This section identifies the variables that bring shifts and movements along the rent transformation frontier. It then describes the nature of the effects of changes in the exogenous variables on the RTF.
(a) Changes in endowment
Changes in the endowments of the factors in the economy bring about changes in the capacity of the economy to produce. In general, these changes are responsible for the shifts in the RTF. For example, an increase in the stock of capital in sector 1 will increase the level of output that it can produce in specialization through the resulting increase in the productivity of labour. If the consequent increase in the marginal product of labour is not very high, so as not to raise wage rates prohibitively high, then the rental income of sector 1 will also increase. However, the rental income of sector 2 under specialization will be unaffected by change in the stock of capital in sector 1. Therefore, the RTF will shift in favour of sector 1. A similar argument applies to the case with an increase in the stock of capital in sector 2. It will induce a shift in the RTF in favour of sector 2.
6 In fact, using the definition of cost share o f labour from the equation (3.28), employment share from (3.30), and noting that rental mix is given by equation (4.17), it can be seen from equation (4.8), by normalizing the sectoral stock of capital to unity, that the slope of the rental transformation function under Cobb-Douglas technologies is given by
äRL = _ ß L 1 dRt f t Pt '
Therefore, if the share o f capital in the two sectors are equal then in equilibrium the slope of the rental transformation frontier will be equal to the slope of the product transformation frontier. That is, the product transformation frontier is a proportionate blow out o f the rent transformation frontier.
Similarly, an increase in the stock of labour in the economy, ceteris paribus, lowers the wage rate which, in turn, contributes to an increase in the rental income of either sector. The extent of shift in the rental income under specialization, as will be indicated below, depends on the distributive shares of labour and the elasticities of factor substitution in the two sectors. The intuitive mechanism can be tracked from equation (3.42) which yields the response of the wage rate as labour supply changes, and from equation (3.39), which yields the response of rental rate as wage rate changes.
Analytically, the effects of the endowment changes in the sectoral rental rate can be observed from the equations (3.46) and (3.47). The extreme points of the RTF can be observed be creating situations of specialization in the employment of the mobile factor, which can be ensured by setting Xl = 1 and A2 = 1 respectively.
When Aj = 1, the effect of an endowment change in the rental rate of sector 1, at constant commodity prices, can be obtained from equation (3.46) and is rewritten as
(4.18) n - / ) .
G \
Therefore, ceteris paribus, for kx > 0, the percentage change in the maximal rental income of sector 1 can be written as ^ + rx = (1 - SLX / Gx )kx that is positive for g x> 1
and; for / > 0, we have rx = (SLX / Gx) l which is always positive. That is, the rental income of sector 1 will increase under specialization as the national endowment of labour and/or the stock of capital in sector 1 increases, and the elasticities of factor substitution are not very small.
Similarly, by setting A2 = 1 we can obtain the effect of endowment changes on the rental income of sector 2. For k2 > 0, ceteris paribus, we can obtain from the equation (3.47) that + r2 = (1 - SL2 / cr2) ^ which is positive for cr2 > 1, and for / > 0, we get r2 = (SL2 / g2)1which is always positive. These results show that the maximal
rental income of sector 2 will increase with an increase in the endowment of labour and/or with an increase in the stock of capital in sector 2, provided the elasticity of factor substitution is not very small.
Figure 4.3 shows typical patterns of shifts on the RTF as endowments change. Panel (a) shows the effect of an increase in the stock of capital in sector 1, panel (b) shows the effect of an increase in the stock of capital in sector 2, and panel (c) shows the effect of an increase in the endowment of the mobile factor on the RTF. The axes measure the rental incomes in units of own output. Numbers on the axis represent the respective sectors or the owners of the specific factors.
Good 1 Good 1 Good 1
Good 2
Good 2 Good 2
(c): /> o
Effects of endowment change on the RTF Figure 4.3
(b) Changes in price variables:
Any change in the domestic relative price, by definition of RTF, causes a movement along the RTF. Changes in the domestic relative price can be caused by a change in the tariff rate and or by a change in the international relative price. Therefore, changes in the world price and the tariff rate cause a movement along the frontier.
Good 1
Price changes: movements along the RTF Figure 4.4
To illustrate, let P* be the initial world price ratio and Tx be the tariff rate. The figure illustrates that the imposition of tariff rate raises the rental income of sector 1 and
lowers the rental income of sector 2. Suppose the world relative price of commodity 1 falls, and the world relative price becomes P*. Then, at an unchanged tariff rate the domestic relative price of commodity 1 also falls and consequently, the combination of equilibrium rental incomes of the sectors is given by the point + Tx)). If the tariff rate is increased to compensate for the fall in world price then the rental income will again be represented by the point marked R(P*(l + T{)) but with a different value for the tariff rate variable, 7J.
Thus, if the source of the shock is the tariff rate or the international relative price, then the effect will be a movement along the RTF. If the source of the shock is a change in one of the factor endowments, then the effect will be a shift on the RTF.
4.5 Summary
Basing on a simple general equilibrium model of a small open economy
described in the previous chapter a rent transformation function has been derived in this chapter. The corresponding rent transformation frontier traces the equilibrium
combinations of the sectoral rental incomes as the tariff rate changes. Along a frontier an increase in the rental income of one sector necessarily reduces the rental income of the other sector. The mechanism behind this transfer is the induced difference in the real wages faced by the two sectors, which further induces a reallocation of labour between the two sectors and hence the outputs and the rents.
It has been shown that if the long run elasticity of factor substitution is at least unity in both sectors and rents are measured in units of own output, then the rental transformation frontier is concave to the origin and lies inside the product
transformation frontier. This shows that the sectoral rental functions, that yield rental income at each relative price, are bounded, and the real-rent possibility set is convex. Any change in the endowment of factors will cause a shift on the frontier and a change in the tariff rate or the international price ratio will cause a movement along the frontier. Since, the tariff rates are such powerful instruments of income redistribution an obvious question that follows is how the tariff rates are determined. An attempt to answer this question using a political economy approach will be made in the next chapter.
CHAPTER 5
EXISTENCE OF A NASH EQUILIBRIUM IN THE TARIFF GAME