Reforms 1 and 2 are concerned with domestic market integration interpreted as a reduction in the spatial variance of prices. Chapter 3 established that considerable rice price differentials persisted across Java in 1981. This result is reinforced by the SUSENAS sample price data
(see Tables 1.2 and A3.1.1). It is usual to attribute price variation to transport costs and market segmentation. It has also been argued that some aspects of government action vary regionally with differential
consequences for prices in those regions (Hughes, 1985). The policies do not generally benefit the population evenly. The gains have tended to be distributed along urban-rural as well as regional lines. These
considerations beg the question of whether policies which encourage greater market integration would be desirable. Such policies may well include the removal of some past policies which have hindered integration as well as more active intervention to promote the private trade such as by improved rural transport facilities and provision of better market information.
TABUS S.l! Summary of Rice Price Policy Reforms
1: Integration at sample mean price, PR 2: Integration at PR* (see text)
3; 20% increase in rice prices 4: 15% increase in rice prices 5: 10% increase in rice prices 6: 10% decrease in rice prices
Assumptions about Income Effects:
a: No current income effects on any households (Reforms la to 6a). b: Price change fully passed on to incomes of rice producers (Reforms
lb to 6b).
c: Producer incomes held constant, compensation by lump-sum transfer to/from all households (Reforms 3c, 5c, and 6c).
d: Producer incomes held constant, compensation by lump-sum transfer to/from all non producing households (Reforms 3d, 5d, and 6d).
on the distribution of welfare can be estimated by comparing the distribution of equivalent incomes in the original position with the simulated distribution obtained when prices are constant between
regions. This is the maximum degree of market integration possible in the extreme case of zero transport costs. It is of policy interest as a limiting case only, as transport costs approach zero. Nonetheless, by studying the welfare distributional effects of this highly stylized reform, one can gain some idea of the likely effects of more realistic reforms in which spatial price differentials persist. It is the natural benchmark when asking "what are the effects of spatial price
differentials on inequality". The revealed tendency for rice price
variability to be inequality reducing (see Section 4.4) suggests a priori that market integration will be inequality increasing.
The first reform simulation fixes the price of rice at the sample mean (Rps 223.1) for all households.
When the demand function is convex, the integrated price holding aggregate supply constant will be lower than the sample mean price. How much lower will, of course, depend on the degree of convexity of the demand function. In Reform 2, this lower rice price level, denoted PR* and referred to as the "integrated price", is imposed on all consumers. It is found by solving the market equilibrium condition at constant aggregate supply. In the loglinear functional form case this is straightforward. Mean demand is given by,
X = SXh/H = EPR^TEX^exp(ZhC)/H (5.1)
when evaluated at the mean residual of the demand model. At PR^ = PR for all h, this can be rewritten as
* . " h X = (PR TEX°exp(Z^c)/H) (5.2) h=l substitution gives. * a !! X = (PR E Xj^/PRJ (5.3) h=l
which is the market clearing condition at a fixed supply X. Thus
PR = exp[(logX - logEXj^/PR^)/a] (5.4) h=l
is the integrated market clearing price. Later, I will consider possible supply responses. The calculated PR* for the sample and demand
parameters from Table 3.19 is 221.8. This is only .583 percent lower than the mean price.
Computation of the integrated price for the AIDS demands turns out to be more complicated. AIDS demands are given by
X^ = [a + yJlogTEXj^ + clogPRj^ + d(logPRj^)^ ]TEXj^/PR^ (5.5)
and when rewritten in mean form.
_ 1 H h X = - ^ \ = l/PR*E(a + /?logTEX^)TEXj^/H H h=l h=l H + [(clogPR* + d(logPR*)^)/PR*]ETEXj^/H (5.6) h=l
The right hand side cannot now be solved explicitly for PR*. Numerical methods sre required. Newton's iterative method is used. Thus, writing the right hand side of (5.6) as a function ^(PR*), the estimate of PR* at iteration t is given by
PR* = PR^_* - (^(PR^.i) - X)/^'(PR)^_* (5.7)
Using the mean price as the start value, convergence to PR* = 227.7 within + 0 . 1 percent is achieved in four iterations. Note that the AIDS demand function turns out to be concave in price at the mean so that PR* is now above the mean price by about 2.6 percent. Corroboration of the function's concavity is found by evaluating the demand function's second derivative at the mean points. (Although convexity of demands is often
implicitly assumed, there is nothing in economic theory which dictates that this must be so.)
It is clear from these calculations that the choice of the demand functional form may strongly affect the integrated price; for the
loglinear the integrated price is slightly below the mean price, while it is above (by a larger margin) for the AIDS. Note, however, that the AIDS is a more flexible functional form in this regard, since (as long as the price elasticity is negative) the loglinear model will always be convex in price (hence yielding an integrated price below the mean). The AIDS is not so constrained.
For the mean price to be the market clearing price when markets are fully integrated (as in Reform 1), demand must be linear in price and supply must be inelastic (fixed). Both assumptions are implausible and it would be nice to relax them. Under Reform 2, demand is allowed to be non linear, although supply continues to be held constant. Supply
analysis is beyond the scope of this study. However, under the weaker assumption of linear supply response, mean quantity and mean price lie on the supply curve, in which case one can readily show that the actual market clearing point will lie somewhere in between the integrated market solutions of Reforms 1 and 2. This proposition can be stated more
formally as follows. If the supply curves in individual markets (S^^) are linear with constant slope across markets, then the X and PR will lie on the integrated supply curve, where
X = Es^(PR^)/n (5.8)
PR = EPR^/n (5.9)
and there are i=l,2,...,n markets. This follows from the fact that, with linearity:
X = Es^(PR^)/n = (6s/3PR)EPRj^/n + constant = Es^(PR) (5.10)
since
9S/9PR
= constant for all i. Without knowing supply responses, or where the integrated aggregate supply curve is situated, the resultenables us to locate a fixed point (PR, X) which is known to lie on that supply curve. When the demand function is convex (concave) this defines
e) the upper (lower) bound for the integrated market clearing price (PR while PR* defines the lower (upper) bound. Figure 5.1 illustrates this
for n=2. Thus the calculations for Reforms 1 and 2 are still of
relevance when (linear) supply responses are considered. The integrated prices used in these reforms are the bounds within which the actual integrated market clearing price will be found.
Figure 5.1; Integrated Market Price Will Lie Between PR* and PR
Price