Ley de Reforma Agraria
LEY DE REFORMA AGRARIA
factor in the other sector. Therefore, the owners of sector specific factors will have a
conflict o f interest with respect to tariff changes A
4.2 The Shape of the Rent Transformation Frontier
Substituting the expressions for rx / px and r2 / px from the equations (3.48) and (3.49) into the equation (4.7) and simplifying the expression making use of equation (3.43), which gives the price elasticity of the wage rate, yields
(4.8) dRL= R, (A2ct25l1 "
dR, R,
Differentiating both sides of equation (4.8) with respect to R2 yields, on further simplification, (4.9) <72A2SLi ( * ' ) ^ OxX xS L2 j
U 2J
R2dRx RxdR2- 1 dX2 dXx X2dR2 XxdR \ r + 2 y ^L\ ^ 2 ^ L 2 ^ 2Since Xi - L i / L, and since the motive variable for change in this general equilibrium system is the domestic relative price, then
4 This may not be true if we are analysing endogenous tariff changes ex ante in which case the owners of the specific factors may agree in the direction of tariff changes. For a demonstration of this and other interesting results see Cassing, Hillman, and Long (1986).
Furthermore, this apparent conflict between the owners of the sector specific factors is a consequence of the adoption of the specific factor model. If we take a long run view and adopt Hecksher- Ohlin-Samuelson model that allows capital to move across the sectors, then the basic conflict will be between labour and capital as predicted by the Stolper-Samuelson theorem (see for example, Brock, Magee and Young, 1989). In this case it would be more useful to obtain the factor income transformation frontier and evaluate its properties than to stay with the RTF defined here.
(4.10) (4.11) dSQ = dSQ/dPx dR2 dR2 / dPx ' dL, _ dLi / dPx . j = 1,2; and i = 1,2. dH2 dtf, / d/J
Using equation (4.8), equation (4.9) can be rewritten as (4.12) d 2R1
_
<
72^
2‘^L
1Y
^1 dR iA ^ J
-<
72^
2^L
1 ^ ct1A15L2
j (^2 ! P\ h ! Pi )~^~ (■$£,! / 5^2 / Pi) r2> AMaking use of the equations (3.28), (3.44) and (3.45) around any arbitrary equilibrium equation (4.12), after a simplification, can be rewritten as
(4.13) %d 2R<S, 1 1 ^2^2^L\ (
Ai
^((TiAiS ^ ) j
U2J
[ (^ 2 ^ '2 '^ L l ^ 1 ^ 1 *^,2 ) ^ 1 ^ 2 (1 ^lX^2^2 ^ 2 ^ 2 * ^ L l) (1
On a further simplification using the adding up property of the distributive and employment shares the equation (4.13) can be rewritten as
(4.14) d 2Rt _ 02^2 $Ll
(Ai
dRl k(oX S L2) >
UiJ
\ ^ 2 ^ 2 ^ L l ^ \ 1 ) + ^ 1 ^ 1 *^£,2 ( ^ 2 1 ) ^ l ^ l ^ K 2 ^ 2 ^ 2 '^ Ä 'l] *
Thus, it is clear from the right hand side of the equation (4.14) that the condition d2 R
(Jj > 1 and cr2 > 1 is sufficient for — j- < 0. These conditions hold under assumption dR2
4.1, and thus we have the following proposition:
Proposition 4.2 I f the rental rates are measured in units o f own output; and the long run elasticities o f factor substitution are at least unity in both the sectors, then the rental transformation function is concave and negatively sloped. That is, the rental transformation frontier slopes downward to the right and is concave to the origin in the rental plane, and the set o f feasible combinations of rental rates (and rental income) is convex.
4 3 The Product and Rent Transformation Frontiers
On the basis of these results, the nature of the rent transformation frontier can be illustrated geometrically. Figure 4.1 shows the rental and product transformation
frontiers for given world price, endowment of sector specific factors, and the economy wide supply of the mobile factor.
Good 1
Product Transformation
Rent Transformation
Good 2
The rent and product transformation frontiers Figure 4.1
In this four quadrant figure, quadrants II and IV show the production functions of sector 1 and sector 2 respectively. The total endowment of labour in the economy is OL(=OL'). The x-axis in quadrant I measures the output of commodity 2, and the y-axis measures the output of commodity 1. The curve AB represents the usual product
transformation frontier - it shows the combination of maximum attainable output of one sector given the output level of the other sector. For example, if all labour is employed in sector 2, OB units of commodity 2 will be produced. Alternately, if all labour is employed in sector 1, OA units of commodity 1 will be produced, while the output of commodity 2 will be zero.5 The curve AB shows the transformation possibilities of commodity 2 into commodity 1 and vice versa.
5 Note that if the production functions are not characterized by unitary elasticity o f factor substitution, then the output of sector 2 will not be zero even if all of the mobile factor is employed in sector 1. Similarly, the output of sector 1 will not be zero even if all o f the mobile factor is employed in sector 2. Each sector can produce a minimum quantity o f its output by employing the sector specific
The product transformations in equilibrium, under the maintained hypothesis that production sectors are profit maximizers, can always be induced by exogenous changes in domestic relative price of commodities. The mechanism behind this transformation is that changes in the relative price of the commodities alter the equilibrium wage rate, which will induce a reallocation of the mobile factor - labour, between the sectors. Thus each point on the curve AB is a point of production equilibrium that corresponds to a particular domestic relative price of commodities.
Since the mobile factor (labour) is paid its marginal product, AC represents the wage bill of sector 1 and OC represents the rent to the specific factor in sector 1 when all labour is employed by sector 1. Rent to the specific factor in sector 1 is zero (see quadrant II). Similarly, when all labour is employed by sector 2, DB represents the wage bill and OD represents the rent to the specific factor in sector 2, while the rent to the specific factor in sector 2 is zero (see quadrant IV). The curve CD traces out the combination of the real rents to the two sector-specific factors through reallocation of labour between the two sectors induced by exogenous change in the domestic relative price of commodities.
The product transformation frontier and domestic price ratios are well known tools of economists that help to locate the equilibrium product mix. It is natural to enquire about the location of equilibrium rents for given commodity prices.
We know from equations (3.11) and (3.12) that the specific factors, in
equilibrium, are paid their corresponding value of marginal product. Therefore, using equation (3.6) and noting that commodity 2 is the numeraire, we can write
(a
,
c\
f f,
/*,)'*»
A ßi(Xi/ K2)'*fl‘
Hence, by expressing the rents in units of own output the equation (4.15) can be rewritten as
(4.16)
M
l- M
l ( Y ' * P 'k2r2
AC
UC
Given the parameters of the production functions and the stock of the specific factors, equation (4.16) provides the translation from output levels to the ratio of
factor only. In this case both the product and the rent transformation frontiers will have some linear segments on both ends. However, the above properties o f the frontiers will remain unchanged. In what follows we will ignore this possibility until chapter 7, since at this level o f aggregation comer solutions are rare possibilities.
sectoral rental incomes. In general, it can be seen from equation (4.16) that the relation between rental mix and output mix is non-linear.
In particular, if the production function in both the sectors are Cobb-Douglas, then both px and p2 tend to zero and the equation (4.16) reduces to
(4.17)
M
lk,r2