Income distribution and market mechanism: A study of watermelon price

The conventional perception is that economic theories don't apply in the economy of Bangladesh or fail to account for the real picture of the economy. This statement is both correct and incorrect. It is correct from the perspective that the conventional theories fail to account for the reality of Bangladesh economy. It is incorrect from the perspective that economic theory in general is not unable to explain the economic situation of Bangladesh. In fact, Bangladesh is just a representative example here not the unique case. The analysis we will develop here will apply to any economy irrespective of its nature and characteristics. Here, we will analyse the market price determination for a particular agricultural goods called watermelon. Therefore, we proceed as follows. First, we document current prices of watermelons for producers and retailers. Second, we analyse the reasons behind huge gap between retail price and producers' price. Third, we extend the analysis to other goods and to elastic and inelastic demand goods. Finally, we draw conclusion.
CURRENT WATERMELON PRICE: We have observed three different ranges of price for both producers and retailers for three different grades of watermelons. The different grades are A, B, and C. The average producers' price for A grade watermelons is Tk 40 to Tk 50 and the retail price (market price) is Tk 130 to Tk 180; the average producers' price for B grade watermelons is Tk 30 to Tk 35 and the retail price is Tk 90 to Tk 120; and the average producers' price for C grade watermelons is Tk 20 to Tk 30 and the retail price is above Tk 60. That means on average producers' price for watermelons ranges from Tk 20 to Tk 50 and retail price ranges from Tk 60 to Tk 180. The price difference between producers' price and retail price of watermelons is abnormally high.  This huge difference at least can't be attributed to any
economic accounting even after taking into account all additions with
producers' price.
Now, the question is: why is the price gap is so big and huge for watermelons? Before we search for a specific answer, we first try to make a sense for this price difference applying our lessons from the microeconomic demand and supply theory. The theory says that market price will adjust to market demand and by this interaction market will settle to equilibrium point where demand and supply are equal. If this so, then why doesn't demand adjust with the prevailing market price? Let's say the pure market equilibrium price for watermelons should be on average Tk 80. Now, assume that the market price  is Tk 140. According to the conventional theory, demand should respond in such a way that the price of watermelons come down to Tk 80 since demand will be less at Tk 140. But in our country we have hardly noticed this kind of phenomenon. Even if retailers conspire and set the price too high, they will be forced in the end to reduce the price since lack of demand will motivate them to do so. This at least points to an objection to the conventional outlook that market is running on syndicate. We are not saying that there are no syndicates as such, rather we are objecting that syndicates can't sustain its influence on market price for long since market demand will force the price to adjust ultimately. Then what is the wrong here. To account for this huge price difference for watermelons, we have to take a different approach to the study of the theory of demand for watermelons.
INCOME DISTRIBUTION AND THE THEORY OF DEMAND: One of the serious limitations of the traditional theory of demand is that it ignores the effect of income distribution on market price. The theory is built on the assumption that market price for a commodity is independent of income distribution. However, this kind of assumption from a very deep insight seems totally untenable and seems utterly unsatisfactory. When income distribution is extremely uneven, market will not work according to the dictates of the conventional theory of demand. For example, in our country income distribution is seriously uneven and the degree of unevenness is on the rise. The degree of unevenness can be seen from Figure-I below. The figure shows income distribution is highly uneven and a majority fraction of the total population belongs to the bottom part of income distribution. In this highly uneven income distribution regime, market will not operate according to the conventional theory of demand. Had the market worked according to the traditional theory, the price differences for watermelons would have been much smaller or almost zero. In the traditional demand theory, market price depends on the level of demand, to phrase more clearly, on the absolute level of demand. Therefore, it doesn't matter who gets what and what amount. That means market price is totally independent of distribution of market demand. This is not true. Market price is not independent of the distribution of market demand which depends on the distribution of income. We can illustrate this point in the following simple way:
The above exposition shows that market price is independent of the distribution of market demand. Even if the total market demand goes to one person only and all others go empty stomach, market price is same as it is in the case where all go with full stomach but one. This conclusion is true as long as market demand is normally distributed. But we argue it is hardly the case when income distribution is supremely uneven. Using this information, we now formulate a function which will show that price not only depends on the absolute level of demand that is independent of distribution but also on the distribution of market demand which is determined by income distribution. Therefore, we proceed as:
From the demand theory we know that demand depends on price. So, we can explain price in terms of demand. But price in the conventional framework depends on the absolute level of demand and not the distribution of market demand. So, to trace the effect of income distribution on price, we have to make price a function of relative distribution of market demand as specified above along with absolute level of demand. So, we get:
The inequality between partial derivates with respect to distribution of market demand and the absolute level of demand shows that the effect of distribution of market demand of watermelons on price is greater than that of the absolute level of demand. If this is so, then market price of watermelons will be determined by the distribution of market demand both in the medium-long run and long-run. When the value of   (q—qave) is almost equal to Q or   (q—qave)    Q, we can make price as the function of   (q—qave) only omitting Q from the right side.
Now, apply this insight to explain the huge price difference between producers' price of watermelons and retail price (market price) of watermelons in our country. For that assume that equilibrium market price for watermelons should be Tk 80 or (p*=Tk 80). But the average market price is, say, Tk 140. Now according to the formal theory of demand, higher price should lead to lower demand and lower demand should lead to price reduction. That means in the ultimate price of watermelons must come down to Tk 80 from Tk 140. But this doesn't happen in our country. Rather watermelons are still sold at Tk 140. This directly implies that there must be sufficient demand even at price Tk 140 per watermelon. Somebody can argue that there can be syndicates that artificially raise the price of watermelons. This logic is correct but to sell watermelons at the syndicated price, demand must be there. Otherwise syndicates will fail to achieve their objectives of setting higher price. Therefore, we can assume that market for watermelons gets cleared even at price Tk 140 per watermelon which is far higher than the equilibrium price of Tk 80 per watermelon. This shows that market of watermelons will get clear even at higher prices such as Tk 140 if and only if the distribution of market demand is supremely uneven. That means
 (q—qave) is equal to Q. We can say more clearly as:
Now we show the above result with the help of the following graph:
In the above figure, price (p) of watermelons is measured off on the vertical axis and demand (D) and Supply(S) on the horizontal axis. We have taken that the supply of watermelons is fixed for the time and this is shown by the vertical line S=Q. The graph shows that the equilibrium price of watermelons is Tk 80 and at this equilibrium price supply and demand is equal or (D* = Q or S).  But when the price is 140 Tk. demand is D1 which is less than the supply. From the theory of demand we know that price must come down to Tk 80 to make demand equal to supply. But price doesn't come down to Tk 80. Instead it just stays at Tk 140. The reason is that in the traditional demand theory, absolute level of demand is the function of price or D = f(p). But when distribution of market demand is so uneven, market price doesn't adjust to the absolute level of demand. If it did, then price must have come down from Tk 140 to Tk 80 when the demand for watermelons is D1 which is less than supply. Rather, the price responds to the relative distribution of market demand or  p = f (  (q—qavg)). Since, we have taken   (q—qavg) = Q, the price will stay at 140 Tk. and this price, market demand and supply becomes equal or   (q—qavg) = Q =D*. Therefore, watermelons price will not come down to 80Tk if the value of    (q—qavg) is significantly positive, and the market price will be dominated by the uneven distribution of market demand rather than by the absolute level of demand or D. That is why watermelons price in our country doesn't come down even when the price is set at much above the normal market equilibrium price.
EXTENSIONS: ELASITC AND INELASITC DEMAND GOODS: The above analysis can be extended to any type of goods having either elastic or inelastic demand. Let us take a quasi-elastic demand good called potato with moderate substitutability.  Though the relative demand distribution of potatoes defined by   (q—qavg) is not very large and may be slightly above zero in the case of uneven income distribution, the small positive magnitude of
(q—qavg) is strong enough to cause a huge difference between market price and producers' prices. The similar case is observed in the price of mangoes that come to market in the summer season. The relative distribution of demand of mangoes or  (q—qavg) determines the market price of mangoes rather than the actually observed absolute level of demand. This conclusion is correct when income distribution is supremely uneven. But when income distribution is more  or less even, the actually observed absolute level of market demand will determine the market price since in this case [   (q—qavg)    0]. But it should be noted that the effect of relatively uneven distribution of market demand on market price for a good having inelastic demand will be drastic even if the value of   (q—qavg) is not very large and moderately above zero. This point shows why in our market daily necessities are sold at much higher price than the normal equilibrium price and why market fails to correct the price. This shows that influence of middlemen and syndicates can't have decisive influence on market price for a long time. But the influence of syndicates and middlemen will be strong when relative distribution of market demand is very uneven. However, their influence will be very weak if the distribution of market demand is more or less even. So, the conventional belief that syndicates and middlemen are controlling market prices in our market is deceptive rather than correct.
CONCLUSION: The above analysis has shown relevantly that to account for the huge difference between market price and producers' price we need to take a different approach to the study of the theory of demand. The conventional theory of demand fails to account for huge price difference since according to that theory price should have responded to market demand. But this has hardly occurred in our country. The analysis has shown that market price is dominated and determined by the relative distribution of market demand rather than by the absolute level of market demand. The traditional theory of demand is based on absolute level of demand and says that market price will adjust in response to the absolute level of demand. This is hardly the case when relative distribution of demand is very much uneven. Our analysis has shown that price adjusts to relative distribution of market demand rather than to absolute level of market demand. The higher uneven the distribution of market demand, the higher the price difference and vice versa. This indicates that the huge price difference for watermelons and other goods are due to highly uneven distribution of market demand for these goods.
Md. Jamal Hossain is with the University of Denver, USA and Md. Mustafizur Rahman  is  with the Bangladesh Institute of Bank Management (BIBM).
 [email protected]