Schmitz and Kennedy [1] and Kennedy et al. [2] provide evidence that, at least in less developed countries, there is support for the government holding of commodity stocks to bring about price stability. But why would producers support such a policy given that producers prefer price instability, or do they? Oi [3] was the first to demonstrate that producers have a preference for price instability as opposed to price stability. Later, Massell [4] showed cases where the opposite result holds. In this paper, we show why both cases are possible. In comparing the results, Oi does not discuss how price stability could be achieved, but rather he assumes that the stable price in his model is given exogenously. On the other hand, Massell uses government holding of stocks to bring about price stability. One of the reasons why the findings on the preference for price stability appear contradictory is that it is unclear how stable prices can be achieved within the price stabilization models. In addition, the source of the price stability plays a major role. Oi considers only cases where price instability is generated by demand shocks, whereas Massell takes into account both demand and supply shocks.

In comparing producer preference for price stability versus price instability, as Schmitz [5] shows, it is not possible to use storage to create price stability, because the amount of storage needed is unavailable. Also, in the Oi case, assuming that price stability is exogenous can be misleading since it is necessary to show how price stability can be achieved endogenously. In both cases of demand and supply shocks, we develop a producer price expectation framework where price stability can be achieved endogenously. This is possible without storage. Our model provides the price stabilization case that is used to compare price stability to price instability. We reach the strong conclusion that regardless of how price instability is generated, producers always prefer price instability to price stability, except in one case where producers are indifferent between the two choices.

The basic argument given by Oi [3] can be found in Figure 1(a). Oi confines his argument to price instability that is generated by demand shocks. Consider Figure 1(a) where producer supply is S and price disturbances are caused by fluctuating demands D₀ and D₁. Using the Oi framework, price p₁ and quantity q₁ in period 1 and p₂ and q₂ in period 2 each occur with 0.5 probability. Oi compares these two outcomes with a two-period model where an important assumption is that price p_u is given exogenously. Within this context, Oi concludes that producers prefer price instability to stability. This is because the sum of the profits attainable for prices p₁ and p₂ exceed the profits at the stabilized price p_u. It follows that total revenue is also greater under instability as

{ ( p 1 0 q 1 a ) + ( p 2 0 q 2 c ) } > { 2 ( p u 0 q u b ) } .

In Figure 1(b), we present the argument given by Massell [4] and Just et al. [6] [7] that supports Oi’s contention that producers prefer price instability due to demand shocks. Price instability is given by p₁ and p₂. The stable price is given by p_u. This is brought about through government storage of the amount gh. For a stable price compared to instability, producers lose ( p 2 p u g f − p u p 1 n g ) .

In Oi’s model, the stable price p_u corresponds to output q_u. However, in the standard results (Figure 1(b)), where producer price instability is also preferred to stability, the point of comparison is very different. The stable price p_u is generated through storage (gh). In the results given by Oi, he compares unstable prices with a stable price where he assumes that this price is given exogenously. The discussion of storage does not enter into his framework.

In the Oi framework, it is not discussed how the stable price p_u can be attained. There is no discussion on the use of storage to bring about stability. But in the Massell framework p_u is allegedly achieved through the government

holding of stocks. However, as shown in Schmitz [5] , while the result that producers prefer instability holds, prices cannot be stabilized at p_u because in Figure 1(a) the storage needed for this result, (be), is unattainable given the unstable prices p₁ and p₂. This is because the mean quantity produced over the two periods 1 and 2 is q* and not q_u. Storage gives rise to prices p* and p** (Figure 1(a)). Thus, while the producers still gain from price instability, the magnitude of the gain can be greatly reduced. The amount is given by { ( p * p u b f ) − ( p * * p 2 c n ) } .

Interestingly, however, price stability (p_u in Figure 1(a)) can be achieved through storage but under a different producer price expectation model. Consider the case where producers expect the same price and quantity, p_u and q_u, in both periods 1 and 2 (price p_u is the mean of p₁ and p₂ and production no longer occurs at q₁ and q₂):

1) Producer price expectations in period 1 = {(p_u) + storage of (q_u q₃)}

2) Producer price expectations in period 2 = {(p_u) - storage of (q_u q₄)}

With no storage, prices fluctuate between p₁ and p₂. To achieve price p_u, the amount of storage needed is (q_u q₃ ), which is equal to the amount released of (q_u q₄ ). We now compare producer preference for price instability verses stability. Producers prefer instability since {(p₁ p_u ba) > (p_u p₂ cb)}. The net gain to producers from instability is (jba) (but storage is needed to bring about price stability). Thus, even under a feasible stable price scenario, we find that producers prefer price instability to price stability.

Oi [3] considered only the case above, where price instability is due to demand shocks. The following discussion focuses on price instability that comes about due to supply shocks. In this case, as Massell [4] and others argue, producers prefer price stability to instability.

In the following, price instability is brought about by supply shocks S₁ and S₂ in Figure 2(a). Demand is given by D. The expected prices and quantities are p₁

and q₁ in period 1, and are p₂ and q₂ in period 2. In the standard result Figure 2(b), producers prefer price stability by {(abc) + (cde)}. However, like in the demand case earlier, Schmitz [5] demonstrates that p_u cannot be achieved through storage. The amount of storage from production q₁ and q₂, (q* q₁) gives rise to a price band of p₃, p₄ (Figure 2(b)).

With storage, price stability (p_u) cannot be achieved. We now derive a producer price framework where p_u can be obtained and compare this with instability of p₁ q₁ and p₂ q₂. Like the demand shock model above, assume that producers have a price and quantity expectation of p_u and q_u over both periods. The price is now stable at price p_u (in this case, producers form price expectations at the mean price p_u). Price instability must be compared to the feasible stabilized price p_u. In this case, like in Figure 1(a), producers prefer price instability. However, in contrast to the demand shock model in Figure 1(a), storage is not needed to bring about price stability when the price instability is generated by supply shocks. This outcome for Figure 2(a) is opposite to the standard result (Figure 2(b)), in which producers prefer price stability. Note that in Figure 2(a), price p_u corresponds to q_u and not to outputs q₃, q₄ as in Figure 2(b).

Using a welfare economic framework to measure producer welfare, producers prefer price instability to stability as { ( p 1 b g ) + ( p 2 a h ) } > 2 ( p u d c ) . The net welfare gain to producers using this measure is { ( f q u q 1 g ) − ( i e f c ) } . The result that producers prefer price instability can be easily seen in Figure 2(a) as { ( d b g c ) > ( a d c h ) } . Note that if demand D is totally price inelastic, producers are indifferent between price instability and stability.

Oi and Massell agree that when price instability is brought about by demand shocks, producers prefer price instability to price stability. A key question in their analyses is what is the meaning of price stability? Oi assumes that the stable price to which instability is compared is given exogenously. Massell argues that the stable price is brought about through storage. Both arguments are problematic. As Schmitz [5] shows, storage cannot bring about price stability; it can only reduce price instability. We develop a model where price stability can be achieved, but the price expectation framework that brings this about is different than the price expectation framework that generates the price instability. But even using this model as the basis to compare price instability, producers prefer price instability.

Oi did not consider price instability generated by supply shocks. Massell demonstrated that in this case producers prefer price stability over instability. The same problem arises in that the stable price used is not obtainable through storage. We develop a model where, under a different price expectation model used to generate price instability, the stable price p_u is attainable. From a comparison between price instability and price stability, producers no longer prefer price stability. At best, producers are indifferent between the two choices.

It is important to stress that in the Oi framework, reference was not made to the government holding of stocks. This discussion came about in the Massell framework, where the government holding of stocks can bring about price stability. We show that in the supply shock model, storage is not required to generate price stability.

Within our welfare economic framework, attention is not given to price uncertainty. This is a limitation that should be considered in future work and would be generally relevant for risk-averse producers. Within this context, models should be developed where the effects of shocks that are a combination of supply and demand changes in the same period are taken into account. In addition, the results in this paper should be integrated with those by Feder et al. [8] , Turnovsky et al. [9] , and Schmitz et al. [10] . Feder et al., Turnovsky et al., and Schmitz et al. show how the existence of futures markets can mitigate the need for price stabilization policies.

The author thanks Carol Fountain for editorial contributions and Claudine Chegini for technical assistance.

Schmitz, A. (2018) Producers’ Preference for Price Instability? Theoretical Economics Letters, 8, 1746-1751. https://doi.org/10.4236/tel.2018.810114