Trade policies and welfare in a Harris-Todaro economy.

Choi, E. Kwan

I. Introduction

In many developing countries rising unemployment is often attributed to increases in foreign imports, triggered by declining foreign prices of imports. To correct the chronic unemployment problem, some developing countries chose an import substitution strategy by shutting off imports, whereas others adopted an outward-oriented policy by promoting exports. North American Free Trade Agreement (NAFTA) was favored by Mexico but opposed by organized labor in this country because it was feared that NAFTA may increase unemployment in the U.S. Which of these policies is more effective$in reducing unemployment and raising domestic income?

Protection has been ardently supported as a practical cure for unemployment in Chile and Argentina and many other LDCs in Latin America.(1) Similarly, India adopted import substitution strategies behind high protection and a considerable bias against exports [1]. The literature has also justified the use of tariffs for small countries under uncertainty and unemployment [10; 9]. But in general, protection distorts the trade pattern and magnify the extent of the Leontief Paradox by limiting imports of capital intensive products into these developing countries that suffer from high labor unemployment [7].

In the literature there have been two types of models that analyze trade problems in the presence of unemployment. The generalized unemployment models have been developed by Brecher [5; 6] and Batra and Seth [3].(2) In these models, wage rigidity is ubiquitous and unemployment exists in all sectors, and they are appropriate to analyze the impact of trade policies on unemployment in developed economies. The Harris-Todaro (HT hereafter) model [13], on the other hand, assumes sector-specific wage rigidity and permits unemployment only in the urban sector. Thus, the HT model is appropriate for investigating the impacts of trade policies of LDCs that suffer from urban unemployment, and it has been subsequently used by Hazari [14], Batra and Beladi [2], Chao and Yu [8], Hazari and Sgro [15], and Marjit [16].

This paper uses the HT model to investigate optimal trade policies for a developing country with labor unemployment. As in Corden and Findlay [11], we assume that capital is mobile between sectors. It is shown that an import tariff is welfare-reducing in an HT economy. If an optimal production subsidy, which is negative, is used, however, the optimal tariff is zero. The negative production subsidy on the importable is equivalent to a production subsidy on the exportable. Our findings have an important policy implication on trade policies of a labor surplus economy; an import tariff is welfare reducing, and therefore, for instance, the reduced tariffs of Mexico implemented by NAFTA would probably improve welfare of Mexico, which may be viewed as an HT economy.(3)

II. The Basic Model

Consider a small open HT economy which has two sectors, a rural sector and an urban sector. Unemployment exists only in the urban area because of a fixed urban wage, but rural workers are fully employed and paid a flexible wage. To analyze optimal trade policies of an HT economy, we employ the following assumptions:

(i) Fixed supplies of capital (K) and labor (L) inputs.

(ii) Capital is fully employed, but labor unemployment exists in the urban area because the fixed urban wage W is higher than the flexible rural wage w.

(iii) The economy is small and imports the urban output X and exports the agricultural output Y, which is used as numeraire.

Let [L.sub.j] and [K.sub.j] denote the labor and capital employed in sector j, respectively. The output of the urban manufacturing sector is

X = F([L.sub.x], [K.sub.x]), (1a)

and the output of the rural sector is

Y = G([L.sub.y], [K.sub.y]), (1b)

where F ([center dot]) and G ([center dot]) are linearly homogeneous production functions.

Capital is a variable input and is mobile between the two sectors. Capital rental r is the same in both sectors and capital is fully utilized. However, due to wage rigidity in the manufacturing sector, some unemployment exists in the urban area.

Profit of the urban sector is

[[Pi].sub.x] = PF - W[L.sub.x] - r[K.sub.x], (2a)

where P is the producer price of the urban output and W is the fixed urban wage. Profit of the rural sector is

[[Pi].sub.x] = G - w[L.sub.y] - r[K.sub.y], (2b)

where w is the flexible rural wage and the price of the numeraire Y is unity. Observe that marginal product of inputs are homogeneous of degree zero in K and L. In the short run, however, capital input is fixed, and marginal product of labor is decreasing in L.(4) The first order conditions for optimal labor employment are:

P[F.sub.L] - W = 0, (3a)

[G.sub.L] - w = 0. (3b)

The solution of (3a) and (3b) yields conditional labor demand functions, [L.sub.x] = [L.sub.x] ([K.sub.x], P, W) and [L.sub.y] = [L.sub.y] ([K.sub.y], P, w).

The rural wage w is equal to the expected urban wage. Thus, the relationship between the wages in the two sectors is given by the HT condition,

w = [Beta]W = W/(1 + [Lambda]). (4)

where [Beta] [is equivalent to] 1/(1 + [Lambda]) is the probability of employment, and [Lambda] [is equivalent to] [L.sub.u]/[L.sub.x] is relative unemployment in the urban sector.

In the HT model, labor demand falls short of labor supply,

(1 + [Lambda])[L.sub.x] + [L.sub.y] = L, (5a)

where [Lambda][L.sub.x] = [L.sub.u] represents labor unemployment in the urban sector. Capital market clearing requires

[K.sub.x] + [K.sub.y] = K. (5b)

Equations (1a)-(5b) complete the description of the production side of the HT model.

III. Responses of Factor Prices and Urban Unemployment

Perfect competition in product markets implies that the zero profit condition holds in "long run" equilibrium, although some labor unemployment exists in the urban sector because of wage rigidity. Thus, prices are equated to unit costs,

P = W[a.sub.Lx] + r[a.sub.Kx], (6a)

1 = W[a.sub.Ly] + r[a.sub.Ky], (6b)

where [a.sub.ij]'s are the input-output ratios.

First, consider how fixing the urban wage W above that for the full employment level affects the flexible rural wage w and capital rental r. Differentiating (6a) and (6b) with respect to W and holding P constant gives

[Delta]r/[Delta]W = -[a.sub.Lx]/[a.sub.Kx] = -[L.sub.x]/[K.sub.x] = -1/[k.sub.x] [is less than] 0, (7a)

[Delta]w/[Delta]W = [k.sub.y]/[k.sub.x] [is less than] 1, (7b)

[Delta](w/r)/[Delta]W = (r[k.sub.y]/[k.sub.x] + w/[k.sub.x])/[r.sup.2] [is greater than] 0, (7c)

where [k.sub.j] [is equivalent to] [K.sub.j]/[L.sub.j] is the capital-labor ratio in sector j. Thus, an increase in the urban wage unambiguously lowers the capital rental and the flexible wage-rental ratio, w/r. The manufacturing sector is assumed to be capital intensive ([k.sub.x] [is greater than] [k.sub.y]), and hence 1 [is greater than] [Delta]w/[Delta]W [is greater than] 0, i.e., as the manufacturing wage increases the flexible rural wage increase less than proportionately. Differentiating (4) with respect to W gives

[Delta][Lambda]/[Delta]W = [[k.sub.x] - (1 + [Lambda])[k.sub.y]]/w[k.sub.x] [is greater than] 0, (7d)

if the Neary [18] stability condition that the urban sector as a whole is capital abundant relative to the rural sector ([k.sub.x] [is greater than] (1 + [Lambda])[k.sub.y]) is satisfied. Thus, an increase in the urban wage increases unemployment in the urban sector.

In the Heckscher-Ohlin trade model, an increase in the price of a traded good necessarily raises one factor price and lowers the other, depending on the capital intensities of traded goods. How does a change in the producer price of the importable affect equilibrium factor prices in the HT model? Since the urban wage is fixed, a change in P only affects capital rental r and the flexible rural wage w. Differentiating (6a) and (6b) and noting that Wd[a.sub.Lx] + rd[a.sub.Kx] = wd[a.sub.Ly] + rd[a.sub.Ky] = 0 yields

dP = [a.sub.Kx]dr,

0 = [a.sub.Ly]dw + [a.sub.Ky]dr.

Thus, we get

[Delta]r/[Delta]P = 1/[a.sub.Kx] = X/[K.sub.x] [is greater than] 0 (8a)

[Delta]w/[Delta]P = -[k.sub.y](X/[K.sub.x]) [is less than] 0. (8b)

Thus, in the HT model, an increase in the price of the importable raises capital rental and reduces the flexible wage. Observe that this result is independent of factor intensities of traded goods. Intuitively, as the price of the importable increases, the capital rental in that sector has to rise to maintain the zero profit condition because the urban wage is fixed, which will attract more capital from the rural sector so as to equalize the capital rental between the two sectors. To maintain zero profit, the flexible wage must decline to offset the rise in unit cost caused by the increase in capital rental.

Differentiating the HT condition (4) with respect to w and P, holding W constant, yields

[Delta][Lambda]/[Delta]w = -(1 + [Lambda])/w [is less than] 0. (9)

[Delta][Lambda]/[Delta]P = ([Delta][Lambda]/[Delta]w)([Delta]w/[Delta]P) = [(1 + [Lambda])[k.sub.Y]]/[k.sub.X]](X/w[L.sub.x]) [is greater than] 0. (10)

This implies that an increase in the price of the importable will decrease the probability of urban employment, [Beta] = 1/(1 + [Lambda]). Intuitively, an increase in the price of the importable decreases the rural wage, which in turn induces more workers to seek employment in the urban area, thereby reducing the chance of urban employment.

The results of this section are summarized in the following proposition.

PROPOSITION 1. In a small open HT economy, an increase in the price of the importable increases capital rental, decreases the rural wage, and increases urban unemployment.

IV. Welfare Analysis

Consumer preferences are represented by a monotone increasing and quasi-concave utility function,

U = U(C, D),

where C and D denote the aggregate consumption of the exportable and the importable, respectively. Let I denote consumer income, p the domestic consumer price, and let C(p, I) and D (p, I) be the demand functions obtained by maximizing U subject to a budget constraint, C + pD = I. Then the indirect utility is written as

V [is equivalent to] V[p, I] = U[C(p, I),D(p, I)].

Import demand is given by

Q = D(p, I) - X(P), (11)

and tariff revenue is

T = (p - p*)Q = tQ, (12)

where p* is the foreign price of the importable, t [is equivalent to] p - p* is a specific tariff on the importable.

We now investigate the effects of a production subsidy and a tariff on the HT economy in the short run. For policy analysis, capital inputs are assumed to be fixed and the supply curves are positively sloped. Let s denote the domestic subsidy on the production of the importable. Then the domestic producer price is P [is equivalent to] p + s = p * + t + s. Profit maximizing competitive firms collectively maximize producer revenue

R = PX + Y. (13)

Consumers receive income from the sale of factor services. Total factor income is w[L.sub.y] + W[L.sub.x] + r[K.sub.x] + r[K.sub.y]. Profit dividends to consumers are [[Pi].sub.X] + [[Pi].sub.Y] = (PX - W[L.sub.x] - r[K.sub.x]) + (Y - w[L.sub.y] - r[K.sub.y]). Net government revenue is G = (tQ - sX). Thus, total income is the sum of factor payments, profits, and net government revenue, and is equal to the sum of producer revenue and the net government revenue, I = R + G. Since P = p + s, we get

I = PX + Y + tQ - sX = pX + Y + tQ. (14)

To analyze the effect of import tariff and production subsidy on welfare, we first consider their impacts of on import, producer revenue and income. Differentiating (13) and using the first order conditions, (3a) and (3b), and the HT condition in (4), we have

dR = XdP + PdX + dY = XdP + Wd[L.sub.x] + wd[L.sub.y] = XdP + w[(1 + [Lambda])d[L.sub.x] + d[L.sub.y]].

Totally differentiating (5a) gives (1 + [Lambda])d[L.sub.x] + [L.sub.x]d[Lambda] + d[L.sub.y] = 0. Thus,

dR = XdP - w[L.sub.x]d[Lambda]. (15)

From (10), we have d[Lambda] = [(1 + [Lambda])[k.sub.y]/[k.sub.x]][X/(w[L.sub.x])]dP = [[Delta]X/(w[L.sub.x])]dP; [Delta] = (1 + [Lambda])[k.sub.y]/[k.sub.x]. Thus,

dR = X(1 - [Delta])dP. (15[prime])

Thus, dR/dt = dR/ds = (1 - [Delta])X. Moreover, if the Neary stability condition is satisfied ([Delta] [is less than] 1), then for given foreign price p*, dR/dP [is greater than] 0. In other words, if [k.sub.x] [is greater than] (1 + [Lambda])[k.sub.y], then an increase in t or s increases the producer revenue.

Next, totally differentiating (14) gives

dI = dR + Qdt + tdQ - sdX - Xds, (16)

where Q = D(p, I) - X, and dQ = [D.sub.p]dp + [D.sub.I](dH + Qdt + tdQ) - X[prime](dp + ds). Rearranging terms, we have

[Mathematical Expression Omitted].

where [Mathematical Expression Omitted] is the slope of the compensated demand curve. Since [Mathematical Expression Omitted], we get dQ/dt [is less than] and dQ/ds [is less than] 0. Thus, an import tariff reduces import more than a production subsidy.

Substituting dR and dQ into (16), we obtain

dI = [1/(1 - t[D.sub.I])]{[D - [Delta]X - (t + s)X[prime] + t[D.sub.p]]dt + [-[Delta]X - (t + s)X[prime]]ds}. (16[prime])

Thus, dI/ds [is less than] 0 for all t [is greater than or equal to] 0, s [is greater than or equal to] 0. However, the sign of dI/dt is indeterminate.

We now examine the effects of changes in a tariff and a production subsidy on welfare. The indirect utility function is rewritten as

V[p, I] = V[p, PX + Y + tQ - sX]. (18)

Totally differentiating (18), using the Roy's identity, and noting dp* = 0, gives

dV = [V.sub.I](-Ddt + dI) = [[V.sub.I]/(1 - t[D.sub.I])]([Alpha]dt + [Beta]ds), (19)

where [Mathematical Expression Omitted], and [Beta] = -[Delta]X - (t + s)X[prime]. Note that dV/ds = [V.sub.I](dI/ds) [is less than] 0 and dV/dt [is less than] 0 for all t [is greater than or equal to] 0, s [is greater than or equal to] 0. That is, a tariff or a production subsidy reduces the welfare of a small country in the HT labor-surplus economy.

The first order conditions for an optimal combination of s and t are

[Mathematical Expression Omitted],

[Beta] = 0. (20b)

This implies that

t = 0, s = -[Delta]X/X[prime] [is less than] 0,

since [Mathematical Expression Omitted]. That is, the optimal production subsidy is negative and the optimal tariff is zero in a HT open economy.

Many LDCs lack revenue source to finance production subsidies, and rely instead on import tariffs. Consider an optimal tariff when the government is constrained to use only tariff (s = 0). From (20a), we get [Mathematical Expression Omitted], or

[Mathematical Expression Omitted].

That is, the optimal tariff is negative when no production subsidy or tax is used. These results are summarized below.

PROPOSITION 2. An import tariff is welfare-reducing in an HT economy and the optimal tariff is negative. If a production subsidy is used, however, the optimal production subsidy on the importable is negative and the optimal tariff is zero.

In the traditional HT model, capital is sector-specific, and the optimal policy consists of a wage subsidy in the manufacturing sector and a restriction of labor migration [13]. Restrictions on labor migration, however, are often considered infeasible by many economists. Bhagwati and Srinivasan [4] instead proposed as first best policy, (i) a uniform wage subsidy, and (ii) a wage subsidy to manufacturing combined with a production subsidy to agriculture, which they claim to be "equivalent" to a tariff. Corden and Findlay [11, 75] objected to tariffs on imports of manufactures because they conjectured that tariffs may fail to raise net output.

Governments of many LDCs lack revenue source to finance the subsidy to agriculture. Instead they tend to tax imports of manufactures. When capital is mobile between sectors, Proposition 2 shows that such an import tariff is welfare-reducing. Optimal trade policy rather requires a negative tariff on imports. Specifically, for instance, a reduction in Mexico's tariff to be implemented by NAFTA would improve welfare of Mexico, which may be considered an HT economy.

V. Terms of Trade Effect under Tariff and Subsidy

We consider the effects of a change in the terms of trade. Using (15) and (16[prime]) and noting that dp /dp* = 1 and dt = ds = 0, we get

dR/dp* = (1 - [Delta])X,

dI/dp* = dR/dp* + t(dQ/dp*) - sX[prime] = (1 - [Delta])X + t[[D.sub.p] + [D.sub.I](dI/dp*) - X[prime]] - sX[prime],

where

dQ/dp* = [D.sub.p] + [D.sub.I](dI/dp*) - X[prime].

Rearranging terms, we have

dI/dp* = [(1 - [Delta])X + t[D.sub.p] - (t + s)X[prime]]/(1 - [D.sub.t]).

Thus, we have

dV/dp* = [V.sub.I]{-D + [1/(1 - t[D.sub.t])]/[(1 - [Delta])X + t[D.sub.p] - (t + s)X[prime]]}

= [V.sub.I][-Q -[Delta]X + t[D.sub.p] - (t + s)X[prime]]/(1 - t[D.sub.I]). (21)

That is, an improvement in the terms of trade necessarily improves welfare of an HT economy.

PROPOSITION 3. An improvement in the terms of trade necessarily improves the welfare of a small open HT economy.

VI. Concluding Remarks

This paper uses the HT model to analyze optimal trade policies of a small open labor-surplus economy with intersectoral capital mobility. An increase in the price of the importable increases the capital rental but decreases the rural wage, regardless of the factor intensities of traded goods. It is shown that an import tariff is welfare-reducing and the optimal tariff is negative. However, if a production subsidy is used, the optimal production subsidy on the importable is negative and the optimal tariff is zero.

East Asia and Latin America have sharply differed in their policies to correct unemployment and to spur economic growth. For example, during the last three decades, East Asian countries, including South Korea and Taiwan, have promoted rapid export expansion, whereas many Latin American countries such as Chile and Argentina relaxed export promotion efforts and shifted to inward orientation [17].

Our analysis has two important implications on trade policies some developing countries adopted during the last three decades. First, when LDCs lack other revenue sources to finance production subsidies, an import tariff raises government revenue but reduces domestic welfare. Thus, an optimal policy is an import subsidy (a negative import tariff), or equivalently, an equal export subsidy. For example, East Asian countries such as South Korea and Taiwan chose outward-oriented strategies. In contrast, Chile and Argentina tightened import controls, raised tariffs, and overvalued their currencies. Our results suggest that import restrictions in these countries may be welfare-reducing. Second, if revenues can be generated, the optimal policy is not an export subsidy, but a production subsidy on the exportable (which is equivalent to a production tax on the importable). Production subsidy is superior to export subsidy, even though the latter promotes export more directly.

1. Chile and Argentina experienced unsatisfactory growth with fluctuating export earnings and rapid inflation that depressed domestic output [17]. Theoretically, Rivera-Batiz and Romer [19] suggest that economic integration increases the long run rate of growth, whereas Edwards [12] explore the linkage between trade policy and growth.

2. As Batra and Seth [3] point out, the Brecher model has limited applications because it results in complete specialization or production indeterminacy.

3. That is, even if the positive welfare effects of lower U.S. and Canadian tariffs are not included.

4. In the long run, both capital and labor are variable inputs, and linear homogeneity implies horizontal input demand curves.

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