Chapter five: Taxation and the surplus under fixed exchange rates

Contents - Previous - Next

The first set of questions we explore deal with agricultural and import taxation under regime Au. In this case the exchange rate is fixed. Increasing agricultural export tax, if the import tariff does not change, implies lower agricultural prices pa and hence appreciation of the real exchange rate (which, as discussed earlier is equal to pa) This, ceteris paribus, means lower average income for agriculture, and hence smaller nominal wage and increased migration to non-agricultural activities. Hence non-agricultural production increases. Given that there is no external constraint, more imports will be forthcoming.

The real wage also declines, as the decrease in the nominal wage is smaller than the decline in the agricultural price. This is a standard result from the literature on the two-good three-factor model of international trade, see Jones (1971) and Mayer 11974), and is illustrated in Figure 3.

In Figure 3 the horizontal axis represents the total labour endowment in the economy. Labour utilized in agriculture is measured from Oa toward the right, while labour utilized in non-agriculture is measured from On toward the left. The left most vertical axis measures the average product of labour in agriculture, while the right-hand vertical axis measures the marginal product of labour in non-agriculture. The two curves AA and NN represent these average and marginal products. Their intersection represents the labour market equilibrium, and is a geometric representation of equation 13.7)

Initially agriculture employs an amount of labour equal to OaK, and non-agriculture an amount equal to OnK. The economy-wide wage rate is equal to w0. When the agricultural price declines, the average product of labour in agriculture also declines for any given agriculture labour input. This is depicted by a downward shift in the curve AA to A/A/ . The new equilibrium allocation of labour is OaK/< OaK to agriculture and OnK/ > OnK to non-agriculture. The nominal wage declines to w/, but the vertical distance between w0 and w/ is smaller than the vertical distance between curves AA and A/A/, which is in turn equal to the decline in the agricultural price.

The demand for the agricultural good could decrease or increase, depending on the relative strengths of the income and price effects of consumer demand. However, the private demand for the non-agricultural good will most likely decline. Since the production of the nonagricultural good increases, this implies that the volume of the surplus S increases. Hence, taxation of agriculture in this case implies a larger fund available for government expenditures as well as investment.

In terms of the three components of the surplus indicated in equation (3.15), namely non-agricultural profits P , foreign saving F and tax revenue T. the first two are likely to increase under this policy. The change in private profits can be readily seen from Figure 3. The size of private profits P is represented in this figure by the area under the curve NN and above the horizontal line BC (this is because when import prices are not changed, profits are equal to the integral of the marginal product of labour, minus the total wage payments). Clearly when the nominal wage declines, this area increases.

Figure 4 illustrates the situation concerning the foreign savings and the tax revenue under fixed exchange rate. When the agricultural tax rate increases, the volume of exports declines to OF/ from an initial level OF. Because of labour reallocation in the economy and increased production of the non-agricultural product, the demand for imports increases, and this is represented by a rightward shift of the curve MM to M/M/ in the figure. The new volume of imports is OG/, and required foreign savings is F/G/.

The import tariff revenue clearly increases, as the rate of tariff does not change. The export tax revenue changes from ABCD to A/B/C/D. This can be an increase or decrease in the tax revenue depending on the elasticity of the export supply curve, and hence the total tax revenue T could increase or decline.

Figure 3 Intersectoral labour allocation in the economy

Note that it is not necessary that the agricultural export supply curve is upward sloping. The volume of agricultural exports is the residual of agricultural production minus domestic "food" demand. An improvement in the agricultural terms of trade will increase agricultural production, but also will improve real incomes, and hence the demand for food. Depending on the relative strength of these two effects the export supply curve could be positively or negatively sloped.

To analyze the welfare of a typical worker or farmer in the economy under the policy changes, consider the nominal wage per labourer w. By assumption this is also equal to the average wage in agriculture. The utility achieved by the typical worker earning an income initially equal to w0, and facing initial prices equal to , is denoted by U0. We have assumed that this worker spends all his income. If we denote by the expenditure function of this worker, namely the function which gives the minimum expenditure needed at income w0 and prices to achieve utility U0, then initially we have


When the price faced by the worker is , then the minimum expenditure needed to achieve the initial level of utility is . If, nevertheless, the worker has income (and expenditure) equal to w, then his welfare is improved if w is larger than .

Hence a unitless indicator of welfare can be specified by W as follows


Initially W= 1. If the wage and pa change so that W increases then there is an improvement in welfare. If on the other hand the changes lead to a decline in W. then worker welfare is worsened. The definition of welfare in this fashion is analogous to the concept of "money metric utility" (Deaton, 1980) which is the theoretically correct way to measure welfare.

Figure 4 Changes in foreign savings and the tax revenue under Au

If we log-differentiate (5.2), namely if we consider the proportional changes of the variables from their initial values , then the proportional change in welfare of the typical worker can be written as follows


Applying the standard result that the partial derivative of the expenditure function with respect to a price is equal to the amount of the relevant consumed product (Varian, 1984, p. 123, 126) we obtain


where q a is the worker initial average budget share for the agricultural product


Hence, as equation (5.4) indicates, worker welfare will improve if the proportional increase in the nominal wage is larger than the proportional increase in the agricultural terms of trade multiplied by the "food" budget share. In essence the second part in equation (5.4) is the change in the consumer price deflator facing the worker. The change in welfare indicated in (5.4), while theoretically rigorous, is nothing more that the percentage change in the real income of the worker. This, as written in (5.4) is equal to the percentage change in nominal income w minus the percentage change in the "cost of living" of the worker. (For an empirical application of this method of viewing welfare see Sarris ( 1 993)).

Under the fixed exchange rate regime, it was seen that the nominal wage declines but by a smaller amount than the decline in the terms of trade of agriculture pa. If the decline in the wage is proportionally smaller than the product of the food budget share and the decline in agricultural price, then equation (5.4) shows that the welfare of the workers (and farmers) could even improve. This would clearly be a felicitous situation, whereby the surplus for public consumption and total investment is increased by agricultural taxation, but at the same time the welfare of workers is improved. The reason that this would be possible is a large increase in foreign finance.

To obtain a feeling for the numbers, we indicate in Table 1 stylized parameter specifications of the model for 20 different types of (hypothetical) developing economies. In all cases the rate of initial import tariff is zero percent while the rate of initial export tax is also zero. The economies are first distinguished according to the share of the labour force employed in agriculture, ranging from those where this share is small to those where the share is large. The lowest such share is 54 percent (economy 121, while the highest is 81 percent (economy 111. The other parameters that vary are the shares of labour in value added, the share of imports in non-agricultural production, the income and price elasticities of demand for the product of agriculture, and the consumer budget share for food. The effort has been to make the stylized parameters compatible among themselves. For instance the food budget shares and the income elasticities of demand for agriculture are higher for economies with higher shares of labour in agriculture. Such economies are most likely to be poor. In all cases the share of the labour force employed in agriculture has been adjusted so that the initial resource balance F is zero, namely the external trade is balanced.

Table 2 indicates the values of various shares of the stylized economies. These shares can be derived from the parameters of Table 1 by the methods outlined in Appendix B. It is clear that economies with higher proportion of labour employed in agriculture, are also those which exhibit a large share of agriculture in GDP. Note that the share of imports in GDP /which under balanced trade is equal to the share of exports in GDP) is generally lower for economies with higher shares of agriculture in GDP.

Table 1 Specification of alternative economies

Share of
employed in agriculture
Labour in
Shares in value added
Labour in non-
Imports in
non- agriculture
Price Elasticity
Elasticity of
Demand for
Consumer Budget
Of Demand for Agriculture
Share for
1 0.59 0 20 0.5 0.30 0.60 -0.8 0.35
2 0.63 0.25 0.5 0.30 0.70 -0.7 0.40
3 0.66 0.30 0.5 0.30 0.70 -0.7 0.45
4 0.69 0.30 0.5 0.30 0.80 -0.7 0.50
5 0.70 0.30 0.6 0.30 0.70 -0.5 0.55
6 0.73 0.35 0.6 0.30 0.75 -0.6 0.60
7 0.75 0.35 0.6 0.25 0.80 -0.6 0.65
8 0.77 0.35 0.6 0.30 0.85 -0.6 0.65
9 0.78 0.40 0.6 0.35 0.80 -0.6 0.65
10 0.80 0.45 0.6 0.30 0.85 -0.5 0.70
11 0.81 0.50 0.6 0.35 0.90 -0.4 0.70
12 0.54 0.20 0.5 0.20 0.60 -0.8 0.35
13 0.57 0.25 0.5 0.20 0.70 -0.7 0.40
14 0.61 0.30 0.5 0.20 0.70 -0.7 0.45
15 0.64 0.30 0.5 0.20 0.80 -0.7 0.50
16 0.66 0.35 0.6 0.20 0.70 -0.5 0.55
17 0.70 0.35 0.6 0.20 0.75 -0.6 0.60
18 0.74 0.40 0.6 0.20 0.80 -0.6 0.65
19 0.75 0.45 0.6 0.25 0.85 -0.6 0.65
20 0.75 0.50 0.6 0.25 0.80 -0.6 0.65

Table 2 Values of various shares for the stylized economies (percent) under the assumption that external trade is balanced

Share of labour
force in
Share of Agriculture in GDP Share of imports in GDP Share of
Share of surplus in non-agricultural production Share of
Surplus in GDP
1 59.4 51.1 21.0 41.1 20.0 14.0
2 62.5 54.3 19.6 36.0 20.0 13.0
3 65.6 57.7 18.1 31.4 20.0 12.1
4 68.8 61.1 16.7 27.3 20.0 11.1
5 70.0 66.7 14.3 21.4 10.0 4.8
6 73.3 70.2 12.8 18.2 10.0 4.3
7 75.3 70.9 9.7 13.7 15.0 5.8
8 76.7 73.8 11.2 15.2 10.0 3.7
9 77.9 76.5 12.7 16.6 5.0 1.8
10 80.0 77.4 9.7 12.5 10.0 3.2
11 81.1 79.8 10.9 13.6 5.0 1.6
12 53.6 41.9 14.5 34.7 30.0 21.8
13 57.1 45.5 13.6 30.0 30.0 20.5
14 60.7 49.1 12.7 25.9 30.0 19.1
15 64.3 52.9 11.8 22.2 30.0 17.6
16 66.3 59.6 10.1 17.0 20.0 10.1
17 70.0 63.6 9.1 14.3 20.0 9.1
18 73.8 67.8 8.0 11.9 20.0 8.0
19 75.3 70.9 9.7 13.7 15.0 5.8
20 75.3 70.9 9.7 13.7 15.0 5.8

The share of total surplus in GDP which in this case of zero taxes is all made up of non-agricultural profits varies inversely proportionally with the share of agriculture in GDP. The reason is that countries with large agricultural sectors cannot generate adequate non-agricultural profits, nor can they generate large amounts of import taxes, given the small share of imports in GDP. This illustrates the difficulties that countries at early stages of development might have in generating surpluses.

The same table was reproduced, under the assumption that the resource balance is 5 percent of GDP. Table 3 illustrates the characteristics of the various stylized economies under this case. All parameters are the same for a given economy as in Table 1 except the share of labour employed in agriculture. The difference between the figures in Table 3 and those of Table 2, is that now the shares of labour employed in agriculture are smaller, and correspondingly the shares of agriculture in GDP are lower. This is so because smaller amounts of agricultural exports are needed to obtain a given level of imports. The share of imports in GDP is larger (the share of exports in GDP is not shown as it is just 5 percent lower than the share of imports in GDP), while the share of agricultural production exported is lower. Almost the full 5 percentage points of increased foreign savings results in higher shares of surplus in GDP, as expected.

Finally in Table 4 we reproduce the shares of the various stylized economies of Table 3 under the further assumption that initially the import tariff rate is 40 percent, and the export tax rate is 20 percent. It can be seen that the shares of labour employed in agriculture are lower, while the taxes make up a significant portion of the total surplus. In the sequel our benchmark economies are those illustrated in Table 2, namely those where the surplus derives initially only from non-agricultural profits.

Table 5 presents the general equilibrium elasticities of the various variables in the 20 stylized economies of Table 4 with respect to the domestic terms of trade of agriculture. The formulas for these numbers are outlined in Appendix B. A 1 percent increase in the terms of trade of agriculture for economy type 1, results in a 0.34 percent increase in the nominal wage, 0.16 percent increase in agricultural output, and 0.86 percent decline in non-agricultural output. The elasticities of aggregate agricultural production with respect to the agricultural terms of trade are between .16 and 0.6, which are within the range estimated by various authors (Bond, 1983, Binswanger et al., 1985).


Contents - Previous - Next