Grant Grigorian 12/17/2003 Willingness to Grieve The loss of an animal companion, whether due to death, being lost or stolen, or placement in a new home, may be one of the most devastating and painful experiences we ever face. For many, such a loss is as traumatic as losing a family member or a dear friend and can trigger an intense grieving process [Dumb Friends League, 2003]. The most difficult of all losses may be the disappearance of one we love. This is true whether it is a person MIA in wartime or a pet that becomes lost or is stolen. They are gone without a trace; we are left behind filled with uncertainty, doubt and hurt. Death gives us permission to grieve. When we don't know what has happened or where our pet may be, we instinctively hold out hope. Our energy is directed toward trying to find the one we've lost. We search, put up signs, place newspaper ads, call animal control and local shelters. We call veterinary clinics, emergency hospitals, and contact pet-finder services [Brandenburg, 2003]. From an economist’s point of view, such a loss clearly results in a negative impact on the grieving individual welfare. In many empirical studies, analysts seek to obtain money measures of welfare changes due to changes in availability of goods. Could we apply the same analysis to a lost dog or cat? But how can we value something as elusive as a loss of a beloved dog? Is there a dollar amount that could completely compensate someone for the loss of her dog? What is the maximum amount a person would be willing to pay to prevent a such a loss?Perhaps we can look at the values indicated on “lost dog” signs to estimate the value of the dog to its owner. In order to do so, it is first important to define precisely what such an estimate would be measuring and what issues might be important to consider. The concept of value that economists typically use is consumer’s surplus. The conventional measures of consumer’s surplus are the compensating and equivalent variations, CV and EV, respectively. The CV and EV are calculated for an individual for a change in the state of the world. In our example of a lost pet, we can define the initial state S0 to be the state in which the dog is lost. And the new state S1 will be the state of the world in which the dog is found (we can say that S0 < S1 because the state S1 is preferable to S0). The individual’s CV for a change from S0 to S1 is how much money would have to be subtracted from her income after the dog is found to make her indifferent between the initial state and the new state with the subtraction from income. Because the individual will be very happy to find her lost dog, CV > 0. An individual’s EV for a change from S0 to S1 is how much money would have to be added to her income when the dog is still lost, to make her indifferent between finding the dog and not finding the dog but receiving the money. Clearly, EV > 0. In other words, V(I0, S0) = V(I0 - CV, S1) and V(I0 + EV, S0) = V(I0, S1) [Morey, 2003] Where V denotes “utility” and I0 denotes income before the dog is lost. Here because S1 > S0, then CV > 0 and EV > 0. So, CV is the maximum dollar amount the individual is willing to pay to get her dog back. Similarly, EV is the amount she is willing to accept to feel indifferent betweenhaving the money and getting the dog back. The CV also corresponds to the maximum amount an individual would be willing to pay (WTP) to secure the improvement and the EV is the minimum amount she would be willing to accept (WTA) to forgo the improvement. Generally speaking, in valuing non-market commodities, economists do not expect CV and EV to be equal, and they certainly do not have to be in that case of a lost dog. The difference between CV and EV also sheds light on why a dog or a cat or any other pet is not a non-market commodity. Why the difference in CV and EV? It is because there is a possibility that there is no amount of money that could possibly be enough to offset the loss of pet in terms of an individual’s preferences, such that there may not be an |EV| ≤ I0 that equates the two sides of the second equation above. On the other hand, the same individual’s willingness to pay is bounded by their income, so the |CV| ≤ I0 for (S0 to S1) [Morey, 2003]. V(I0, S0) < V(0, S1), therefore for (S0 to S1): |CV| ≤ I0 and |EV| ≤ ∞. Notice that |EV| is not bounded by anything except by how much an individual is grieving. The amount is determined completely by individual preferences. The divergence between |EV| and |CV| is consistent with Michael W. Hanemann’s explanation of why such a value divergence occurs and by how much. By recognizing that substitution effects have an important role, Hanemann demonstrated that the divergence can range from zero to infinity, depending on the degree of substitution between goods and given a positive income elasticity [Hanemann, 1991]. In other words, if the lost dog can be easily replaced by another, the individual’s |EV| will not be as highas for someone who has just lost an irreplaceable companion in life. In the latter case the fact that a lost dog is a non-market commodity becomes clear. Hanemann showed that one should only expect convergence of WTP and WTA value measures when the good in question has a very close substitute. When the good has an imperfect substitute, a value divergence will exist and will expand as the degree of substitution decreases (the more irreplaceable the dog, the higher will be the |EV|) [Shogren, 1994]. Another explanation for the difference in WTA and WTP, favored by some psychologists, is that there is a basic fallacy in the way economists model the valuation of commodities, and the ownership itself makes a commodity more valuable, resulting in a high selling price. This has been called the “endowment effect” [Davis, 1993]. The endowment effect describes the fact that people demand much more to give up an object than they are willing to spend to acquire it. This phenomenon - that people attach higher values to goods if they are in their possession - is very well established in the experimental literature. Of coarse the two explanations are tightly related. The reason someone feels that no amount of money could compensate them for the loss of their dog is that they have come to know and love the dog (endowment effect). For them, their dog is not just a dog; the dog is part of a family and can not be