the effect of consumption taxes and production subsidies

5
The Effect of Consumption Taxes and Production Subsidies YEONG-HER YEH* The purpose of this paper is twofold. In Section I, it will be shown that a consump- tion tax on the importable good could increase rather than decrease the consump- tion of the importable good. In Section II, it will be shown that a production subsidy given to the import competing industry could decrease rather than increase the production of the importable good. These two paradoxical cases could take place if the country concerned is a large country (namely, it has monopoly power in trade) and the foreign elasticity of demand for imports is inelastic. The offer curve ap- proach will be used in this study [Mead, 1952]. It will be assumed that neither the exportable good nor the importable good is an inferior good. Section I First, it will be shown how to derive an offer curve when there is a consumption tax. In Figure I, EF is the production possibility curve. The horizontal axis and vertical axis measure the exportable good X and importa- ble good Y, respectively. Given an interna- tional price line Pf, P and C are the production point and consumption point, respectively. Now, suppose that a consump- tion tax on good Y is imposed in order to reduce its consumption. If the terms of trade remained constant, the new consumption point would be at C'. The slope of the indifference curve at C' measures the tax- inclusive domestic price ratio facing consu- mers, whereas producers still face the same international price line Pf. After the con- sumption tax, the consumption of good Y is decreased, and the country would like to *University of Hawaii. The author is grateful to an anonymous referee for his valuable comments. How- ever, the author is responsible for any errors which remain in the paper. export less of good X and import less of good Y. Keeping the consumption tax rate constant and repeating the same process for any other international price line, one can derive the offer curve under the consumption tax, which would lie above the tax-free offer curve. Figure I The Derivation of on Offer Curve in the >- Presence of Consumption Taxes, -o P' c L__L .... F Home Export Good X In Figure II, OA1 and OA2 are the offer curves before and after a consumption tax, respectively. OB is the foreign offer curve. (Assume that the foreign elasticity of demand for imports is inelastic.) Before the consumption tax, OT1 is the equilibrium terms of trade and Qt is the equilibrium trading point. The welfare of the country is represented by the trade indifference curve t4 or the corresponding consumption indiffer- ence curve c4. C~G1 of good Y is consumed which is equal to the sum of C1D1 (provided by domestic production) and QIR1 (provided by imports). Under the consumption tax, the terms of trade have improved to OTz. The slope of the trade indifference curve t8 at the new trading 57

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Page 1: The effect of consumption taxes and production subsidies

The Effect of Consumption Taxes and Production Subsidies

YEONG-HER YEH*

The purpose of this paper is twofold. In Section I, it will be shown that a consump- tion tax on the importable good could increase rather than decrease the consump- tion of the importable good. In Section II, it will be shown that a production subsidy given to the import competing industry could decrease rather than increase the production of the importable good. These two paradoxical cases could take place if the country concerned is a large country (namely, it has monopoly power in trade) and the foreign elasticity of demand for imports is inelastic. The offer curve ap- proach will be used in this study [Mead, 1952]. It will be assumed that neither the exportable good nor the importable good is an inferior good.

Section I

First, it will be shown how to derive an offer curve when there is a consumption tax. In Figure I, EF is the production possibility curve. The horizontal axis and vertical axis measure the exportable good X and importa- ble good Y, respectively. Given an interna- tional price line P f , P and C are the production point and consumption point, respectively. Now, suppose that a consump- tion tax on good Y is imposed in order to reduce its consumption. If the terms of trade remained constant, the new consumption point would be at C'. The slope of the indifference curve at C' measures the tax- inclusive domestic price ratio facing consu- mers, whereas producers still face the same international price line Pf. After the con- sumption tax, the consumption of good Y is decreased, and the country would like to

*University of Hawaii. The author is grateful to an anonymous referee for his valuable comments . How- ever, the author is responsible for any errors which remain in the paper.

export less of good X and import less of good Y. Keeping the consumption tax rate constant and repeating the same process for any other international price line, one can derive the offer curve under the consumption tax, which would lie above the tax-free offer c u r v e .

Figure I The Derivation of on Offer Curve in the

>- Presence of Consumption Taxes, -o

P' c

L _ _ L . . . .

F

Home Export Good X

In Figure II, OA1 and O A 2 a r e the offer curves before and after a consumption tax, respectively. OB is the foreign offer curve. (Assume that the foreign elasticity of demand for imports is inelastic.) Before the consumption tax, OT1 is the equilibrium terms of trade and Qt is the equilibrium trading point. The welfare of the country is represented by the trade indifference curve t4 or the corresponding consumption indiffer- ence curve c4. C~G1 of good Y is consumed which is equal to the sum of C1D1 (provided by domestic production) and QIR1 (provided by imports).

Under the consumption tax, the terms of trade have improved to OTz. The slope of the trade indifference curve t8 at the new trading

57

Page 2: The effect of consumption taxes and production subsidies

58 ATLANTIC E C O N O M I C JOURNAL

Figure II The Consumption Effect of Consumption Taxes

under Inelastic Foreign Demand for Imports.

C8

'D

A~ AI

mz

4T

G Gi R z Ri Home Export Good X

point Q2 is equal to that of the consumption indifference curve c8 at C2. However, the consumption point (or production point) is not at Cz, but at (~. Lines dt and ds at (~ measure the domestic marginal rate of transformation and domestic marginal rate of substitution, respectively. Producers would face line dt (which is parallel to OT2), whereas consumers would face line ds (which includes the consumption tax on good Y). The welfare of the country is represented by the consumption indifference curves Cx. 1

Now, examine how the consumption of good Y is affected by the consumption tax. The slope of the production possibility curve EF at C (which is measured by dt o r OT2) is greater than that at C~ (which is measured by OT~). Thus, the domestic production of good Y after the consumption tax (CD2) is less than that before the consumption tax (C~D1). On the other hand, imports of good Y are increased from Q~RI to Q2R2 after the consumption tax. (This is due to the fact that the foreign elasticity of demand for imports

1 tt is assumed that the consumption tax revenue is redistributed to the private sector in the form of a general proportionate rate of subsidy to all incomes [Meade, 1952, p. 55].

is inelastic and the terms of trade have moved against the foreign country.) There- fore, the consumption of good Y after the consumption tax could be equal to, greater than, or less than that before the consump- tion tax. Figure II demonstrates the case where the former (CG2) is greater than the latter (C~G0. This means that a consumption tax on the importable good increases rather than decreases its consumption.

This paradoxical outcome will not take place when the foreign elasticity of demand for imports is elastic. This is shown in Figure III. (The notations used in Figure III are the same as those in Figure I1.) In this case, a consumption tax on the importable good must decrease its consumption. On the one hand, the domestic product ion of the importable good Y after the consumption tax is decreased from C1DI to CD: due to the terms-of-trade effect. (Producers after the consumption tax would face line dt o r line OT2, whereas they would face line OT~ before the consumption tax.) On the other hand, imports of good Y are also decreased (from Q1R1 to Q2R2) because the foreign elasticity of demand for imports is elastic. Therefore, the consumption of good Y after

Figure III The Consumptlon Effect of Consumption

Taxes under Elastic Foreign D~mand for Imports.

c8 C2 g ~

i/F ,o, / " F ID2

dt

Gz Gi 0 Rz Ri Home Export Good X

Page 3: The effect of consumption taxes and production subsidies

YEH' TAXES AND SUBSIDIES 59

the consumption tax (CG2) must be less than that before the consumption tax (CtGt).

Section II

First, it will be shown how to derive an offer curve when there is a production subsidy. MN in Figure IV is the production possibility curve. The horizontal axis and vertical axis measure the exportable good X and importable good Y, respectively. Given an international price line Pf, the production point and consumption point are at P and C, respectively. Now, suppose that a production subsidy is given to the import competing industry in order to expand its production. If the terms of trade remained constant, the new production point after the production subsidy would be at P'. The slope of MN at P' measures the subsidy-inclusive domestic price ratio facing producers, whereas consu- mers still face the same international price line Pf. After the production subsidy, the production of good Y is increased. Under the assumption that there are no inferior goods, the country would like to export less and import less under the production subsidy. Keeping the production subsidy rate con- stant and repeating the same process for any other international price line, one can derive the offer curve under the production subsidy, which would lie above the subsidy-free offer curve.

OAi and OA2 in Figure V are the offer curves before and after a production subsidy, respectively. OB is the foreign offer curve. (Assume that the foreign elasticity of demand for imports is inelastic.) Before the production subsidy, OT] is the equilibrium terms of trade and E, is the equilibrium trading point. The welfare of the country is represented by the trade indifference curve t~ or the corresponding consumption indiffer- ence curve c5. C~F~ of good Y is consumed which is equal to the sum of CiD] (provided by domestic production) and E1H1 (provided by imports).

The terms of trade have improved to OTz under the production subsidy. The slope of

Figure IV The Derivation of on Of fer Curve in the

Presence of Product ion Subsidies.

-r

0 N

Home Expor t Good X

Figure V The Protection Effect of Production Subsidies

under Inelostic Foreign Demond for Imports. p. -o

Cqc d x s dt

w C2 ^

/ / i i N ~ ~D2 i

/ 1 N JDi

~ M

AzJ Tz

B

F~ F I H 2 H i Home Export Good X

the trade indifference curve t9 at the new trading point E2 is equal to that of the consumption indifference curve c9 at C2. However, the production point (or consump-

Page 4: The effect of consumption taxes and production subsidies

60 ATLANTIC E C O N O M I C JOURNAL

tion point) is not at C2 , but at t~. Lines dt and d~ at (~ measure the domestic marginal rate of transformation and domestic margi- nal rate o f substitution, respectively. Produc- ers would face line dt (which includes the production subsidy), whereas consumers would face line ds (which is parallel to OT2). The welfare of the country is represented by the consumption indifference curve cx. 2

Now, examine how the domestic produc- tion of good Y is affected by the production subsidy. The slope of c5 at C1 (measured by OT0 is less than that of Cx at (~ (measured by ds or OT2). Based on the assumption that there are no inferior goods, (~ must lie above C1. 3 This means that the consumption of good Y after the production subsidy ((~F2) is greater than that before the production subsidy (C]F0. However, imports of good Y are also increased from E~H~ to EzH/ after the production subsidy. (This is so because the foreign elasticity of demand for imports is inelastic and the terms of trade have moved against the foreign country.) There- fore, the production of good Y after the production subsidy could be equal to, less than, or greater than that before the production subsidy. Figure V shows the case where the former ((~D/) is less than the latter (C~D0. 4 This means that a production subsidy to the import competing industry decreases rather than increases the produc- tion of the importable good.

This paradoxical result will not occur if the foreign elasticity of demand of imports is

2 It is assumed that the production subsidy is raised from the private sector in the form of a general proportionate rate of tax on all incomes [Meade, 1952, p. 55].

3 Draw a line from C~ horizontally to intersect the production possibility curve MN at W. (~ cannot lie below W on MN, unless good Y is an inferior good.

4 The slope of MN at C (measured by dr) is less than that of MN at C~. However, the slope of MN at C2 (also measured by the slope of e9 at C2 or that of t9 at E2) could be equal to, less than, or greater than that of MN at C~ (also measured by the slope of e5 at C~ or that of t5 at E0. Thus, the slope of MN at C could be greater than that of MN at Ct. This implies that less of good Y could be produced at t~ than at C1.

elastic. This is shown in Figure VI. (The notations used in Figure VI are the same as those in Figure V.) In this case, the domestic production of the importable good must increase after a production subsidy is given to the import competing industry. The slope of MN at (~ (measured by dt) is less than that of MN at C2. The slope of MN at C2 is, in turn, less than that of MN at C1.5 Thus, more of good Y must be produced at (~ after the production subsidy than at C1 before the production subsidy.

Figure VI The Protection Effect of Production Subsidies

under Elastic Foreign Demand for imports,

>-

-; u Cq ~ I

C2 Az AI

Tz t~ T,

d~ I I I q

F 2 F~ 0 H 2 H~ Home Export Good X

In conclusion, it has been shown above that when the country concerned is a large country and the foreign elasticity of demand for imports is inelastic: (1) a consumption tax on the importable good may increase rather than decrease the consumption of the importable good; and (2) a production subsidy to the import competing industry

5 The slope of MN at C2 is equal to that of c9 at C2 or that of t9 at E2. Similarly, the slope of MN at C] is equal to that of e5 at C~ or that of t5 at El. Under the assumption that neither good X nor good Y is an inferior good, the slope of t9 at E2 is less than that of t5 at Et. Therefore, the slope of MN at C2 should be less than that of MN at C~.

Page 5: The effect of consumption taxes and production subsidies

YEH: TAXES AND SUBSIDIES 61

may decrease rather than increase the production of the importable good. These paradoxical outcomes never take place when

the country concerned is a small country, or when it is a large country but the foreign elasticity of demand for imports is elastic.

REFERENCES

James E. Meade, A Geometry of lnternational Trade, George Allen and Unwin, 1952.