2.4 Dividing Value


[2.2 Economic Decision-Making]    

[2.3 Determinants of Value]     [2.5 Monopoly]


By trading or co-operating, economic agents can create value. In a trading context, value is created when a customerís willingness-to-pay exceeds a sellerís willingness-to-sell. Value is created by co-operation when more total value is created by engaging in the co-operative activity than by not engaging in it.


Having identified a potential value-creating trade or co-operative activity, agents then need to negotiate over how that value is divided between them. In many situations, negotiations will focus on the price that must be paid from one agent to another. Suppose a customer values a good at $100 and it costs a supplier $40 to produce. So $100 is the customerís willingness-to-pay and $40 is the supplierís willingness-to-sell. If willingness-to-pay is WTP, willingness-to-sell is WTS and the price paid by the customer to the seller is p, then the customer receives WTP Ė p while the supplier receives p Ė WTS. The amount WTP Ė p is called the consumer surplus while the amount p Ė WTS is the supplier surplus. The total surplus is the sum of consumer and supplier surplus.


Click here to view the following animation, which demonstrates the concept of consumer surplus and how it relates to demand curves.


Trade will be valuable if the total surplus when trade occurs exceeds $0. In this case




In this case, WTP Ė WTS = 100 - 40 = 60. Thus, a value of $60 is created by producing the good for the customerís use. Notice that trade is desirable here regardless of what the price, p, is. In principle, even if p were very low (close to $0) or very high (greater than $100), it would still create value for trade to take place.


However, in practice, not only must value be created by trade but the customer and supplier must individually prefer trading to not trading; that is, both consumer and supplier surplus must be greater than $0. For the customer, this means that p must be lower than their willingness-to-pay of $100 while for the supplier, p, must be greater than their willingness-to-sell of $40. So long as p lies between $40 and $100, both consumer and supplier surplus will be positive.


The following figure summarises this situation:



Added Value


You have now seen how, in trading situations, for trade to occur, not only must value be created but it must be divided in a way that leaves all agents that are parties to trade with more surplus as well. In the above trading example, we saw that for trade to occur, price must lie below the customerís willingness-to-pay and above the supplierís willingness-to-sell.


An alternative and more generally applicable way of looking at the outcomes of negotiations is to use the notion of added value. Adam Brandenburger and Barry Nalebuff define added value as




The size of the pie when you are in the game




The size of the pie when you are out of the game


When they talk about the ďsize of the pieĒ, they are talking about the total surplus and when they talk of being ďin the gameĒ, they are talking about being a party to the trade or co-operative venture. Thus, another way of defining added value in a trading context is




Total surplus when you are engaged in the trade




Total surplus when you are not engaged in the trade


Added value is a measure of what an individual agent is bringing to a trading situation; that is, how much additional surplus or value is being created when you participate in the transaction. It is a useful concept because it defines the most that an individual agent can obtain from a trade in terms of their own surplus.


When there is only a single customer and a single seller, each agentís added value is very easy to derive. In that situation, an agentís added value is equal to the total value created by the potential exchange. The reason is simple: in this case, if either the supplier refuses to sell or the customer refuses to buy, no trade takes place and no value is realised.


Economists have a term for this type of trading relationship: bilateral monopoly. Recall that a monopoly is a situation where there is only a single seller of a product. A bilateral monopoly refers to a situation where there is a single buyer and a single seller. This ties the buyer and seller to each other.


Click here to see in what situations is there only a single buyer and seller.


In our earlier trading example, we can calculate the range of possible prices that could be negotiated by calculating the customer and supplierís respective added values.


         Customerís added value: If the customer were not to engage in trade, ie, refuse to purchase the service from the supplier, it would lose $100 and the supplier would save $40. In effect, there would be no surplus. Therefore the customerís added value is $60 (= 60 - 0).


         Supplierís added value: If the supplier were not to engage in trade, ie, refuse to provide the service to the customer, it would save costs of $40. Therefore the supplierís added value is also $60 (= 60 - 0).


In this trading example, the customer and the supplier have the same added value. This is because each is essential to the value being created from trade. If either party did not participate, a valuable trade would not be made. We can state this result as a basic principle:


When every player is essential to a value-creating activity, each playerís added value is identical and equal to the total value created.


How does this determination of added values translate into a price range? The customer cannot pay a price that would allow them to obtain a consumer surplus greater than their added value. Thus, p must be such that $100 Ė p < $60 or p > $40. This makes sense as a price less than $40 would leave the supplier with a negative surplus from trade and they would not participate in it.


Similarly, the supplier cannot be paid a price that would allow them to obtain a supplier surplus greater than their added value. Thus, p must be such that p - $40 < $60 or p < $100. Again, if the supplier was to earn a price that gave them more than their added value, ie, a price greater than $100, the customer would have a negative surplus from trade and would refuse to participate in it.


Thus, the added value approach gives the same outcome in terms of a price range as willingness-to-pay and willingness-to-sell. You will see, however, that in other situations, added value will be more easy to apply; especially when there are more than two parties to the transaction.


Specific Price Predictions


Added value analysis can determine the range of possible prices in a trading situation. To make our pricing predictions more precise, we need to impose additional assumptions on the relative negotiating abilities of the customer and supplier.


To see this, suppose that the customer had far superior negotiating abilities than the supplier. This might occur, for instance, when the customer can make a take-it-or-leave-it offer to the supplier. The customer names a price that the supplier can either take, in which case, trade takes place at the price, or leave, in which case, no trade will take place. In choosing a price, the customer first puts itself in the position of the supplier and asks: what is the lowest price the supplier will accept? In our example, the supplier will not accept a price lower than its willingness-to-sell of $40, so the lowest price is $40. The customer will then announce this price (or a cent more than it). The supplier, faced with a choice of a very small amount of surplus or no surplus, chooses to accept the price. Because the customer ends up appropriating all of the value created in this case, we can refer to this situation as one where the customer has all of the bargaining power.


On the other hand, it is conceivable that the supplier has all of the bargaining power. This may occur if the supplier can make a take-it-or-leave-it offer to the customer. This time, the supplier considers the customerís decision and asks what is the highest price she can demand and still have the customer agree to purchase the service? By definition of willingness-to-pay, this price must be $100 (or a cent less than it). Therefore when the supplier has all of the bargaining power, her surplus is equal to the total value created.


In reality, such extremes are not likely. Counter offers are possible and, in many situations, both customer and supplier will be equally sophisticated. In this case, an equal bargaining power solution would be a reasonable outcome. This would leave the customerís consumer surplus equal to the supplierís surplus or producer surplus.


In an equal bargaining power solution, p is such that








In the example, WTP + WTS is $140 and a price of $70 would be likely.


When, in topic 2.5, we consider the effect of competition, you will see how this changes each agentís added values but we will still assume that an equal bargaining power solution is a reasonable bargaining outcome.


Now try the following exercise to test your knowledge of added value and equal bargaining power. Click here to launch the exercise.


Sharing Costs


Some important economic transactions involve two or more players who each wish to share an asset, good or service in order to realise some value. Indeed, sometimes it is possible for one or both players to realise sufficient value to cover the costs of the asset, good or service on their own. However, at other times, one or both players will not be able to generate sufficient value on their own and are forced to enter into a sharing arrangement. This will be possible so long as sharing is feasible, ie, both players can use the asset or consume the good or service without a diminution in the quality of its use. We refer to these types of transactions as cost-sharing arrangements. Here, negotiations are focused upon how much each player contributes to the costs involved.


Examples of cost-sharing arrangements

People share costs all of the time. Sometimes, this is explicitly recognised while other times it is implicit. An excellent example of an implicit cost-sharing decision is the decision of couples to have and raise a child. It is obvious that, by biological necessity, some costs will be vested with just one person. Nonetheless, each partner derives benefits from child rearing and without explicitly identifying all of the costs, they arrive at some allocation of them by assigning different tasks to each other.


Here we will concentrate on explicit cost-sharing arrangements that potentially involve monetary transfers. Nonetheless, you should keep in mind that the considerations involved will often apply to implicit arrangements as well.


There are many examples of explicit cost-sharing arrangements.


         Research and development costs can often be large but nonetheless, research outcomes can benefit more than a single company. Moreover, even when duplicate research effort can be individually profitable, two companies (even if they compete elsewhere) might benefit from forming a joint venture to avoid resource waste. Such joint ventures might be a separate company funded by the firms involved or a jointly owned and operated lab. In either case, the parties must agree upon what share each will contribute to the costs of the joint venture.

         Some companies have come to recognise that certain back office functions can be shared. Typically, these involve processing and information technology resources. These companies have moved to integrate those back office functions while retaining separate downstream or retailing arms. Once again, while each company could have its own separate back office, each recognises that they could economise on these resources by integrating these functions and sharing the costs involved.


These examples have in common that the costs involved do not rise considerably when more than one player is involved. The players are, therefore, complementors on the supply side. The sum of opportunity costs of supplying the resource to each player individually is greater than the opportunity cost of joint supply. In research and development and back office integration, costs were lower because the duplication of certain resources and effort would be avoided by a joint venture or integration arrangement.


Click here to examine how buyer-seller exchange and cost-sharing arrangements are related to one another?


Cost-sharing agreements

In cost-sharing arrangements, the basic principles of how value is divided remain the same as in a trading situation, except that the calculations become more difficult. This is because, in many situations, the underlying basis for the total value created can change dramatically depending on the particular situation. While agents may jointly benefit from sharing costs, it may be possible for some agents to go it alone and bear their own costs. Hence, value created may, in some situations, involve an avoidance of cost duplication while in others a joint relationship may be the only way in which one or more players can earn value.


Asset Costs


As in the trading situation, we will demonstrate the application using a simple example. Suppose there are two agents A and B. If they have access to an asset, each agent can earn some revenue. For A, this revenue is $100 and for B it is $200. The asset is, however, costly to acquire. It may cost $50, $150 or $250. Nonetheless, for each level of costs, the asset can be easily used by both A and B. Hence, it would not be efficient for the asset to be duplicated.


The key issue in any negotiation is: how much of the assetís cost should A and B pay respectively? Their respective shares of the assetís cost will be determined by their added value. However, before calculating these, we have to consider what the total value created by the relationship is. This is not a trivial matter because, for some level of costs, without a joint acquisition, it may be still worthwhile for one or both players to go it alone. In this case, the total value created by the relationship is the avoidance of duplication in the investment costs.


High asset costs

Nonetheless, to build intuition, we will begin with the case where investment costs are high, equal to $250. Notice that here, neither A nor B can go it alone. Individually, the costs of acquiring the asset exceed the revenue they might earn. In this case, the only way to make a positive profit is to agree to a joint acquisition of the asset. That is, their joint revenues of $300 will exceed the assetís cost of $250. Total value created by the relationship in this case is $50 because neither player would earn a positive profit outside of the game.


The high costs mean that both A and B are essential to the relationship. No profits will be earned if either decides not to participate. We know from the trading situation that when players are essential, their respective added values are identical and equal to the total value. Given the revenues each expects to earn, the highest contribution A could make would be $100 (leaving B with $150 to contribute) and the highest B could make would be $200 (leaving A with $50 to contribute). So the range of cost allocations for A would be $50 to $100 and $150 to $200 for B.


Medium asset costs

Turning now to the case where the asset cost is $150, while A would still not find it profitable to go it alone, B would. So if either A or B were to decide not to enter into a joint relationship, B would earn a value of $50. Hence, given that the total profits of a joint acquisition would be $150 (= 100 + 200 - 150), A and Bís added value would each be $100 (= 150 - 50).


Another way of looking at the total value created is from a buyer-seller perspective. We can do this because B would acquire the asset regardless of whether A is involved or not. Hence, we can consider the relationship from the point of view of B selling access to the asset to A. Note that such access has the potential to allow A to earn $100 in revenue. In this light, $100 represents Aís willingness-to-pay for access to the asset. If B owns the asset, it faces no opportunity cost in allowing A access to it, hence, the total value created is $100. As this is akin to a buyer-seller exchange and both A and B are essential to the creation of the $100, their respective added values will be identical and equal to the total value created.


In either case, the focus on Aís revenues mean that the maximum it can contribute to the assetís costs is $100 and the minimum is $0. Thus, Bís contribution will lie from $50 to $150.


Low asset costs

When the asset costs are low (= $50), then it becomes profitable for both A and B to go it alone in the absence of a joint relationship. If they do not use the asset jointly, then A will earn $50 and B will earn $150. The profits from a joint relationship, however, would be $250. This exceeds the sum of profits each would earn on their own, ie, $200. Hence, a joint relationship is valuable. If either player left the relationship, the total value would fall by $50 as a duplication of the assetís costs would occur. Hence, both A and Bís respective added values is $50.


Once again, A and B are both essential to the creation of value from a joint relationship. As such, each has identical added values equal to the total value created. Given this, each would end up contributing between $0 and $50 depending on their respective bargaining power.


The difference between the three cases lies in the source of the value from a joint relationship. Here, when asset costs are low, that value is in the avoidance of a duplication of those costs. On the other hand, for medium levels of asset costs, the value of a joint relationship was in the ability it afforded for A to earn revenue of $100. Finally for high asset costs, a joint relationship was the only way for both A and B to earn their respective revenues.


Equal Bargaining Power Cost-Sharing Rules


In many situations, people choose cost-sharing rules that are fair, ie, each person contributes an equal amount to the costs involved. For A and B, this would mean splitting an asset's costs evenly. This would be fine if the asset's cost were less than $200 but when it is higher than this, say, $250, A would not find it worthwhile to enter into the arrangement as 50 percent of $250 exceeds Aís revenue of $100. Without A to share costs, B would not find it profitable to go it alone as the cost of $250 exceeds Bís revenue of $200. So to insist upon fairness would lead to no value created at all.


In other situations, cost-sharing rules are proposed that are ďequi-proportionalĒ to each personís relative benefit. This would mean that B would contribute two-thirdís of the assetís cost since it would receive 50 percent more value than A. As such, both A and B would earn some positive value from the project. However, this rule still might not be the best solution for A. Regardless of the assetís cost, its surplus is always less than that earned by B.


These rules do not reflect the economics of a cost-sharing situation. Therefore, while they might be desirable for fairness reasons, such rules are unlikely to be good predictors of actual bargaining outcomes. Such rules can also lead to poor decisions. To learn more, view the following animation.


Economic analysis suggests that the shares of costs paid will be determined by each playerís relative bargaining power, ie, their relative sophistication as negotiators. If they have equal bargaining power, then this will lead to cost-sharing rules that equate the surplus each player earns from a joint relationship. As such, A would expect to come away with the same surplus as B, not less. The table below summarises the contributions we would expect A and B to make if they had equal negotiating abilities.



Aís Contribution

Bís Contribution











Notice that when costs are low, A and B share equally in their contributions. This is because the value created by their relationship is an avoidance of the duplication of those costs. When costs are at a medium level, the bargaining solution mirrors an equi-proportional rule. Finally when costs are high, the sharing rule does not reflect equality or equi-proportional outcomes. In that case, B contributes relatively more because A can prevent it from earning its high revenues if A walks away from the joint arrangement. Click here to see is the added value outcome actually desirable.


Click here for a discussion point.


Topic Summary


In this topic, you have learnt how to


         determine the range of prices in a trading situation by examining willingness-to-pay and willingness-to-sell and by looking at a customer and supplierís respective added values

         establish the equal bargaining strength price that might be agreed to in a trading situation

         determine an agentís added value in a cost-sharing situation

         determine an agentís equal bargaining strength contribution to costs


Now go on to topic 2.5, ďMonopolyĒ.