Transaction Costs and Negotiation

So we all know that one of the simplistic assumptions many people have about economics is that everything has a measurable value and that a given quanitity of one thing can be exchanged for a derivable quantity of another thing. But this misses the mark in that the entire economy is driven by actors who value things differently..

Without some sort of inherent disequilibrium, there would never be any transactions carried out that had positive transaction cost, and even for a transaction that had a transaction cost of zero there would be no incentive to actually carry out the transaction. If a can of Diet Coke was really valued at 60 cents, you would never sell it and i would never buy it unless the price were exactly 60 cents. What's more, the sale could only occur if the transaction cost were 0, and even then the sale is not assured because both parties are merely indifferent. Let us assign a universal indifference factor Q between 0 and 1 such that one will transact at the indifference point with probablity Q. (For symmetry reasons, must Q equal 1/2?) Thus in the present example, the Diet Coke will sell at 60 cents with probability Q^2..

What this means is that if you are a merchant of Diet Coke, you probably value a can of Diet Coke less than i do. Let's say you value the can at 55 cents and i value it at 65 cents. It seems a sale can be completed as long as the cumulative elective transaction cost is less than 10 cents. Keep in mind that certain fixed transaction costs may already be internalized in the values we assign. You as a merchant may have only paid 40 cents for the can, but you are adding 15 cents as the Diet Coke's pro rata share of the cost of keeping your store open today. Similarly, i may value the Diet Coke at 70 cents but have already spent 5 cents worth of resources and time to get to your store. Once we arrive at the bargaining table, hopefully our additional transaction costs will not exceed 10 cents or there will be no sale..

But let's assume no transaction cost in our example. Surely i am willing to buy the Diet Coke at 55 cents, but you are indifferent, so that transaction will occur with probability Q. Likewise, at 65 cents the transaction would also occur with probability Q. But what about somewhere in between? We would not assume that you would agree to my offer of 56 cents with certainty any more than we would assume i would pay 64 cents with certainty. But why is this? Without any knowledge of how you value the good, what reason do i have to reject a price of 64 cents? But what constraints exist on where in this acceptable range the price ends up? How can we model each person's situation to account for bargaining within this range? Is there some function that is 0 to one side of the indifference point, and increasing from Q at the indifference point asymptotically toward 1?

Perhaps it comes down to the transaction cost of the bargaining process itself. If i offer you 56 cents, it may cost you 2 cents worth of time to give me an answer in which you offer me 63 cents (because you can't accept my offer, but you offer something symmetric to a position that would have been acceptable to you). But perhaps my time is worth less than yours, and i feel that i have not wasted enough time for the Diet Coke to be worth less than 63 cents and i take it..

Or perhaps my time per round of negotiation is worth 3 cents but i assume your time is only worth 1 cent. You on the other hand think that both of us value our time at 2 cents per round. i will offer 56 cents, but you will counter with 63 cents. i may bump my offer up to 58 cents because of the 2 cents you offered me, but you still haven't been compensated for two rounds. If you counter with 59 cents, we both end up at our value for the Diet Coke, adjusted by our transaction cost in bargaining, and we are both indifferent to the sale. If you offer anything other than 59 cents, we have gone through two rounds of bargaining at 5 cents a round, using up the full 10 cent price differential, and the Diet Coke never gets sold..

But regardless of whether the Diet Coke is sold or not, 10 cents has gone into the void in the last example. A starting offer of 59 cents on the other hand would have allowed us both to claim a profit. But what is to prevent you from countering with 61 cents that would also have given me a profit, although a smaller one? There seems to be something inherent in the bargaining process in which each party assesses the profit potential of both sides while attempting to attain a price that will achieve maximum profit among all the prices the other side is willing to transact at. As with the example above, this process would seem to be modeled better by a function rather than a dichotomous variable (transact versus don't)..