Farm-gate Tomato Price Negotiations under Asymmetric Information
Moti Jaleta a
[1]
and Cornelis Gardebroek b
a
Debub University,
b
Agricultural Economics and Rural
Policy Group,
Abstract
This paper
focuses on farm-gate tomato price negotiations under asymmetric information. A
sequential bargaining model is described to explain how sellers and buyers set
their initial ask and offer prices when they are uncertain on their trading
partner’s valuations. Regression models are estimated to analyze when and by
how much sellers stick to their initial ask prices and what explains the
variation in initial ask and offer price spread. Detailed information on 66
farm-gate tomato transactions and daily tomato wholesale price data from the
central vegetable market in
JEL
classification: C7, D4, D82, Q13
Key words:
farm-gate pricing, sequential bargaining, asymmetric information, tomatoes,
1. Introduction
The
textbook case of perfect competition is full of strong assumptions like large
number of buyers and sellers, complete information, free entry and exit and
price taking by all agents (MasCollel et al. 1995). This ideal situation,
however, does not exist in the real world. When market participants do not have
equal information on prices, quality and quantities of the item under
transaction and the number of trading agents in the market, there is an
incentive for better informed agents to uphold information and maximize their
private benefits (Sobel and Takahashi 1983, Cramton 1984, Srivastava et al.
2000).
Access to
market information helps both buyers and sellers in setting their reservation
prices for the product under transaction. Trade may occur when the buyer’s
maximum reservation price exceeds the seller’s minimum acceptable selling
price. However, how a buyer and a seller share the margin between the two
reservation prices is dependent on various factors among which the relative
bargaining (market) power of both agents is an important one (Sexton and Zhang
1996, Sexton et al. 2005). An agent
with relatively more market power due to, for instance, better market
information or low cost of delay is expected to obtain the highest share of the
margin (Cramton 1984). Cramton shows that agents with high cost of delay reveal
information faster and get a smaller share from the margin in bargaining.
In their study on the Californian lettuce market, Sexton and Zhang (1996) found that buyers obtained the lion’s share of the surplus generated from lettuce production and sale. Farmers never obtained more than 14.5 percent. The unbalanced share results from the farmer’s impatience in bargaining over prices due to the perishable nature of their vegetable supply (Perry 1986).
According
to Cramton (1984), incomplete information leads to bargaining inefficiency,
which increases as private valuations are more uncertain. In contrast to the
complete information case where buyers and sellers know the size of marketing
surplus to share, the presence of uncertainty on the trading partner’s
valuation impedes efficient negotiations and motivates higher initial ask
prices and lower initial offer prices resulting in an extended bargaining
process (Chatterjee and Samuelson 1983, Samuelson 1984, Yilankaya 1999,
Srivastava et al. 2000). Lengthy price negotiations are usually common to
reveal the private reservation prices and to come to an agreement on a given
specific transaction price. Such price negotiations are traditional for farm
households growing tomatoes in central
Figure 1. Daily tomato wholesale
price at central vegetable market in
Source:
Horticultural Development
One of the
possible reasons for uncertainty on the trading partner’s valuation is the
fluctuating tomato wholesale price at the central vegetable market (see Figure
1). Lack of accurate central market price information and the perishable nature
of tomato products affect farmers’ valuation for their tomatoes and bargaining
power. When farmers cannot wait for better prices by storing their harvest they
are forced to accept a lower price to avoid the risk of not selling. Resulting
low vegetable prices have a direct impact on the next household resource
allocation decisions on food and cash crop production.
The objective of this paper is to assess how tomato
prices are determined at farm-gate and to estimate factors explaining the
variation in bargaining power in negotiations on tomato prices. A detailed set
of variables including information on central market prices is used to explain
bargaining power and the spread in the initial ask and offer prices.
The
remainder of this paper is organized as follows. Section 2 develops a bilateral
bargaining model adapted to farm-gate tomato marketing practices taking place
in
2. The Theoretical Price Bargaining Model
In building
up the theoretical price bargaining model, the following basic assumptions are
made. Tomato producers and merchants buying tomato directly from the producers
at farm-gate have different valuations for the same tomatoes under transaction.
There are various reasons for this difference in valuation of which information
asymmetry is one. Tomato buyers and sellers may not have similar price
information or may get their price information from different sources. Unlike
the case of coffee, there is no centralized vegetable price information
disseminated via public media to rural
These
issues all confirm that there are valuation differences between tomato
producers and tomato purchasing merchants on the same tomato harvest under
transaction. Buyers’ and sellers’ private valuations can be specified as:
; 
(1)
where 
is agent i’s
valuation on transaction date 
, 
is private information
on tomato prices at the central market on the previous day (viz. true or expected
price), 
is agent i’s estimate for a unit transportation
and handling costs to bring the tomatoes to the central vegetable market, 
is expected profit
margin that a trader earns, 
is the expectation on
the future tomato wholesale price movements at the central vegetable market, is the date of
transaction at the farm-gate and the subscript 
refers to either a
buyer or a seller of the tomatoes under transaction.
Assume that
sellers’ and buyers’ valuations are uniformly distributed within the range of
maximum and minimum valuations, 
and 
, respectively and these distributions are also common
knowledge. Figure 2 gives a simple scheme for a uniformly distributed valuation
function with overlapping valuations so that trade can take place.
Figure 2. A buyer and seller’s overlapping valuations allowing trade occurrence.
Normally,
trade only occurs if the maximum affordable buying price is higher than the
minimum acceptable selling price
. Thus, for a transaction to take place, the transaction
price (
) that both parties agree upon as a final transfer price
should be between these two reservation prices, i.e., 
. The exact point where the final transfer price lies
depends on the agents’ (the buyer and seller’s) relative bargaining power which
is determined by other economic and non-economic/psychological factors (Kreps,
1990:551).
Assuming a
linear bargaining rule, the final price,, is set at:
(2)
Where 
and 
refer to the seller’s
initial ask price and buyer’s initial offer price, respectively. 
is the relative
bargaining power of a seller. So, a high 
means relatively more
bargaining power for the seller than for the buyer. The seller negotiates more
aggressively to bring the final transfer price close to his/her own initial ask
price, . The reverse is true for a low. When trade occurs at the final transfer price (), the payoff for a seller is 
while it is 
for a buyer.
Buyer’s
offer and seller’s ask price setting strategies are a function of their own
valuations and whether these valuations are common knowledge to both parties or
not. Moreover, price setting strategies differ when bargaining is just a
one-shot game under complete information or a game that allows sequential
bargaining to reveal private information over time. How sellers and buyers set their
ask and offer prices under both situations is presented below.
To start with the complete information case, assume that both buyers and sellers are maximizing their payoff by choosing an offer and ask price conditional on the fact that these chosen prices allow a transaction to take place. Thus, the buying merchant’s objective function is given as:
(3)
where 
. By substituting 
for 
in equation (3) and optimizing
the objective function over , the first order condition gives us:
(4)
Referring
to the earlier assumption 
, the equilibrium
offer price for a buyer is:
(5)
Similarly,
the producer/seller’s objective function is:
(6)
where
, and by substituting for the probability and optimizing the
objective function over, we get:
(7)
This
equilibrium ask-offer price is attained when both trading partners have common
knowledge on the valuations and both know that there will be no more trade once
negotiations failed (Gibbons,1992:155). The equilibrium is efficient as it has
been reached without any cost of delay and also shares the existing marketing
surplus equally into two,
, and = 0.5.
However,
when both agents have private valuations and these are not exactly known to their
trading partners, such an efficient trading equilibrium does not exist
(Chatterjee and Samuelson 1983). With this two-sided uncertainty, both the
buyer and the seller have an incentive to hide information on their individual
valuations. These hidden valuations can only be learned by the trading partners
if multi-stage bargaining is allowed to communicate some of their private
information before an agreement can be reached (Crawford 1982, Cramton 1984).
A simple
multi-stage bargaining model with incomplete information is developed below to
show the strategic initial ask and offer prices made by a seller and a buyer
based on their expectations and what they learned from the equilibrium history
of the game. The equilibrium of such a game with an infinite horizon was
derived by Cramton (1984).
For a
quantity of tomatoes under transaction, let’s assume that a seller and a buyer
have private valuations of 
and 
, respectively. Though the buyer does not know the exact
valuation of the seller, he assesses that seller’s valuation is given by the
distribution 
on 
. Similarly, the seller assesses the buyer’s valuation given
by the distribution 
on 
. Also assume that both the buyer and the seller have a cost
of delaying the bargaining process. 
and 
are the seller’s and
the buyer’s discount factor for a delayed agreement, with 
. The cost of delay for a seller could be loss of product
quality, increased risk of not transacting at all. For the buyer it is mainly
the risk of having a full truckload at the next transport to the central
market. For both parties there is also a potential cost of not trading in case
of high central market prices. Another assumption is that both the buyer and
the seller follow a bargaining strategy which is sequentially rational and must
be the best response to the other’s strategy, given their probabilistic beliefs
on the state of the world (Cramton 1984, Kreps 1990).
In
sequential bargaining a seller with private valuation maximizes his payoff
by choosing an ask price 
at each period 
of the bargaining process. The optimization problem is
specified as:
(8)
Where is what the seller
asks at period dependent on his
private valuation, , discount factor,, and his belief about the buyer’s valuation at period , 
The seller’s belief
about the buyer’s valuation at period is determined based on
the seller’s offer rejected by the buyer at period 
For ease of notation
the ask price 
is written as . 
refers to the probability distribution of seller’s belief on
the buyer’s valuation at period .
The
seller’s optimization problem is subject to the sequential rationality
assumption that states that a buyer accepts the ask-price at period if:
(9)
Equation
(9) indicates that a buyer accepts what a seller offers at period if he rationally
believes that the payoff at period is higher than the
discounted payoff at period 
, given the buyer’s belief on what the seller offers the next
period.
Though cumbersome, it is possible to compute the optimal ask prices at each period using the first order conditions. For our interest, it is enough to show that the first initial seller’s ask and buyer’s offer prices are not equal under a sequential bargaining game with asymmetric information. See the Appendix for a simplified Perfect Bayesian Equilibrium prices adapted from the work of Sobel and Takahashi (1983) and Gibbons (1992: 219-224).
When the
initial ask price is higher than the initial offer price,
, and there is a final transfer pricethat both agents finally agree upon after 
periods of price
negotiations and this final transfer price lies within the acceptable range for
trade to occur, 
, then by rewriting equation (2) given above, one can specify the seller’s commitment to his initial ask price
as a proxy to his bargaining (market) power as:
(10)
Where 
measures the seller’s
commitment to stick to his/her initial ask-price as a final transfer price. A
seller is fully committed when 
, i.e., 
and a buyer is fully
committed to his/her initial offer as a final price when 
, i.e., 
. Generally, 
is a proxy to the
seller’s market power where 
is for a buyer. The
intuition is that agents with relatively more bargaining power can have strong
commitment to their initial ask/offer prices.
Moreover,
the size of the difference between the initial ask and offer prices, 
, may indicate the extent of uncertainty prevailing in
estimating the actual valuation of the corresponding trading partner.
3. Empirical model and data
3.1
Empirical model
In order to
estimate to what extent tomato sellers and buyers at farm-gate stick to their
initial price quotes, we consider the price difference between the initial ask
(offer) price and the finally agreed upon transaction price weighted by the
spread between the two initial quotes as given in equation (10). The share of
the initial ask-bid spread is regressed on different attributes expected to
have an effect on the agent’s bargaining power. These attributes consist of
both economic and non-economic factors. The functional form is given as:
(11)
Where 
represents and 
, respectively as defined in the previous section. Since 
, there is no need to estimate the buyer’s bargaining power
as it can be inferred from the estimation results of the seller’s bargaining
power. 
includes characteristics of buyers and sellers like age and
education, 
refers to information
related variables like access to the central vegetable market price information
and number of potential buyers visited tomato seller during the last one week, 
stands for variables explaining the
economic relationship between a buyer and a seller like whether they traded
with each other before and, in case they did, how many times, etc. 
refers to agent’s
tomato quality perception and if there is any quality perception difference
between the buyer and the seller, 
is quantity of
tomatoes under transaction, which is fixed during the transaction period. 
and 
are parameters to be
estimated and 
is a disturbance term.
Sellers’ and buyers’ characteristics influence their respective bargaining power as they contribute towards better market understanding and processing of information. The more an agent is informed, the less uncertain he is on market prices and the better able to form price expectations and trade efficiently in a short time span. Long experience in trading with each other can facilitate trade as it helps to build trust between buyers and sellers. Buyers and sellers with the same quality standard have a similar valuation for a product under transaction as compared to trading partners with different quality perceptions. Difference in quality perceptions widens the difference between initial ask and offer prices and extends the bargaining process. In the literature, it is shown that sellers supplying a bulk volume of perishable products usually have less bargaining power (Sexton and Zhang, 1996). On the other hand buyers prefer purchasing a larger volume of products at once as it reduces transaction costs and also helps them to get products with homogeneous quality as compared to assembling smaller quantities from different farms. Thus, buyers are expected to commit themselves less to their initial offer prices while transacting on larger volumes of tomato products.
3.2
Data
Data used
for this analysis was collected in 2004 both from the central vegetable market
in
On average,
the final farm-gate transaction price is 25 per cent of the farmer’s initial
ask price and 75 per cent of the buyer’s initial offer prices. This could be
due to the fact that sellers ask higher initial prices due to their uncertainty
on the valuations of their corresponding buyers or because they stick less to
their initial ask price as they have high cost of delaying the transaction. The
spread between seller’s initial ask and buyer’s initial offer prices varies to
a maximum of 1.2 Birr[2]
per kg and it is larger in magnitude than the average farm-gate tomato price,
which is 0.94 Birr per kg. Such a wide spread in initial ask and offer prices
implies longer negotiations to settle the final transaction price.
Descriptive statistics of the generally recorded transaction data at a farm-gate are presented in Tables 1 and 2. Description of daily tomato wholesale price data at the central vegetable market for three different quality standards are also presented in Table 3. The wholesale prices cover a period of three months, from 07 June 2004 to 05 September 2004.
Table1. Descriptive statistics of farm-gate tomato transaction data
|
Variables |
Mean a |