Applied Economic Analysis of Information and Risk

This book examines interesting new topics in applied economics from the perspectives of the economics of information and risk, two fields of economics that address the consequences of asymmetric information, environmental risk and uncertainty for the nature and efficiency of interactions between individuals and organizations. In the economics of information, the essential task is to examine the condition of asymmetric information under which the information gap is exploited. For the economics of risk, it is important to investigate types of behavior including risk aversion, risk sharing, and risk prevention, and to reexamine the classical expected utility approach and the relationships among several types of the changes in risk. Few books have ever analyzed topics in applied economics with regard to information and risk. This book provides a comprehensive collection of applied analyses, while also revisiting certain basic concepts in the economics of information and risk.

The book consists of two parts. In Part I, several aspects of applied economics are investigated, including public policy, labor economics, and political economics, from the standpoint of the economics of (asymmetric) information. First, several basic frameworks of the incentive mechanism with regard to transaction-specific investment are assessed, then various tools for market design and organization design are explored.

In Part II, mathematical measures of risk and risk aversion are examined in more detail, and readers are introduced to stochastic selection rules governing choice behavior under uncertainty. Several types of change in the random variable for the cumulative distribution function (CDF) and probability distribution function (PDF) are discussed. In closing, the part investigates the comparative static results of these changes in CDF or PDF on the general decision model, incorporating uncertain situations in applied economics.  

• Language: English
• Publisher: Springer
• Release date: Mar 25, 2020
• ISBN: 9789811533006

Book preview

Part IInformation and Its Applications

© Springer Nature Singapore Pte Ltd. 2020

M. Hosoe, I. Kim (eds.)Applied Economic Analysis of Information and Risk https://doi.org/10.1007/978-981-15-3300-6_2

2. Incomplete Contract, Transaction-Specific Investment, and Bargaining Power

Moriki Hosoe¹  

(1)

Emeritus Professor, Kyushu University, 4-39-8-404 Najima, Higashi-ku, Fukuoka city Fukuoka, 813-0043, Japan

Moriki Hosoe

Email: [e-mail]

2.1 Introduction

In this paper, after reviewing the basic concepts of incomplete contract, we conduct a fundamental analysis of the transaction mechanism, focusing on the role of bargaining power and transaction-specific investment. When one considers a basic pattern of market transaction (one-to-one and buyer-to-seller transaction), one finds that two important questions—what information who holds and who holds bargaining power—have an extremely important influence on the model and the outcome of the transaction. Moreover, the effectiveness of bargaining power depends on various factors related to the environment in which the transaction occurs (e.g. the existence of external options, the structure of information possession, and so forth).

The central idea to this consideration is the concept of transaction-specific investment. In other words, even if the market is competitive, is it possible for each pair of contracting parties to easily secure benefits from the outside parties? Otherwise, if the relationship between the two parties collapses, will it incur heavy losses to them? In the latter situation, the benefits and costs are called transaction-specific. For example, to increase the gains from a transaction, one of the parties makes an investment. However, this investment can be effective only for the existing transaction. If the two parties stop transacting, all the investment becomes virtually worthless. Consequently, after making investment, it is impossible for the investing party to capture the benefit. This is called the ‘Lock-in’ effect. As a result, the other party’s bargaining power will increase. This will result in too little investment taking place, as is indicated by Williamson (1985) and Klein et al. (1978).

In such situations, the important question is what kind of information on the level of investment is available before the transaction takes place. If the information can be observed and verified by both parties, the level of the investment can be specified in the transaction contract, so that the efficient level of investment will occur. However, if the information is not verifiable, investment will only be made in the private interest of each party, and as described above, too little investment may occur.

While considering these points, this paper indicates that in some cases excessive investment will occur, depending on the degree of the transaction-specificity of the investment. Furthermore, depending on the distribution of the bargaining power and the structure of information possession, the transaction specified in the contract may be inefficient. In such situations, renegotiation may occur to create a better contract. The importance of the problem of ex-post renegotiation is described by Hart and Moore (1988), Huberman and Kahn (1988), and so forth. In this paper, our analysis will be confined to ex-ante renegotiation.

2.2 Contract Incompleteness and Hold-Up

2.2.1 Unverifiability of the Level of Effort and the Quality of Goods

If there are clauses that cannot be verified, parties cannot commit themselves never to engage in mutually beneficial contract on in their relationship. A transaction-specific investment is often unverifiable. Then, an immediate consequence of the incomplete contracting approach is the so-called hold-up problem. What if the seller’s efforts and the quality of the goods made cannot be included in the contract? Such an information structure will be usually seen in many market transactions. In that case, subsequent negotiations between the seller and the buyer are important. Now suppose the seller can make an investment (effort) to increase the value of the product. This is formulated as follows. First, if the seller makes no further investment, the quality of the product is expressed at the level of v, and the quality of the product becomes $$v (1 + s)$$ by performing the investment level s. However, the cost of making such an investment is

$$C (s) (C '> 0, C '' <0)$$

. On the other hand, the production unit cost of this product is constant c. The flow of time is as follows. First, the seller and buyer get acquainted, and the seller makes an investment in advance, and the result of the investment is realized. Then, transaction negotiations are conducted.

Considering backwardly, let’s consider the transaction negotiation of price. At this stage, the seller and buyer will know the value of the product, though it is unverifiable, and negotiate the price of the goods. In other words, information is symmetric at the negotiation stage. If the negotiation breaks down, what will be the situation of each person? In this case, the investment they have made will be vain and the quality of the product will be v if they trade with other buyers. The price of the product at this time is assumed to be $$p^0$$ . Therefore, the seller’s profit when the negotiation breaks down is $$p^0-c$$ , and the buyer can trade with other sellers and gain $$v-p^0$$ . Each gain gained when the negotiation breaks down is a mutual gain that must be realized at least in the negotiation. The negotiation will otherwise break down. In this sense, the combination of gains obtained when negotiations break down is called the threat point of negotiations. On the other hand, when negotiations succeed at a certain price of p, the respective gains are $$p-c$$ for the seller and

$$v(1 + s)-p$$

for the buyer. Negotiations are made to increase this gain from each other, but will also depend on the values of the threat. A person with a higher threat gain will not be satisfied unless the bargain gain is higher. How the negotiations are advanced can be thought of as a game in itself, but will be influenced by the magnitude of the profits beyond the threat of the negotiations. Here, let’s think that the increase in profits resulting from negotiations is concluded where they are equal to each other. This can be called a compromise condition when the bargaining power is equal, and is called a Nash bargaining solution. This condition can be expressed as a price for p.

$$\begin{aligned} v(1 + s)-p-(v-p^0) = p-c- (p^0-c) \end{aligned}$$

(2.1)

Price from this condition

$$\begin{aligned} p = p^0 + \frac{sv}{2} \end{aligned}$$

It becomes. Therefore, the higher the level of effort, the higher the price, but the overall value of that was sv, so the profit was split by negotiations and a part of the value corresponding to the magnitude of the effort (here Only half) will be reflected in the price.

Now that we have described price negotiations once we know the quality of the product, we must go back and think about determining the seller’s level of effort. This takes into account the overall profit of the seller, taking into account the level of effort affecting the outcome of the negotiation. Profit of the seller at the effort level of s is

$$\begin{aligned} p-c-C (s) = p^0 + \frac{sv}{2} -c-C (s) \end{aligned}$$

Therefore, the seller can decide the effort level s to maximize this profit. Then, the optimal effort level $$s^*$$

$$\begin{aligned} G'(s^*) = \frac{v}{2} \end{aligned}$$

That is, the effort level is determined so that the marginal cost of effort matches the marginal increase in price due to the increase in effort. It is easy to see that the level of effort determined in this way is less than the level of effort with complete information, that is, the level of effort with the first best. The effort level of the first best is to maximize the welfare of the effort level from the social viewpoint. The problem is

$$\begin{aligned} \max _{s} (1 + s) v-c-C (s) \end{aligned}$$

Thus, the first best effort level is given by the condition $$C'(s) = v$$ . This shows that the effort level of incomplete contracts is lower than the first best level. Also, in the case of a complete contingent contract, where the level of effort can be written as a contract clause, the contract offered by the buyer shows the level of effort and price by solving the following problem.

$$\begin{aligned} \max _{s, p} (1 + s) v-p \end{aligned}$$$$\begin{aligned} s.t.p -c -C(s) \ge p^0 -c \end{aligned}$$

and offer a level of effort and price. The level of effort offered by the seller under this agreement is consistent with the level of best effort because the seller can take all the benefits of increased effort. Thus, since the level of effort cannot be written as a contract clause in an incomplete contract, after effort is made, the seller can only take a portion of the overall benefit of the effort through negotiation, and in the end, the seller only makes an under-effort. This is called the holdup problem.

Hold-Up Problem and Ownership

How can we overcome this hold-up problem? One is to eliminate incompleteness of contracts related to investment. If this can be done, it will be difficult to eliminate the incompleteness of the contract due to the very nature of trade-specific investments. Therefore, another solution is the integration of ownership. What is decisive in the hold-up problem is that the seller’s investment $$=$$ the right to determine the level of effort and the right to dispose of the goods affected by the effort are separated into the buyer and seller, respectively. This hold-up problem will be solved if these two authorities are unified to either player. Now, suppose that the buyer purchases the seller’s investment $$=$$ the right to make decisions. First of all, how much will the purchase amount be? As shown above, if the transaction is conventional, the profit of the seller is

$$\begin{aligned} \pi _B = p^0 + \frac{s^{*}v}{2} -c-C (s^{*}) \end{aligned}$$

Therefore, if the buyer presents a purchase price that is at least above this profit, the seller will let go of that right. The question then is whether it would be profitable for the buyer to purchase the right. If the seller purchases the right to determine this investment $$=$$ effort level, it is only necessary to determine the optimal investment $$=$$ effort level for him. Since the seller’s profit generated by purchasing this right is

$$(1 + s) v-c-C (s)-\pi _B$$

, the optimal investment $$=$$ effort level at that time is consistent with the solution of the first best problem. Since the first-best problem is to determine the level of an investment $$=$$ effort that maximizes the sum of the gains of the two players, it is clear that the seller makes the first-best investment by transferring such rights.

2.2.2 Sequential Investment and Option Contract

Double Moral Hazard

In the previous section, we considered the case where buyers can invest and raise the value of goods, but sellers cannot influence the value of the goods. Next, let’s examine the efficiency of transactions when sellers can increase the value of goods. First, when the seller offers a contract and the buyer accepts the contract, the buyer invests to increase the value of the goods. The seller then makes a similar investment. These investments cannot be verified in advance as before and therefore cannot be written into the contract. In this case, if the seller makes a contract to sell the goods to the buyer at a certain price, the seller has no motivation to invest. If the seller is expected not to invest, the buyer will not make an efficient investment. Thus, the buyer is less likely to purchase the good. Thus, if each investment cannot be verified, the efficiency of the investment will be impaired, and a double moral hazard will occur.¹

First, let’s find the first best investment level in this case.

First Best Investment Level

Now, the investment level of seller and buyer is measured by cost respectively as a, b. In addition, the value of the goods becomes r(a, b) by the investment. Let each marginal value decrease. At this time, each of the first-best investment level is determined where each marginal value is equal to the marginal cost 1. Let the values be $$a^*$$ and $$ b^*$$ , respectively.

Introduction of Option Contract

So, suppose the seller offers the following option contract $$(p_1, p_2)$$ to the buyer. Here, $$p_1$$ is the selling price of the seller’s goods, the seller has the right to buy the goods after the buyer invests, and $$p_2$$ is the buying price at that time. What will be the level of investment that both parties will carry out with this option contract? Let’s say that the buyer has made an investment level of a by solving backwards. At that level, the seller decides whether to make the option.

Therefore, the investment level of the seller at that time is

$$\begin{aligned} \max _{b} r (a, b) -b \end{aligned}$$

This level is generally expressed as b (a), depending on the buyer’s investment level a. Therefore, the seller’s gain is

$$\begin{aligned} r (a, b (a))-b (a) -p_2 \end{aligned}$$

It becomes. Here, if a increases, asset value r(a, b(a)) also increases. On the other hand, if you do not exercise the option, it will belong to the buyer, so the seller will make no investment $$(b = 0)$$ . Therefore, the seller’s gain is zero. Therefore, after the buyer makes an investment, whether the seller exercises the option depends on the following inequality.

$$r(a, b (a))-b (a) -p_2 \lesseqqgtr 0 \Longleftrightarrow 0 $$

Given the investment level at which this gain is just zero, it depends on $$p_2$$ . Let’s express the relationship with $$a (p_2)$$ . Therefore, if you purchase the goods for the selling price $$p_1$$ of the goods in the first period and invest $$a \ge a (p_2)$$ , options will be exercised from the above discussion. Buyer gain is

$$ p_2-a-p_1 $$

. In this case, $$a = a (p_2)$$ . Therefore, the buyer’s gain at that time is

$$p_2-a (p_2) -p_1$$

. On the other hand, if $$a \le a (p_2)$$ is invested, the option is not exercised, and the buyer’s gain at that time is

$$r (a, 0) -a-p_1$$

. Considering the above, let us say

$$p_2^* = r(a^*, b^*)$$

. At that time,

$$a^* = a(p_2^*)$$

. At that time, the buyer’s gain when exercising the option is

$$p_2^*-a^*-p_1$$

. On the other hand, if the option is not exercised, the buyer’s gain is

$$r(a, 0) -a-p_1(a \le a^*)$$

. Here, since $$(a^*, b^*)$$ is the first-best solution,

$$\begin{aligned} r(a^*, b^*)-a_2^*> r (a, 0) -a \end{aligned}$$

is held. Therefore, in this case, the buyer makes an investment $$a^*$$ that causes the option to be exercised. Therefore, the selling price of the first term is

$$p_1^* = r(a^*, b^*)-a^*$$

and the option price is

$$p_2^* = r(a^*, b^*)$$

Then the two investments will be at the first best level and the seller will be able to absorb all the surplus.

In this way, it was found that the efficiency of sequential investment is realized through option contracts. paragraph Possibility of renegotiation However, if renegotiation is allowed, this option contract may not necessarily be an efficient transaction. Where will renegotiation occur? This is a renegotiation between the buyer and seller after the buyer has invested. The reason is why, at that time, the seller has the right to exercise the option and therefore has the option of not exercising the option. Then, the buyer is only worth r(a, 0) for the good. But if the seller collaborates on b, the value of the goods is

$$\begin{aligned} \max _ {b} ~~ r(a, b) -b = r(a, b (a))-b (a) \end{aligned}$$

Here, when the Nash negotiation solution is adopted as the negotiation solution, the negotiation solution is that the increase in gain caused by the negotiation is equal to both. That is, Negotiations to invest b(a) at the price p that satisfies

$$\begin{aligned} r(a, b (a))-b (a) -p = p-r (a, 0) \end{aligned}$$

is realized. That is, the transfer price p(a) that can be negotiated is

$$\begin{aligned} p(a) = \frac{r (a, b (a))-b (a) -r (a, 0)}{2} \end{aligned}$$

(2.2)

Therefore, if $$p \le p_2$$ with respect to the option price $$p_2$$ in the first contract, the determined option price is discarded and the seller buys back at the negotiated price p. $$P \ge p_2$$ does not bother to purchase at a high price, so it will be purchased at $$p_2$$ . From this, in the case of option price $$p_2^* $$ in an efficient option contract without renegotiation,

$$p_2^*> p(a^*)$$

will always hold if renegotiation is carried out. The right will be not purchased at an efficient option price. There is a possibility that buyers do not make an efficient investment considering this. In this section, when unverifiable investments are made sequentially by buyers and sellers, option contracts over the ownership of the assets in which the investments are embodied are effective in order to realize the efficiency of those investments. However, it has been shown that if an option contract can be renegotiated, the efficiency may not necessarily be restored by the option contract.

Incomplete Contracts and Ownership

Ownership is not a particular issue when complete contracts are possible. For example, when dealing with goods between companies, and trying to trade in a ordinal market, the transaction results are not affected, no matter whether the goods supplier merges with the demand company or the demand company merges with the supply company. This corresponds to the Coase theorem. In that case, it is important to determine what will happen when the negotiation breaks, as it determines the outcome of the negotiation. It is important how the ownership is allocated among the parties in advance. That is, it can be decided by the contract, but when unexpected event happens, it is the right that the owner can decide how to use the goods. Depending on how this ownership is allocated, the transaction is known to be inefficient. In the previous section, we examined the possibility that the option allocation rule of option contracts can realize efficient investment.

Hart and Moore (1988), Grossman and Hart (1986) and Schmitz (2006) pointed out the relationship between ownership and organizational efficiency. In particular, if trading-specific investment is important to increase efficiency in trading, depending on how ownership is established, there is a possibility that the return from this trading-specific investment may not be obtained sufficiently. Therefore, it has been shown that the investment may be under-estimated. This arises from the fact that it is not possible to negotiate a contract in a clear form with respect to the level and content of the investment. This incomplete contract theory is intended to provide a theoretical basis for the intuition of economics of transaction, by Williamson (1979) and is being developed in various discussions on comparative trading in economic systems including corporate theory. This is an area that needs further study. See Hart and Moore (2008), Goltsman (2011), and Aghion et al. (2016) as recent contributions.

2.3 Bargaining Power and Information

2.3.1 The Allocation of Bargaining Power and Information

Here we consider the economic welfare problem brought about through the allocation of bargaining power and information. Farrell and Shapiro (1989) and Tirole (1988), Hart and Moore (1988) analyze this point in great detail. As general discussion, Hart and Holmstrom (1987) and Green and Laffont (1987) are useful.

First, consider the situation in which the seller’s reservation price (cost) c is known to the both parties, but the buyer’s reservation price v is only known to the buyer. However, the seller believes that the buyer’s reservation price v lies in the interval $$[\underline{v}, \bar{v}]$$

$$\left( 0< \underline{v}< \bar{v}\right) $$

and is given by the probability function F(v), where

$$F(\underline{v})=0, F(\bar{v})=1$$

. We suppose $$0< \underline{v}< \bar{v}$$ holds. This means that probability of making a profit from the transaction is less than one but positive. Let us assume that the seller holds the bargaining power and can therefore offer any price he wishes to the buyer. If the buyer refuses the seller’s asking price P, the negotiation breaks. In this case, the possibility of transaction occurring is $$1-F(P)$$ and the buyer’s expected profit margin