Team:HZAU-China/eco/2

     Before presenting the four types of possible GMO markets, we have some assumptions to make, some of which are to simplify questions.

     First, assume that the value of a GMO contains solely of one factor, the safety condition. Namely, we assume that the consumers only worry about the safety conditions of GMOs, so as long as the GMO is safe, it has value.

     Second, we omit the difference of GMO companies and GMO sellers and GMO developers, and call them by ``GMO seller''.

     Third, we assume that both the GMO sellers and the GMO consumers follow sequential rationality [23], namely, they all expect maximum payoff in every one of their choice.

     Fourth, we assume that the information is complete, which means that, both the sellers and the consumers know the type, strategies and payoffs of each other.

     Fifth, we assume that consumers are perfectly rational (to know more about the word rationality, see [24] or [25]), so their belief of the GMO safety condition could be said to reflect the intrinsic safety condition of said GMO.

     We can draw the outline of these four types of markets under the above assumptions.

     Suppose that there are roughly two kinds of GMOs, one that is intrinsically safe whose value is $A$, another that is intrinsically not so safe and may be hazardous whose value is $B$, and $A>B$. Since any consumer will want to buy the safe products and not the unsafe, so any seller of GMO will try to make the product as safe-looking as possible; and since the consumers cannot tell which category the product belongs to by simply looking at it in the market, the seller of the unsafe product will be able to pull off as the safe, and therefore the safe and unsafe products all share the same level of price $P$, but pretending to be safe will generate a certain cost of $W$, and $A>P>B$. The probability of consumer $x$ believing that GMO $y$ being safe is $p_{safe}$, the probability of consumer $x$ believing GMO $y$ to be unsafe is $p_{unsafe}$ ($x$ and $y$ being random). If we further assume that the consumers are perfectly rational, then their belief could be said to reflect the virtual safety condition of GMO.

     And a decision tree could be drawn:

     According to Shiyu Xie, the market equilibrium of a game under complete but imperfect information can be divided into four types by market efficiency: total failure, total success, near failure, partial success [22]. The four types of market are determined by the parameters $A$, $B$, $C$, $p_{safe}$, and $p_{unsafe}$.

2.1 Partial Success

     Suppose that the consumer believes that the probability of unsafe GMO occurring in the market $p_{unsafe}$ is small. Suppose, however, that the pretending cost of the unsafe product $C$ is also very small comparing with the selling price $P$. This is to say that the unsafe products can easily sneak into the market without much additional cost while the consumers trust and are optimistic about the GMO market.

     The consumer’s payoff $\pi$ if he decides to buy a certain GMO will then be $p_{safe}(A-P)+p_{unsafe}(B-P)$. since $A>P>B$ and here we suppose that $p_{unsafe}$ is small, then $\pi>0$. If the consumer decides not to buy, then his payoff will be that $\pi=0$. So as long as the GMO is sold, he will choose to buy it.

     Now back trace to the GMO seller’s decision. Because the above track of decision routes can be deducted by the GMO sellers, they will know that their products can be sold if they choose to sell it. So, will they? If its product is safe, the payoff for selling it will be $P$, $P>0$, which is the payoff if it chooses not sell, and its rational choice will be to sell. If its product is not safe, then the payoff of selling will be $P-C$, which is still greater than $0$ since $C$ is assumed to be small, so it will still choose to sell it.

     In this situation, the GMO sellers will sell their products regardless of their virtual safety condition, and the consumers will buy whatever that is presented to them by these sellers.

     In a GMO market like this, the conducts of the sellers do not reflect the safety condition of the GMO they sell, however, since the unsafe GMOs are not very prevailing (small $p_{unsafe}$), the buyers and sellers both can have a positive payoff in most times, though the consumers can sometimes stumble upon the unsafe GMO.

2.2 Total Success

     Now suppose that it will be very, very costly for the GMO sellers to put an unsafe GMO into the market, whether by sneaking it in, or by some unintentional mistakes in the censoring procedures, all in all $P

     Therefore, if the seller sells the unsafe GMO, it will be costly, and the payoff will be negative, i.e. $P-C<0$. If the GMO seller is rational, then it will not choose to sell it. So $p_{safe}=1$ and $p_{unsafe}=0$. Since it’s a game under complete information, the consumer knows it too. When they are making the choice of buy or not to buy, the payoff of buying as they perceive it will be $\pi=1\cdot (A-P)+0\cdot (B-P)=A-P>0$, while the payoff of not buying is $0$. Therefore, rational consumers will choose to buy the GMO.

     In this situation, all GMOs sold are safe GMOs, and the unsafe GMOs will not gain entrance to the market, so the consumers can freely buy any GMO without worrying about its safety condition, and the social welfare is at its maximum. If there IS any GMO, that is. Because certain GMOs could be banned by the government so it could be that only the ``unsafe GMO will not gain entrance to the market'' part stands valid.

2.3 Near Failure

     Two conditions must stand valid for the market to be near failure: first, the cost of ``cover up'' for the unsafe GMO does not exceed its price, $P>C$; second, the consumer expects loss entering the market, i.e. $p_{safe}(A-P)+p_{unsafe} (B-P)<0$. In this condition, if only pure strategies (e.g. buy or not to buy) are employed, the market will reach its dismal state, where no consumer will buy GMO and therefore no seller would sell it. This is the situation of total market failure which will be discussed later.

     So instead of pure strategy, mixed strategies[26] will be employed here, which is to say, the seller will sell the GMO when it’s safe (with probability 1), and sell the GMO with a probability of $\alpha$ when the GMO is unsafe; and the consumer decides with a probability of $\beta$ whether or not to buy said GMO. According to Bayesian law[27], the conditional probability of GMO being safe when the seller chooses to sell is:

     \begin{equation} p({safe}|{sell})=\frac{p_{safe}\cdot p({sell}|{safe})}{p_{safe}\cdot p({sell}|{safe})+p_{unsafe}p({sell}|{unsafe})} \end{equation}

     And the payoff $\pi$ when the consumer chooses to buy is

     \begin{equation} \pi=p({safe}|{sell})(A-P)+p({unsafe}|{sell})(B-P). \end{equation}

     Xie Shiyu has proved that the mixed strategies of both the seller and buyer in near failure markets like this can pass the test of sequential rationality [22], i.e.

     \begin{equation} \pi_{buy}=\pi_{not buy} \end{equation} and \begin{equation} \pi_{sell}=\pi_{not sell} \end{equation}

     Therefore, it means that the seller of safe GMO can only sell it with a probability which is not $1$.

2.4 Total Failure

     The four types of market can be determined either by the payoffs, i.e. $C$ and $P$, or in many situations, directly deducted by the buyer according to his own experience or other factors.

     If, due to various reasons, the consumer has somehow reached the conclusion that the GMOs sold in the market are all unsafe, then his $p_{safe}=0$, $p_{unsafe}=1$. The payoff if the consumer chooses to buy is $0\cdot (A-P)+1\cdot (B-P)=B-P<0$, so the consumer will not choose to buy. So the seller’s payoff will be $–C$ is he sells, smaller than $0$, the payoff if he chooses not to sell. So he will not choose to sell. The market is in its total failure.

     ``Lemon'' can mean ``second hand goods'' or ``goods that are not so good'' in the American slang, the concept of Lemon Market was first introduced into economic theories by the Nobel winner George. A. Akerlof in his essay The Market for ``Lemons'': Quality Uncertainty and the Market Mechanism where he explains the market failure caused by information asymmetries and externalities, illustrated with the example of the second-hand car market [28]. In the GMO market, information asymmetry means that the sellers can tell safe from unsafe while consumers cannot, because safe and unsafe goods look similar.

     In a GMO lemon market, the highest price a consumer is willing to pay will not exceed the value (in this case we assume it solely means safety conditions) he expects of the GMO product, and the expected safety condition of a product is the weighted average of both the safe and unsafe products [29]. Choosing so will result in a gradual withdrawal of the safe GMO sellers from the market, because the average price in the market is lower than the value his products possess.

     As this happens, the ratio of the safe products in the market will gradually drop, and the highest price the consumer is willing to pay will drop further with the downfall of consumer’s expectation of the product, resulting in the withdrawal of GMO products which are of relatively high quality.

     This kind of adverse selection will make the market end up filled with the worst kind of GMO. Therefore, unless consumers are willing to buy this kind of GMOs, the market fails spectacularly.

     Before getting a second look at the five assumptions or getting a closer look at the four types, let’s look at some surveys done by former scholars to have some understanding on consumers’ real attitudes towards GMOs across the world in recent years.