint A Budget Constraint represents the combinations of goods and services that a consumer can purchase given current prices and his income. Consumer theory uses the concepts of a budget constraint and a preference ordering to analyze consumer choices.  

[Mathematical Expression A group of characters or symbols representing a quantity or an operation. See arithmetic expression.  Omitted], (2)

where [p.sub.j] and [X.sub.j] denote, respectively, the domestic nominal price Nominal price

Price quotations on futures for a period in which no actual trading took place.
 and the production level of good j, [Mathematical Expression Omitted] is the nominal money Nominal money, in economics, is the quantity of money measured in a particular currency and is directly proportional to the price level.

This means, among other things, that if the price level rises by 10%, people needs to have 10% more money than before in order to maintain
 holdings (money supply), and S represents the quota revenue in nominal terms, which is assumed to be re-distributed to households (private agents) in a lump-sum fashion.
Table IIa. Developing Countries' Outstanding Trade Credits
as a Percentage of 1987 Exports

Traditional exports                             16.7
Non-traditional exports, of which:             155.1

  * capital goods                              403.2
  * consumer durables                           17.7
  * other manufactures                          44.0

Total                                           81.9
Table IIb. Average Maturity of Trade Credits (Months) in
Selected Developing Countries

Traditional exports                              1.9
Non-traditional exports, of which:

  * capital goods                               48.4
  * consumer durables                            2.1
  * other manufactures                           5.2

Notes: Non-traditional goods refer mainly to manufactured
goods excluding steel, fertilizers, pulp and paper, which
have been traditionally traded on the same basis as
primary commodities. They include consumer durables,
capital goods and other manufactures.

Source: [21].

Money serves as a medium of exchange. Hence, building on Stockman [17] and Lucas and Stokey [12], we introduce a generalized cash-in-advance (CIA CIA: see Central Intelligence Agency.

(1) (Confidentiality Integrity Authentication) The three important concerns with regards to information security. Encryption is used to provide confidentiality (privacy, secrecy).
) or liquidity constraint A liquidity constraint in economic theory is a form of imperfection in the capital market. It causes difficulties for models based on intertemporal consumption.

Many economic models require individuals to save or borrow money from time to time.
 which captures the transactions role of money, that is,

[[Phi].sub.1][p.sub.1][D.sub.1] + [[Phi].sub.2][p.sub.2][D.sub.2] [less than or equal to] M, (3)

where [[Phi].sub.j] [element of] [0, 1], j = 1, 2, denotes a constant share of purchases of good j. This constraint Constraint

A restriction on the natural degrees of freedom of a system. If n and m are the numbers of the natural and actual degrees of freedom, the difference n - m is the number of constraints.
 requires the individual to hold sufficient money balances to finance at least a certain part of consumption purchases. In general, consumption of one good requires larger cash balances, per unit of value, than consumption of the other good and hence [[Phi].sub.1] [not equal to] [[Phi].sub.2].(3) This may be justified in a number of different ways. First, it can be considered as the outcome of existing (a) regulations regarding the terms of payments of imports and the obtaining and use of credit (foreign and domestic) to finance imports [11]; and (b) export credits (as Tables IIa and IIb indicate even export credits alone differ across sectors). Second, one can actually view [D.sub.1] and [D.sub.2] as being composite goods In economics, demand for a good is often the focus as to a change in its price. A composite good is an abstraction used in economics that represents all consumption goods besides the one in question. , consisting of different proportions of both non-durable goods and flow services of durables. Since non-durable goods are subject to a different degree of credit rationing rationing, allotment of scarce supplies, usually by governmental decree, to provide equitable distribution. It may be employed also to conserve economic resources and to reinforce price and production controls.  than durables, one can expect [[Phi].sub.1] [not equal to] [[Phi].sub.2].(4) Third, empirical evidence found in Cramer and Reekers [6] indicates different money demands and liquidity/sales ratios across sectors, which provides additional support for the assumption [[Phi].sub.1] [not equal to] [[Phi].sub.2]. Finally, notice that if [[Phi].sub.1] = [[Phi].sub.2] = [Phi] then the velocity of circulation, defined as [Mathematical Expression Omitted], is constant (= [Phi]) and, in particular, independent of income and of monetary expansions. This, however, contradicts empirical evidence found in a series of papers [13; 15].

The optimal allocation of income between [D.sub.1] and [D.sub.2] is described by:

[U.sub.2]/[U.sub.1] = (1 + [Gamma])p, (4)

where [U.sub.j] [equivalent to] [Delta]U/[Delta][D.sub.j], j = 1, 2, denotes the marginal utility marginal utility

In economics, the additional satisfaction or benefit (utility) that a consumer derives from buying an additional unit of a commodity or service. The law of diminishing utility implies that utility or benefit is inversely related to the number of units
 of good j, [Gamma] [equivalent to] ([[Phi].sub.2] - [[Phi].sub.1])/(1 + [[Phi].sub.1]), with [absolute value of [Gamma]] [less than] 1, and p is the domestic price of good 2 in terms of good 1. At the optimum, the marginal domestic rate of substitution (MDRS MDRS Mars Desert Research Station (Utah)
MDRS Marconi Digital Radio System
MDRS Midwest Double Reed Society
MDRS Multilingual Distributed Referential System
MDRS Maintenance Data Recording System
MDRS Message Distribution & Retrieval Subsystem
) between the two goods must be equal to the market trade-off. Notice that [Gamma] gives the proportional increase or decrease in the market price, depending on whether [[Phi].sub.2] is greater or smaller than [[Phi].sub.1], due to the monetary distortion (the CIA constraint). If [[Phi].sub.1] = [[Phi].sub.2] = 0, as it is the case in any barter economy, then [Gamma] = 0, resulting in the familiar condition MDRS = p. The same result also holds in the more general case where [[Phi].sub.1] = [[Phi].sub.2] [greater than] 0.(5)

For simplicity, we assume that there are no barriers to export while a quota (Q) is imposed on imports, i.e.,

Q [equivalent to] [D.sub.2](p, Y) - [X.sub.2](p) [greater than] 0, (5)

where Y denotes the real national income of the economy. Let [p.sup.*] be the world relative price of good 2 in terms of good 1, taken as constant by this small open economy. Then the real quota revenue is given by (p - [p.sup.*])Q. Furthermore, in equilibrium, [Mathematical Expression Omitted] and so the private budget constraint, equation (2), becomes

[D.sub.1] + p[D.sub.2] = [X.sub.1] + p[X.sub.2] + (p - [p.sup.*])Q. (2[prime])

To close the model, we next provide a brief description of the supply side of the economy. The two goods are produced with constant-returns-to-scale technologies which use two factors of production, capital (K) and labor (L). Furthermore, both of these factors are assumed to be inelastically supplied and inter-sectorally mobile. Profit maximization In economics, profit maximization is the process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to this problem.  then on behalf of the firms and competitive factor markets yield the standard condition for equilibrium in the production side of the economy; namely, that the marginal domestic rate of transformation (MDRT MDRT Million Dollar Round Table ) equals the domestic-price ratio (p), that is,

MDRT = -d[X.sub.1]/d[X.sub.2] = p, (6)

where [X.sub.1] and [X.sub.2] denote the production levels of the two goods.

III. The Welfare Analysis

In this section, we study the welfare implications of an import quota. This is accomplished in three steps. First, totally differentiating (1) and applying (4), we have

dU/[U.sub.1] = d[D.sub.1] + (1+ [Gamma])pd[D.sub.2]. (7)

Second, differentiating (2[prime]), in conjunction with (6), yields

d[D.sub.1] = (p - [p.sup.*])dQ - pd[D.sub.2]. (8)

Finally, substituting (8) into (7), we obtain

(1/[U.sub.1])(dU/dQ) = (p - [p.sup.*]) + [Gamma]p(d[D.sub.2]/dQ). (9)

According to according to
1. As stated or indicated by; on the authority of: according to historians.

2. In keeping with: according to instructions.

 (9), the welfare effect of an import quota has two components. The first term on the right-hand side right-hand side nderecha

right-hand side right nrechte Seite f

right-hand side nlato destro 
 of (9) gives the standard direct welfare impact of a change in the quota level. The second term, on the other hand, represents the indirect effect of the quota on welfare and is due to the existence of a CIA constraint. In the special case of a barter economy, [[Phi].sub.1] = [[Phi].sub.2] = [Gamma] = 0 and this indirect effect vanishes; hence, a tightening of the import quota (dQ [less than] 0) always lowers social welfare [notice from (9) that if [Gamma] = 0 then dU/dQ = (p-[p.sup.*])[U.sub.1] [greater than] 0, where p [greater than] [p.sup.*] since the quota generates a wedge between the domestic- and world-price ratio]. This is a well-known result in the trade literature with barter exchange barter exchange barter nTauschbörse f , which also holds when [[Phi].sub.1] = [[Phi].sub.2] [greater than] 0. Nevertheless, under a generalized CIA constraint this conclusion is in need of revision due to the presence of the indirect effect mentioned above. Notice that a tightening of the quota (a decrease in Q) reduces the consumption of the importables (i.e., d[D.sub.2]/dQ [greater than] 0; see the next section for further elaboration). According to (9), if [[Phi].sub.1] [less than] [[Phi].sub.2], ([Gamma] [element of] (0, 1]), then the two effects work in the same direction and hence the traditional negative effect of an import quota on welfare is strengthened. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2] and hence [Gamma] [element of] [- 1, 0), then the two effects mentioned above work in opposite directions. The economic intuition intuition, in philosophy, way of knowing directly; immediate apprehension. The Greeks understood intuition to be the grasp of universal principles by the intelligence (nous), as distinguished from the fleeting impressions of the senses.  is as follows. In the case where [[Phi].sub.1] [less than] [[Phi].sub.2] (or [Gamma] [element of] (0, 1]), the MDRS = (1 + [Gamma])p is greater than the world-price ratio [p.sup.*] (= the marginal foreign rate of transformation, MFRT MFRT Maryland Functional Reading Test ). Thus, eliminating the import quota will bring MDRS as close to the world-price ratio [p.sup.*] as possible, which is welfare-enhancing. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2], and hence [Gamma] [element of] [-1, 0), then a free-trade policy will result in MDRS = (1 + [Gamma])[p.sup.*] [greater than] [p.sup.*] = MFRT, which is a sub-optimal situation. Since the MDRS is a decreasing function of [D.sub.2], tightening the quota level (decreasing Q) lowers the consumption of importables, raises the domestic price, and reduces the gap between the MDRS and [p.sup.*] (= MFRT).(6) This raises in turn the level of welfare, working thus against the adverse direct welfare effect of import quotas.

IV. The Optimal Quota Level

To determine the optimal level of the import quota we set dU = 0 in equation (9). Hence, we obtain

[1 + [Gamma](d[D.sub.2]/dQ)][p.sup.Q] = [p.sup.*], (10)

where [p.sup.Q] stands for the optimal domestic-price ratio. Next, notice that differentiation of [D.sub.2] = [D.sub.2](p, Y) implies

pd[D.sub.2] = -[Epsilon 1. (language) EPSILON - A macro language with high level features including strings and lists, developed by A.P. Ershov at Novosibirsk in 1967. EPSILON was used to implement ALGOL 68 on the M-220. ]Qdp + [Mu]d Y, (11)

where [Epsilon] [equivalent to] -(p/Q)(d[D.sub.2]/dp) [greater than] 0 denotes the demand elasticity of good 2 and measures the substitution in consumption in response to a change in p, given a utility level. [Mu] [equivalent to] p([Delta][D.sub.2]/[Delta]Y) [[Mu] [element of] (0, 1)], on the other hand, is the marginal propensity to consume The marginal propensity to consume (MPC) refers to the increase in personal consumer spending (consumption) that occurs with an increase in disposable income (income after taxes and transfers).  good 2. Also, total differentiation of (5) yields

dQ = d[D.sub.2] - [Sigma SIGMA - A scientific visual programming environment from NASA.
]Qdp/p, (12)

where [Sigma] [equivalent to] (p/Q)(d[X.sub.2]/dp) [greater than] 0 denotes the output elasticity In economics, output elasticity is the percentage change of output (GDP or revenue for a single firm) divided by the percentage change of an input.

It is calculated as marginal product of an input to its average product. It is a local measure, defined at a point.
 of good 2 and measures the substitution in production in response to a change in p. Substituting (11) into (12) yields

pdQ = -([Epsilon] + [Sigma])Qdp + [Mu]dY. (13)

Moreover, equation (9), in conjunction with (11), (13) and the definition dY [equivalent to] dU/[U.sub.1], yields the following expression for the effect of quotas on domestic-price ratio:

dp/dQ = -[Beta]/Q, (14)

where [Beta] [equivalent to] {[1 - [Mu](1 + [Gamma])]p+ [Mu][p.sup.*]}/([Epsilon]+[Sigma][Alpha]) and [Alpha] [equivalent to] 1 - [Mu][Gamma] [greater than] 0. The stability of the equilibrium requires dp/dQ [less than] 0.(7) We, therefore, assume that [Beta] [greater than] 0 so that a tightening of import quotas (dQ [less than] 0) always raises the domestic-price ratio. Finally, combining (10), (12) and (14), we obtain the following expression for the optimal domestic-price ratio under an import quota:

([p.sup.Q] - [p.sup.*])/[p.sup.*] = - [Gamma][Epsilon][p.sup.*]/[(1 + [Gamma])[Epsilon] + [Sigma]]. (15)

Notice that if [Gamma] = 0, which is the case if [[Phi].sub.1] = [[Phi].sub.2] [greater than or equal to] 0, then the standard result [p.sup.Q] = [p.sup.*] emerges; namely that free trade is the optimal policy.(8) If the degree of monetization in the exportable sector is lower than in the importable sector, i.e., [[Phi].sub.1] [less than] [[Phi].sub.2], then [Gamma] [equivalent to] ([[Phi].sub.2] - [[Phi].sub.1])/(1 + [[Phi].sub.1]) [element of] (0, 1] and [p.sup.Q] [less than] [p.sup.*]. This implies that if the initial situation is free trade, then a zero quota remains the optimal policy since lowering the quota level beyond the free-trade level cannot decrease p further. However, if an effective import quota already exists, then loosening loosening /loo·sen·ing/ (loo´sen-ing) freeing from restraint or strictness.

loosening of associations
 the quota restriction (increasing Q) is desirable because it will result in a lower domestic-price ratio. This in turn reduces the wedge between the MDRS and the world-price ratio, which is welfare-improving. If, on the other hand, [[Phi].sub.1] [greater than] [[Phi].sub.2], then we have [Gamma] [element of] [- 1, 0) and [p.sup.Q] [greater than] [p.sup.*]. Thus, an optimal (positive) quota level exists and is given by [Q.sup.*] ([p.sup.Q]) = [D.sub.2] ([p.sup.Q], Y([p.sup.Q]))-[X.sub.2]([p.sup.Q]). As mentioned in the previous section, this occurs because raising the quota level increases the domestic-price ratio and hence the MDRS. This again narrows the gap between the MDRS and [p.sup.*], offsetting thus the direct adverse welfare effect at a positive level of the import quota ([Q.sup.*] [greater than] 0).

V. Technical Progress and the Possibility of Immiserizing Growth

To examine the possibility of immiserizing growth, we next extend our framework to allow for technical progress. Accordingly, the production process of good j is described by the following constant-returns-to-scale production function:

[X.sub.j] = [F.sub.j]([K.sub.j], [L.sub.j], [[Tau].sub.j]), j = 1,2, (16)

where [[Tau].sub.j] denotes a Hicks-neutral technological parameter (1) Any value passed to a program by the user or by another program in order to customize the program for a particular purpose. A parameter may be anything; for example, a file name, a coordinate, a range of values, a money amount or a code of some kind.  of industry j. Totally differentiating (16), we have

d[X.sub.j] = [F.sub.Kj]d[K.sub.j] + [F.sub.Lj]d[L.sub.j] + [F.sub.[Tau]j]d[[Tau].sub.j], j = 1, 2, (17)

where [F.sub.ij], denotes the partial derivative partial derivative

In differential calculus, the derivative of a function of several variables with respect to change in just one of its variables. Partial derivatives are useful in analyzing surfaces for maximum and minimum points and give rise to partial differential
 of [F.sub.j] (marginal product In economics, the marginal product or marginal physical product is the extra output produced by one more unit of an input (for instance, the difference in output when a firm's labour is increased from five to six units). ) with respect to i, i = K, L and [Tau]. Under the assumption of competitive factor markets, each of the two factors is paid the value of its marginal product, i.e.,

w = [p.sub.j][F.sub.Lj] and r = [p.sub.j][F.sub.Kj], j = 1,2, (18)

where w and r stand for the wage rate and the rental rate of capital, respectively. Moreover, full employment of factors of production implies

[L.sub.1]+[L.sub.2] = L and [K.sub.1]+[K.sub.2] =K. (19)

Without loss of generality Without loss of generality (abbreviated to WLOG or WOLOG and less commonly stated as without any loss of generality) is a frequently used expression in mathematics. , we assume that technical progress takes place in industry 2 only, so that d[[Tau].sub.1] = 0 [less than] d[[Tau].sub.2] [equivalent to] d[Tau]. Totally differentiating (19) and using (17) and (18), we derive the new condition for equilibrium in the production of the two goods:

MDRT = -d[X.sub.2]/d[X.sub.1] = p/(1 + g), (20)

where g [equivalent to] [p.sub.2][F.sub.[Tau]2]d[Tau]/(rd[K.sub.2] + wd[L.sub.2]) [greater than] 0 denotes the shift factor due to technical progress. Given Q, total differentiation of (2[prime]) together with (20) yield

d[D.sub.1] + pd[D.sub.2] = -gd[X.sub.1]. (21)

Substituting (21) into (7), we then have

dU/[U.sub.1] = [Gamma]pd[D.sub.2] - gd[X.sub.1]. (22)

Next, since [D.sub.2] = [D.sub.2] (p, Y) and [X.sub.2] = [X.sub.2] (p, [Tau]), totally differentiating (5), for a given level of import quota, implies

[Mu]dY = ([Epsilon] + [Sigma])Qdp + ([Delta][X.sub.2]/[Delta][Tau])pd[Tau]. (23)

Substituting (20) and dY = dU/[U.sub.1] into (23), we obtain

[Mu]dU/[U.sub.1] = ([Epsilon] + [Sigma])Qdp - (1 + g)([Delta][X.sub.1]/[Delta][Tau])d[Tau]. (23[prime])

Also, (5) and (20) together imply pd[D.sub.2] = [Sigma]Qdp - (1 + g) ([Delta][X.sub.1]/[Delta][Tau])d[Tau]. Substituting this expression into (22) and noting that gd[X.sub.1] = g([Delta][X.sub.1]/[Delta][Tau])d[Tau], we obtain

dU/[U.sub.1] = [Gamma][Sigma]Qdp - ([Delta][X.sub.1]/[Delta][Tau])[(1 + g)[Gamma] + g]d[Tau]. (22[prime])

Using (22[prime]) and (23[prime]), straightforward application of Cramer's rule Cramer's rule is a theorem in linear algebra, which gives the solution of a system of linear equations in terms of determinants. It is named after Gabriel Cramer (1704 - 1752).  yields the welfare effect of technical progress:

dU/[U.sub.1] = -[U.sub.1]([Delta][X.sub.1]/[Delta][Tau])[[Epsilon][Gamma](1 + g) + g([Epsilon] + [Sigma])]/([Epsilon] + [Sigma][Alpha]). (24)

Recall next that technical progress takes place in the second industry and hence, given factor prices, it raises the production level of the second good at the expense of the first, i.e., [Delta][X.sub.1]/[Delta][Tau] [less than] 0.(9) Thus, from (24), we conclude that

dU/d[Tau] [greater than] 0 if [[Phi].sub.2] [greater than or equal to] [[Phi].sub.1] and dU/d[Tau] [greater than or less than] 0 if [[Phi].sub.2] [less than] [[Phi].sub.1]. (25)

The following proposition summarizes the main results of this section.

PROPOSITION. For a small monetary economy with import quotas, growth induced by Hicks-neutral technical progress is welfare-enhancing if the degree of monetization in the growing sector is higher than the one in the static sector, i.e., if the consumption of the goods produced in the growing sector requires larger cash balances. If the static sector displays a higher degree of monetization, then growth can be immiserizing.

Consider first the special case of a barter economy where [[Phi].sub.1] = [[Phi].sub.2] = 0, as in Alam [1]. Equation (24) then simplifies to

dU/d[Tau] = -g[U.sub.1]([Delta][X.sub.1]/[Delta][Tau]) [greater than] 0.

This confirms Alam's finding; namely, in the presence of an import quota, growth is always welfare-enhancing, which is an important exception to Bhagwati's [2] result on the possibility of immiserizing growth. In the case of a monetary economy, however, this exception is disputable dis·put·a·ble  
Open to dispute; debatable: disputable testimony.

 and the possibility of immiserizing growth emerges once again. Specifically, as it can be seen from (24), if the growing sector is more monetized (i.e., more liquidity-wise constrained con·strain  
tr.v. con·strained, con·strain·ing, con·strains
1. To compel by physical, moral, or circumstantial force; oblige: felt constrained to object. See Synonyms at force.

) then [[Phi].sub.1] [less than] [[Phi].sub.2] and growth once again always improves social welfare. The economic explanation of this result is similar to the one given before; namely, if [[Phi].sub.1] [less than] [[Phi].sub.2], (4) implies that the MDRS is greater than the world-price ratio [p.sup.*].(10) Since technical progress in industry 2 raises the production level of good 2 at the expense of good 1, the domestic-price ratio p falls, [D.sub.2] rises, and hence MDRS decreases. This then reduces the wedge between MDRS and MFRT, and hence it works together with the direct effect of growth in enhancing welfare. Nevertheless, if [[Phi].sub.1] [greater than] [[Phi].sub.2] so that the MDRS is initially below the MFRT, technical progress in industry 2 drives MDRS further away from MFRT. Thus, if this adverse monetary distortion effect dominates the direct welfare-enhancing effect of technical progress, then growth will be immiserizing.

VI. Concluding Remarks

We have studied the effects of import quotas in a generalized cash-in-advance economy and have shown that, depending on the degree of credit-rationing in each sector, the standard conclusion that a tightening of an import quota reduces social welfare may not hold. In particular, if the exportable sector is more liquidity constrained, then an optimum import quota exists. If, on the other hand, the importable sector is more liquidity constrained, then an export quota is in order. Finally, in a small monetary economy with quota distortions, growth can be immiserizing, contrary to findings by Alam [1] in the context of a barter economy.

Although our results indicate that quotas may be desirable to enhance social welfare, they are only second-best policies. The first-best policy in the presence of a liquidity (CIA) constraint is a consumption tax, which can restore the optimal situation where MDRS = MDRT = MFRT.(11) Intuitively, the cash-in-advance constraint introduces a demand-side distortion which makes the consumption tax unavoidable. A quota restriction, however, affects the consumption as well as the production side of the economy, creating thus an unnecessary divergence divergence

In mathematics, a differential operator applied to a three-dimensional vector-valued function. The result is a function that describes a rate of change. The divergence of a vector v is given by
 between the given world-price ratio and the domestic marginal rate of transformation.

We would like to thank an anonymous referee of this journal for helpful comments and suggestions.

1. In 1981 (1986) about 19.6 (23.1) per cent of all industrial-country imports were subject to NTBs, with quantitative restrictions covering 12.2 (14.4) per cent. Also, in a study involving 50 developing countries, Erzan et al. [8] show that NTBs are sometimes responsible for at least half of the protection impact, with quantitative restrictions being the most frequently used non-tariff measures. On average, 24 per cent of all tariff lines were affected by quantitative restrictions.

2. For instance, Drabicki and Takayama [7] show that the theory of comparative advantage breaks down in a monetary world under fixed exchange rates when the balance of payments is not in equilibrium. Similarly, in a real trade model with a transactions-based demand for money, Stockman [18] shows that changes in inflation can cause changes in the pattern of trade even in the absence of real changes in comparative advantage.

3. This formulation formulation /for·mu·la·tion/ (for?mu-la´shun) the act or product of formulating.

American Law Institute Formulation
 of the CIA constraint is slightly more general than the one considered in Stockman [17], where [[Phi].sub.j] = 1, j = 1, 2, as well as the one adopted in Lucas and Stokey [12] where there are two types of goods, pure cash goods with [Phi] = 1 and pure credit goods with [Phi] = 0.

4. A similar argument can be made with regard to necessary and luxury goods.

5. It should be noted that in a dynamic model, [Gamma] will also depend on the nominal interest rate Nominal Interest Rate

The interest rate unadjusted for inflation.

Not taking into account inflation gives a less realistic number.
See also: Inflation, Interest Rate, Real Interest Rate

Nominal interest rate
. This point is further developed in Palivos and Yip [16].

6. Following the standard practice in the literature, we assume that both consumption goods are normal which implies that the MDRS is a decreasing function of [D.sub.2].

7. To see this, consider the price-adjustment rule dp/dt = [Xi](p), where t denotes time, [Xi](Q(p)) is a smooth, sign-preserving function of excess demand Q(p) [equivalent to] [D.sub.2](p, Y(p)) - [X.sub.2](p), and [Xi][prime] [greater than] 0. The stability of the equilibrium requires that (dp/dt)/dp [less than] 0 or, equivalently, [Xi][prime]dQ/dp [less than] 0.

8. Recall that [[Phi].sub.1] = [[Phi].sub.2] = 0 represents the case of a barter economy.

9. This can readily be obtained from (20).

10. Recall that, in the presence of an effective import quota, p [greater than or equal to] [p.sup.*].

11. A more comprehensive examination of the first-best policies as well as of the effects of a tariff for a small monetary economy is provided in Palivos and Yip [16].


1. Alam, M. Shahid Mohammed Shahid (born 12 December 1969) is an Indian politician. He stood for the 2004 Lok Sabha elections on the BSP ticket and is currently a Member of Parliament from Meerut. External links
  • Official biography from Parliament of India records
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2. Bhagwati, Jagdish N. "The Generalized Theory of Distortions and Welfare," in Trade, Balance of Payments, and Growth: Papers in International Economics in Honor of Charles P. Kindleberger, edited by J. N. Bhagwati, R. W. Jones, R. A. Mundell and J. Vanek. Amsterdam: North-Holland, 1971, Ch. 4.

3. Chao, Chi-Chur, Hong Hwang and Eden S. H. Yu, "Welfare Effects of Quotas under Variable Returns to Scale." Southern Economic Journal, July 1990, 160-66.

4. -----, ----- and -----, "Effects of Quotas under Variable Returns to Scale: The Large Country Case." Southern Economic Journal, April 1993, 675-86.

5. Chao, Chi-Chur and Eden S. H. Yu, "Immiserizing Growth for a Quota-Distorted Small Economy under Variable Returns to Scale." Canadian Journal of Economics, August 1991, 686-92.

6. Cramer, J. S. and G. M. Reekers, "Money Demand by Sector." Journal of Monetary Economics, January 1976, 99-112.

7. Drabicki, John Z. and Akira Takayama, "The Theory of Comparative Advantage in a Monetary World." Southern Economic Journal, July 1983, 1-17.

8. Erzan, Refik, Hirohaki Kuwahara, Serafino Marchese mar·che·se  
n. pl. mar·che·si
1. An Italian nobleman ranking above a count and below a prince.

2. Used as the title for such a nobleman.
 and Rene Vossenaar, "The Profile of Protection in Developing Countries." UNCTAD UNCTAD United Nations Conference on Trade & Development  Review, 1989, 29-49.

9. Finger, Michael J. and Patrick A. Messerlin, "The Effects of Industrial Countries' Policies on Developing Countries." Working Paper No. 3, World Bank, 1989.

10. Johnson, Harry G., "The Possibility of Income Losses from Increased Efficiency or Factor-Accumulation in the Presence of Tariffs." Economic Journal, March 1967, 151-54.

11. Laird laird  
n. Scots
The owner of a landed estate.

[Scots, from Middle English lard, variant of lord, owner, master; see lord.
, Sam and Alexander J. Yeats. Quantitative Methods for Trade-Barrier Analysis. New York New York, state, United States
New York, Middle Atlantic state of the United States. It is bordered by Vermont, Massachusetts, Connecticut, and the Atlantic Ocean (E), New Jersey and Pennsylvania (S), Lakes Erie and Ontario and the Canadian province of
: New York University Press New York University Press (or NYU Press), founded in 1916, is a university press that is part of New York University. External link
  • New York University Press
, 1990.

12. Lucas, Robert E. Jr. and Nancy Stokey Nancy Laura Stokey is a Distinguished Service Professor of economics at the University of Chicago. She has earned her BA in economics from the University of Pennsylvania in 1972 and her PhD from Harvard University in 1978, her thesis advisor being Nobel Prize in Economics laureate , "Money and Interest in a Cash-in-Advance Economy." Econometrica, May 1987, 491-513.

13. Mayor, Thomas H. and Lawrence R. Pearl, "Life-Cycle Effects, Structural Change and Long-Run Movements in the Velocity of Money The velocity of money is the average frequency with which a unit of money is spent. When the period is understood, the velocity may be present as a pure number; otherwise it should be given as a pure number over time. ." Journal of Money, Credit and Banking, May 1984, 175-84.

14. Neary, Peter J., "Tariffs, Quotas, and Voluntary Export Restraints with and without Internationally Mobile Capital." Canadian Journal of Economics, November 1988, 714-35.

15. Palivos, Theodore, Ping Wang and Jianbo Zhang, "Velocity of Money in a Modified Cash-in-Advance Economy: Theory and Evidence." Journal of Macroeconomics macroeconomics

Study of the entire economy in terms of the total amount of goods and services produced, total income earned, level of employment of productive resources, and general behaviour of prices.
, Spring 1993, 225-48.

16. Palivos, Theodore and Chong K. Yip, "The Gains from Trade for a Monetary Economy Once Again." Canadian Journal of Economics, forthcoming.

17. Stockman, Alan C., "Anticipated Inflation and the Capital Stock in a Cash-in-Advance Economy." Journal of Monetary Economics, November 1981, 387-93.

18. -----, "Effects of Inflation on the Pattern of International Trade." Canadian Journal of Economics, August 1985, 587-601.

19. Young, Leslie, "Ranking Optimal Tariffs and Quotas for a Large Country under Uncertainty." Journal of International Economics, May 1979, 249-64.

20. United Nations Conference on Trade and Development United Nations Conference on Trade and Development (UNCTAD)

Organ of the United Nations General Assembly, created in 1964 to promote international trade. Its highest policy-making body, the Conference, meets every four years; when the Conference is not in session, the
 (UNCTAD). Trade and Development Report. Geneva Geneva, canton and city, Switzerland
Geneva (jənē`və), Fr. Genève, canton (1990 pop. 373,019), 109 sq mi (282 sq km), SW Switzerland, surrounding the southwest tip of the Lake of Geneva.
: UNCTAD, 1991.

21. -----. Trade and Financing in Developing Countries: An Assessment and Evaluation of Existing Schemes and Future Requirements. Geneva: UNCTAD, 1992.
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