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An extension of the simple analytics of segmented grain markets and the case for liberalization
World Development, Vol. 16. No. 6. pp. 759-763.
1988.
0305-750x/88 53.00 + 0.00 Pergamon Press plc
Printed in Great Britain.
An Extension of the Simple Analytics of Segmented Grain Markets and the Case for Liberalization HARSHA V. SINGH* GA TT Secretariat, Geneva Summary. -This note extends the model used by Roemer (1986) to analyze the effect of maintaining a low consumer price in the grains market by the government. It is shown that Roemer’s result that government intervention is unlikely to have an adverse impact on domestic output is not valid if some other, different grain-purchase schemes of the government and the possibility of smuggling are incorporated in the analysis.
from the producers at a price lower than that in the free market and sells it to the consumers at this low price. Regarding the sales decisions of farmers, he assumes that they “may sell to the [grain marketing] board, to private intermediaries who will resell in the parallel market, or directly to the consumers” (1986, p. 430). The main results of this model can be explained by using Figure 1 given below, which is a slightly modified version of Roemer’s Figure 1. The model is that of a closed economy; one could assume an open economy case but that would introduce other features in the analysis. Panel A shows the official market with the free market total demand (DD) and total supply (SS) for grain.’ The government fixes a price P, less than the free market price PO, and buys and sells grain at this low price. The farmers supply only Q, level of output to the official market, while the consumer demand is equal to Q,. The unsatisfied demand spills over to the parallel market, which is shown in Panel B. Two extreme assumptions can be made about the unsatisfied demand in order to get the range of the parallel market price. If we assume that the quantity at controlled price is supplied entirely to those at the upper price range of the demand curve, then the unsatisfied demand which
1. INTRODUCTION A recent article by Roemer (1986) in this journal analyzed several aspects of segmented markets for grain, credit, labor and foreign exchange. This note extends his analysis of the grain market, for which segmented markets, i.e. an official market and a black market, arise because of government intervention. Section 2 of this note explains the results of the Roemer model. This serves two purposes. One is to explain the method of analysis by which we also will determine the range of price and output under market segmentation. Second is to give us a set of results to contrast with those of the other models we discuss in this paper. These models, which are analyzed in Section 3 of this note, extend the set of assumptions made by Roemer by including government procurement of grain in ways other than that assumed by him, and by including the possibility of smuggling. The last section gives the conclusion of this analysis. It is evident that this note does not provide an exhaustive treatment of the issues under discussion, and like Roemer, we also hope that this analysis will induce others to further investigate the problem.
2. THE ROEMER
MODEL
‘I have benefited from the comments of my colleagues, especially Richard Eglin. However, the views expressed here are my own and should not be attributed to either my colleagues or the GATT Secretariat.
Roemer has analyzed the situation of price control when the government purchases grain 759
760
WORLD
DEVELOPMENT
Price I
(a )
(b)
S
Quantity Figure
spills over to the parallel market is DzDz. Since the controlled (or official) market is supplied only by those who are willing to supply at P, the rest of the supply curve, i.e. beyond Q,, spills over to the parallel market. This supply curve, S,S,, will intersect D2Dz at P,,, the free market price. The reason is straightforward. The situation in the parallel market is equivalent to a leftward shift of the vertical axis by OQ,. After this the supply and demand curves are the same as in the free market, thus leading to the same price. The other extreme assumption about the supply of grain at controlled price is that it is supplied entirely to those at the lower price range of the demand curve. In this case the spillover demand curve is DD, and the equilibrium price is higher than PO, the free market price. Based on this analysis Roemer concludes that the parallel market price is likely to be above the free market price. The only situation in which the parallel market price will drop below the free market price is when the risk premium (and other transaction costs) in the parallel market for consumers exceed those for the sellers. Another conclusion reached by Roemer is that parallel markets are likely to compensate for much of the reduced sales in the controlled markets, and can fully compensate if they are efficient and not foo risky. Thus liberalization of grain markets may not elicit much, if any, additional production, as some advocates claim, but is likely to improve overall marketing efficiency. . The more liberalization lowers marketing cosfs, the more likely it will also increase marketed quantities. (Roemer. 1986. p. 433)
1.
3. SOME EXTENSIONS This section will extend the Roemcr model by introducing some other assumptions about the way in which the government collects the grain to be sold at the low price, the production decision of farmers being linked to their price expectations and the possibility of smuggling. A proper comparison of the results of this section with those of the Roemer model involves a comparison of the equilibria to which the system converges under the different sets of assumptions. Therefore, except in one case, we ivill also rule out the situation of a non-convergent system as is implicitly done by Roemer also. (a) Otherpw-chase schemes In the previous section, the assumption is that grain at low price is supplied to the government only by those farmers who are willing to do so (see Figure 1). There may be other situations when the farmers may not be free to decide how much to supply to the government, i.e. the government may stipulate the quantity (or proportion) of output to be supplied at the low price. Even otherwise, if a high price in the black market is expected then even those farmers capable of supplying at the low price may not be willing to do so. In this situation there is a possibility for the farmer to sell a part of his output in the black market and the weighted average of the black market price and the government price
SEGMENTED
GRAIN
MARKETS
becomes the relevant price for his production decisions. (We will refer to this as the effective when the farmer can price.) Consequently. simultaneously participate in both the government and the black market, the process by which the system converges to its equilibrium differs from a normal cobweb process (see below). As a result of this new situation the output under segmented markets may be less than the free-market level even if there is no cost premium in the black market. However, the black market price will still be above the free-market price. To simplify the analysis, we assume that the government buys a fixed proportion of the total output of the farmers at the low price.? This situation is shown in Figure 2, which combines the two panels of Figure 1. The free-market demand and supply curves are given by DD and SS. With the government taking a fixed proportion of production the residual supply curve for the black market is given by SJ, provided there is no under-reporting of production in order to divert it to the black market.3 The horizontal distance between SS and Si.S shows the quantity collected by the government. The effective price (EP) is equal to UP + (1-n)P,, where a is the proportion of total output sold at the low price, P, and Pj is the ruling black market price. Similar to Roemer, we can also get the upper and lower limits of the black market price by considering the two extreme positions of the demand curve. To begin with, we will conduct the analysis with the lower limit of the demand curve. It will be easier to understand the new equilibrium con-
AND
LIBERALIZATION
761
dition if we follow the time path of the equilibrating process. Assume that the economy is at the free market equilibrium.’ Now the government takes a fixed proportion of the output, and with the lowest limit of the demand curve, DID,. the black market price is the same as the free-market price (see Figure 2). However, the effective price (EP) is lower and the farmers will change their production according to their expectations about the EP they will receive for their output. If we now assume, as in a simple cobweb model. that supply in the next time period depends on the current EP, then thissupply will be lower than the free market level of supply. For example, as shown in Figure’2, if the EP is P2 (equal to UP + (l-rr)P,) then production in the next time period is Q2, and the quantity given to the government is CD. This results in the lowest demand curve shifting from DIDI to DzDz. The black market price PJ is higher because of both a shift along the demand curve and a shift of the demand curve.’ The new black market price will raise EP and hence supply in the next time period. If the new EP. i.e. UP + ( 1-a)P3, exceeds the free market price PI. then the cobweb process will not converge to an equilibrium because the subsequent EP will be less than that in period 1 as a result of escess supply. This in turn will lead to excess demand in the next time period and hence the corresponding EP will exceed nP + (1-a)Ps. It can be easily assessed from Figure 2 that this process will not converge to an equilibrium. Convergence requires that aP + (1-a)P3 is less than PI. namely
Ouantity
Figure 2.
762
WORLD
DEVELOPMENT
the free market price. The equilibrium level of supply is now not defined by the intersection of demand and supply curves but by the level of output at which the corresponding EP results in the same level of output in the next time period. We can see from Figure 2 that when the system converges to an equilibrium, the total output level under segmented markets will be less than that under free trade because EP is a weighted average of the black market price and the price fixed by the government. However, this also implies that the corresponding black market price shown by the “excess-demand” curve at equilibrium will be higher than the free market price. If we now consider the upper limit of the demand curve DD, then a similar analysis suggests that the black market price will be higher than the free market price. Consider Figure 3. A convergent equilibriating process will lead to a black market price such as P3, which will be greater than PZ, the corresponding EP, which in turn will be higher than P because EP is a weighted average of P and the black market price. Consequently, the equilibrium level of EP will be less than P4, the price level at which SJ intersects DD, since the black market price is determined by the demand curve. Hence the black market supply will be less than Qz. the level of output at which SrS intersects DD. It is evident that the total level of supply could now be higher than, equal to, or less than the free market level of supply depending on whether the black market supply price (shown by SrS) is greater than. equal to, or less than the free market price f’t.h
(b) S~rlcggling Till now we have not included
the possibility
1
of
smuggling. This situation is shown in Figure 1. Suppose the smugglers would bring unlimited grain from outside as long as the price is at least P.s. This now becomes the upper limit of the black market price. If the latter is less than Ps then there will be no smuggling. The two panels in Figure 4 show two of the possible situations with smuggling. The analysis is conducted with the lower limit of the demand curve to highlight two specific possibilities. One is the likelihood of an even lower level of production when smuggling is introduced in the model. Second is the sustenance of an (unstable) equilibrium in a system which would be divergent in the absence of smuggling. Panel A of Figure 4 shows the case when the EP (equal to aP + (I-n)P,) results in a level of supply Qz, which would have led to a black market price higher than P, if smuggling were not possible. However, with smuggling. the black market price is P, and the corresponding EP and the level of supply define the equlibrium in this case. Since smuggling becomes relevant only if the black market price without smuggling was higher than P,, the EP with smuggling would be lower than in the situation when we assume that smuggling is not possible. Therefore, the equilibrium level of output with smuggling will be lower than that when smuggling is not possible. Panel B in Figure 4 shows the situation when supply at the EP equal to PI or nP + (1-n)P,, is Q,, and results in a black market price P? which is lower than P,. The EP now is P3. The supply in the following time period is Qz, and uould have led to a black market price Pa, higher than P,, provided smuggling was not possible. However, with smuggling, the black market price will continually alternate between Pz and P,. This situation cannot be compared to one without smuggling because the latter involves a divergent cobweb process. The level of production which results in a black market price P, has to be less than the free market level of output. The following year’s production could exceed, be equal to. or be less than the free market level depending on whether the EP exceeds, is equal to. or is less than the free market price. It is important to emphasize that this situation will arise only if P, exceeds the free market price.
4. CONCLUSION
I
0, 02 Ouantity Figure 3.
In a recent paper in this journal, Roemer discussed some of the implications of maintaining a low consumer price for grain and the consequent segregated markets, i.e. the black market and the sales by the government. One of his important
SEGMENTED
GRAIN
MARKETS
AND
763
LIBERALIZATION
(b)
S
S
0
03 02 0, f?% ___-___-----
P, p2 PI 6
P
0, 4
0
Quantity Figure
results was that there would not be much impact on total output even if the grain market were liberalized. This article has extended his analysis by introducing a different method by which the government collects grain for sale at the low price, and the possibility of smuggling. Our analysis shows that if these new assumptions are made then there is a stronger possibility of the total output under segregated markets being lower than the level of output with a free market.
4.
In fact, strong coercion on the part of the government in the limit could also lead to barter or subsistence farming. The supply function specified here obviously does not cover in detail all the different possibilities. A topic for future research could be to specify alternative supply responses, or to generalize the results so that the conditions giving rise to different types of equilibria can be identified.
NOTES 1. “Free market” here denotes a market government does not intervene.
in which the
2. The basic elements of the analysis remain unchanged even if we have other criteria for government purchase. 3. As shown by Roemer (1986). such a diversion not affect the black market price. 4. The analysis is not affected equilibrium position.
by starting
will
5. If the government would have insisted on taking the same quantity then price would have increased only because of a shift along the demand curve. 6. The equilibrium condition assumed in this paper could be satisfied for one time period even if there is excess supply in the grain market. However, this will not denote a longer-term equilibrium because of the increasing level of stocks accumulated with the farmers in this situation.
from a dis-
REFERENCE Roemer, M., “Simple analytics of segmented markets; What case for liberalization?” World Developmenr, Vol.
14, No.
3 (March
1986).
pp. 429-%39.
1988.
0305-750x/88 53.00 + 0.00 Pergamon Press plc
Printed in Great Britain.
An Extension of the Simple Analytics of Segmented Grain Markets and the Case for Liberalization HARSHA V. SINGH* GA TT Secretariat, Geneva Summary. -This note extends the model used by Roemer (1986) to analyze the effect of maintaining a low consumer price in the grains market by the government. It is shown that Roemer’s result that government intervention is unlikely to have an adverse impact on domestic output is not valid if some other, different grain-purchase schemes of the government and the possibility of smuggling are incorporated in the analysis.
from the producers at a price lower than that in the free market and sells it to the consumers at this low price. Regarding the sales decisions of farmers, he assumes that they “may sell to the [grain marketing] board, to private intermediaries who will resell in the parallel market, or directly to the consumers” (1986, p. 430). The main results of this model can be explained by using Figure 1 given below, which is a slightly modified version of Roemer’s Figure 1. The model is that of a closed economy; one could assume an open economy case but that would introduce other features in the analysis. Panel A shows the official market with the free market total demand (DD) and total supply (SS) for grain.’ The government fixes a price P, less than the free market price PO, and buys and sells grain at this low price. The farmers supply only Q, level of output to the official market, while the consumer demand is equal to Q,. The unsatisfied demand spills over to the parallel market, which is shown in Panel B. Two extreme assumptions can be made about the unsatisfied demand in order to get the range of the parallel market price. If we assume that the quantity at controlled price is supplied entirely to those at the upper price range of the demand curve, then the unsatisfied demand which
1. INTRODUCTION A recent article by Roemer (1986) in this journal analyzed several aspects of segmented markets for grain, credit, labor and foreign exchange. This note extends his analysis of the grain market, for which segmented markets, i.e. an official market and a black market, arise because of government intervention. Section 2 of this note explains the results of the Roemer model. This serves two purposes. One is to explain the method of analysis by which we also will determine the range of price and output under market segmentation. Second is to give us a set of results to contrast with those of the other models we discuss in this paper. These models, which are analyzed in Section 3 of this note, extend the set of assumptions made by Roemer by including government procurement of grain in ways other than that assumed by him, and by including the possibility of smuggling. The last section gives the conclusion of this analysis. It is evident that this note does not provide an exhaustive treatment of the issues under discussion, and like Roemer, we also hope that this analysis will induce others to further investigate the problem.
2. THE ROEMER
MODEL
‘I have benefited from the comments of my colleagues, especially Richard Eglin. However, the views expressed here are my own and should not be attributed to either my colleagues or the GATT Secretariat.
Roemer has analyzed the situation of price control when the government purchases grain 759
760
WORLD
DEVELOPMENT
Price I
(a )
(b)
S
Quantity Figure
spills over to the parallel market is DzDz. Since the controlled (or official) market is supplied only by those who are willing to supply at P, the rest of the supply curve, i.e. beyond Q,, spills over to the parallel market. This supply curve, S,S,, will intersect D2Dz at P,,, the free market price. The reason is straightforward. The situation in the parallel market is equivalent to a leftward shift of the vertical axis by OQ,. After this the supply and demand curves are the same as in the free market, thus leading to the same price. The other extreme assumption about the supply of grain at controlled price is that it is supplied entirely to those at the lower price range of the demand curve. In this case the spillover demand curve is DD, and the equilibrium price is higher than PO, the free market price. Based on this analysis Roemer concludes that the parallel market price is likely to be above the free market price. The only situation in which the parallel market price will drop below the free market price is when the risk premium (and other transaction costs) in the parallel market for consumers exceed those for the sellers. Another conclusion reached by Roemer is that parallel markets are likely to compensate for much of the reduced sales in the controlled markets, and can fully compensate if they are efficient and not foo risky. Thus liberalization of grain markets may not elicit much, if any, additional production, as some advocates claim, but is likely to improve overall marketing efficiency. . The more liberalization lowers marketing cosfs, the more likely it will also increase marketed quantities. (Roemer. 1986. p. 433)
1.
3. SOME EXTENSIONS This section will extend the Roemcr model by introducing some other assumptions about the way in which the government collects the grain to be sold at the low price, the production decision of farmers being linked to their price expectations and the possibility of smuggling. A proper comparison of the results of this section with those of the Roemer model involves a comparison of the equilibria to which the system converges under the different sets of assumptions. Therefore, except in one case, we ivill also rule out the situation of a non-convergent system as is implicitly done by Roemer also. (a) Otherpw-chase schemes In the previous section, the assumption is that grain at low price is supplied to the government only by those farmers who are willing to do so (see Figure 1). There may be other situations when the farmers may not be free to decide how much to supply to the government, i.e. the government may stipulate the quantity (or proportion) of output to be supplied at the low price. Even otherwise, if a high price in the black market is expected then even those farmers capable of supplying at the low price may not be willing to do so. In this situation there is a possibility for the farmer to sell a part of his output in the black market and the weighted average of the black market price and the government price
SEGMENTED
GRAIN
MARKETS
becomes the relevant price for his production decisions. (We will refer to this as the effective when the farmer can price.) Consequently. simultaneously participate in both the government and the black market, the process by which the system converges to its equilibrium differs from a normal cobweb process (see below). As a result of this new situation the output under segmented markets may be less than the free-market level even if there is no cost premium in the black market. However, the black market price will still be above the free-market price. To simplify the analysis, we assume that the government buys a fixed proportion of the total output of the farmers at the low price.? This situation is shown in Figure 2, which combines the two panels of Figure 1. The free-market demand and supply curves are given by DD and SS. With the government taking a fixed proportion of production the residual supply curve for the black market is given by SJ, provided there is no under-reporting of production in order to divert it to the black market.3 The horizontal distance between SS and Si.S shows the quantity collected by the government. The effective price (EP) is equal to UP + (1-n)P,, where a is the proportion of total output sold at the low price, P, and Pj is the ruling black market price. Similar to Roemer, we can also get the upper and lower limits of the black market price by considering the two extreme positions of the demand curve. To begin with, we will conduct the analysis with the lower limit of the demand curve. It will be easier to understand the new equilibrium con-
AND
LIBERALIZATION
761
dition if we follow the time path of the equilibrating process. Assume that the economy is at the free market equilibrium.’ Now the government takes a fixed proportion of the output, and with the lowest limit of the demand curve, DID,. the black market price is the same as the free-market price (see Figure 2). However, the effective price (EP) is lower and the farmers will change their production according to their expectations about the EP they will receive for their output. If we now assume, as in a simple cobweb model. that supply in the next time period depends on the current EP, then thissupply will be lower than the free market level of supply. For example, as shown in Figure’2, if the EP is P2 (equal to UP + (l-rr)P,) then production in the next time period is Q2, and the quantity given to the government is CD. This results in the lowest demand curve shifting from DIDI to DzDz. The black market price PJ is higher because of both a shift along the demand curve and a shift of the demand curve.’ The new black market price will raise EP and hence supply in the next time period. If the new EP. i.e. UP + ( 1-a)P3, exceeds the free market price PI. then the cobweb process will not converge to an equilibrium because the subsequent EP will be less than that in period 1 as a result of escess supply. This in turn will lead to excess demand in the next time period and hence the corresponding EP will exceed nP + (1-a)Ps. It can be easily assessed from Figure 2 that this process will not converge to an equilibrium. Convergence requires that aP + (1-a)P3 is less than PI. namely
Ouantity
Figure 2.
762
WORLD
DEVELOPMENT
the free market price. The equilibrium level of supply is now not defined by the intersection of demand and supply curves but by the level of output at which the corresponding EP results in the same level of output in the next time period. We can see from Figure 2 that when the system converges to an equilibrium, the total output level under segmented markets will be less than that under free trade because EP is a weighted average of the black market price and the price fixed by the government. However, this also implies that the corresponding black market price shown by the “excess-demand” curve at equilibrium will be higher than the free market price. If we now consider the upper limit of the demand curve DD, then a similar analysis suggests that the black market price will be higher than the free market price. Consider Figure 3. A convergent equilibriating process will lead to a black market price such as P3, which will be greater than PZ, the corresponding EP, which in turn will be higher than P because EP is a weighted average of P and the black market price. Consequently, the equilibrium level of EP will be less than P4, the price level at which SJ intersects DD, since the black market price is determined by the demand curve. Hence the black market supply will be less than Qz. the level of output at which SrS intersects DD. It is evident that the total level of supply could now be higher than, equal to, or less than the free market level of supply depending on whether the black market supply price (shown by SrS) is greater than. equal to, or less than the free market price f’t.h
(b) S~rlcggling Till now we have not included
the possibility
1
of
smuggling. This situation is shown in Figure 1. Suppose the smugglers would bring unlimited grain from outside as long as the price is at least P.s. This now becomes the upper limit of the black market price. If the latter is less than Ps then there will be no smuggling. The two panels in Figure 4 show two of the possible situations with smuggling. The analysis is conducted with the lower limit of the demand curve to highlight two specific possibilities. One is the likelihood of an even lower level of production when smuggling is introduced in the model. Second is the sustenance of an (unstable) equilibrium in a system which would be divergent in the absence of smuggling. Panel A of Figure 4 shows the case when the EP (equal to aP + (I-n)P,) results in a level of supply Qz, which would have led to a black market price higher than P, if smuggling were not possible. However, with smuggling. the black market price is P, and the corresponding EP and the level of supply define the equlibrium in this case. Since smuggling becomes relevant only if the black market price without smuggling was higher than P,, the EP with smuggling would be lower than in the situation when we assume that smuggling is not possible. Therefore, the equilibrium level of output with smuggling will be lower than that when smuggling is not possible. Panel B in Figure 4 shows the situation when supply at the EP equal to PI or nP + (1-n)P,, is Q,, and results in a black market price P? which is lower than P,. The EP now is P3. The supply in the following time period is Qz, and uould have led to a black market price Pa, higher than P,, provided smuggling was not possible. However, with smuggling, the black market price will continually alternate between Pz and P,. This situation cannot be compared to one without smuggling because the latter involves a divergent cobweb process. The level of production which results in a black market price P, has to be less than the free market level of output. The following year’s production could exceed, be equal to. or be less than the free market level depending on whether the EP exceeds, is equal to. or is less than the free market price. It is important to emphasize that this situation will arise only if P, exceeds the free market price.
4. CONCLUSION
I
0, 02 Ouantity Figure 3.
In a recent paper in this journal, Roemer discussed some of the implications of maintaining a low consumer price for grain and the consequent segregated markets, i.e. the black market and the sales by the government. One of his important
SEGMENTED
GRAIN
MARKETS
AND
763
LIBERALIZATION
(b)
S
S
0
03 02 0, f?% ___-___-----
P, p2 PI 6
P
0, 4
0
Quantity Figure
results was that there would not be much impact on total output even if the grain market were liberalized. This article has extended his analysis by introducing a different method by which the government collects grain for sale at the low price, and the possibility of smuggling. Our analysis shows that if these new assumptions are made then there is a stronger possibility of the total output under segregated markets being lower than the level of output with a free market.
4.
In fact, strong coercion on the part of the government in the limit could also lead to barter or subsistence farming. The supply function specified here obviously does not cover in detail all the different possibilities. A topic for future research could be to specify alternative supply responses, or to generalize the results so that the conditions giving rise to different types of equilibria can be identified.
NOTES 1. “Free market” here denotes a market government does not intervene.
in which the
2. The basic elements of the analysis remain unchanged even if we have other criteria for government purchase. 3. As shown by Roemer (1986). such a diversion not affect the black market price. 4. The analysis is not affected equilibrium position.
by starting
will
5. If the government would have insisted on taking the same quantity then price would have increased only because of a shift along the demand curve. 6. The equilibrium condition assumed in this paper could be satisfied for one time period even if there is excess supply in the grain market. However, this will not denote a longer-term equilibrium because of the increasing level of stocks accumulated with the farmers in this situation.
from a dis-
REFERENCE Roemer, M., “Simple analytics of segmented markets; What case for liberalization?” World Developmenr, Vol.
14, No.
3 (March
1986).
pp. 429-%39.