Nivel macroestructural: guarda relación directa con el rudimento de asunto o tema general del texto

In this appendix we first show that definition 1 characterizes a Nash-equilibrium and subsequently proof propositions 5 to 7. Where no confusion can arise we simply write θ instead of, for example, θ(m).

Proof that definition 1 is a Nash-equilibrium.

Consider the payoff matrix below. Players are denoted by P and C, the agent that produces and the one that consumes first respectively. They can either be honest, H, or cheat, D (defect). The pay-offs are in utility terms. As an example, consider P playing honest and C cheating, then P produces the good, bearing cost in utility terms of c and enters the market the next period after finding out of being cheated, δVu. C consumes yr, does not produce in return and enters the market getting δVu. Thus in the upper-right cell we have the pay-offs −c + δV^u and yr+δVu.Consider then the strategies {H; H}. This can, by construction, only be a (weak) Nash-equilibrium if it is in both players advantage not to deviate:

−c + δy^r+ δ²V_r ≥ δV^u and −c + δV^r ≥ V^u. Fortunately, we can show that first inequality is implied by the second. Note that _(1−δ)¹ y_r ≥ _2(1−δ)¹ (yr− c^r) = Vr (see equation 4.5). Then δyr+ δ²V_r ≥ δV^r. If now −c + δV^r ≥ V^u (second constraint) then it is surely the case that −c^r+ δyr+ δ²V_r ≥ V^u ≥ δV^u which proves the first inequality. Finally note that {D; D} is always a (weak) Nash-equilibrium.

P ↓; C → H D

H −c + δy^r+ δ²V_r; yr− δc + δ²V_r −c + δV^u; yr+ δVu

D δV_u; δVu δV_u; δVu

Proof of Propositions 5 and 6.

We try to find values of θ for which definition 1 is satisfied with equality: −c + δV_r = Vu. Label this equality D1. For this value agents are indifferent between reciprocal exchange and entering the market given the market size. For higher values of θ they prefer reciprocal exchange, for lower values they prefer market exchange. In particular we try to find values of θ, say θ, for which the equality is satisfied but will not be satisfied for any lower θ for any market size. It is instructive first to consider the case where θ is (weakly) monotonically decreasing in m and then generalize the results, as in the main text. The advantage of this is that if reciprocal exchange is enforceable at all, it is certainly enforceable at

m= 0since Vr is decreasing in m and Vu increasing in m. Thus, we can focus on the equality holds (and is in this particular case easy to find). (As a marginal comment, note that as δ → 1, the numerator of the LHS of (4.11) approaches

1

2(θym − c) which equals zero for some 0 < θ ≤ 1.). Since the LHS of D1 is increasing in δ, θ is lower for higher values of δ.

Generalizing the argument, we see that the RHS can be positive for markets m > 0, but also that θ(m) may be larger than θ(0). So even if the equality holds at m = 0, it may well be that the LHS is larger than the RHS at positive market sizes. The critical value of θ (i.e. θ) can therefore be lower than the value of θ for which the equality holds at m = 0. The caveat in the generalization is, however, the fact that Vuis now increasing in δ as well. At m = 0, Vu = 0 no matter what the rate of time preference is. This remains true up to the market size where Vu becomes strictly positive. For the range of values for which Vu is strictly positive, Vu is also increasing in δ. Thus both sides can be increasing in δ at some market sizes, and the relation between θ and δ becomes ambiguous. We stress however that for low values of δ, Vu = 0, and hence there exists an interval where θ and δ are negatively correlated. The intuition behind this increasing part is that because on the market costs are made before revenues, for sufficiently low discount rate the present value is negative, whilst in a reciprocal exchange with some probability you consume before you produce and so even for low (but positive) discount rates expected gains are positive for some valuation ratio.

As a special case, if θ(m) ≤ θ(0) ∀m (in other words θ is nonincreasing), then θ can be determined by inspection of m = 0 alone (since if then reciprocal exchange is not enforceable at m, and since Vu is nondecreasing and Vr nonincreasing in the market size, then it is not enforceable at any m). Since at m = 0, Vu = 0, if the discount rate increases a little, Vu remains zero but Vr increases so θ unambiguously declines. But note that such an unambiguously declining θ-curve is only a special case and that it is not directly related to the shape of θ(m).

The same line of argument can be used to derive proposition 6. Here the aim is finding the θ such that market exchange is just enforceable at one particular market size, and not for any higher θ. We first try to find θ in the case of

non-increasing θ so that the focus can be restricted to m = 1. We do not state the proof here.

Proof of proposition 7.

The proof consists of showing that it need not be contradictory to have a stable equilibrium that is inefficient in the sense that it is Pareto-dominated by another stable equilibrium. Denote the two equilibria under investigation by mi and me

(the subscripts stand for inefficient, efficient). Let the initial point be the inef-ficient equilibrium mi. Three cases are to be considered: 1. mi is at one of the corners of the economy. If mi = 0 then it is stable if −c + δV^r ≥ V^u. 2. If m = ˜m then it is stable if −c + δV^r > V_u. 3. mi is an interior solution. It is stable if

−c + δV^r= Vu and if δ_dm^dVr

i ≥ ^dV_dm^u_i.

We have to show that the following set of equations need not be inconsistent:

V_r(me) ≥ V^r(mi), (4.12)

V_w(m_e) ≥ Vw(m_i). (4.13)

Additionally, the enforceability constraints have to be satisfied as indicated at mi

and me. Consider for example the case where mi is the corner solution m = 0 and me is an interior stable solution that Pareto-dominates the corner solution.

Thus we have:

V_r(me) ≥ V^r(0), (4.14)

V_w(me) ≥ V^w(0), (4.15)

−c + δV^r(0) ≥ V^u(0). (4.16)

−c + δV^r(me) = Vu(me) (4.17) The second inequality is naturally satisfied. (Indeed, since V_w⁰(m) > 0, the only case where an equilibrium can be dominated by a smaller market size is where m= 0since otherwise all remaining market participants would lose some welfare.

Except, of course, when nobody stays). Since we put no restrictions on θ the first inequality can be satisfied as well (not, however, when θ(m) is nonincreasing in the market size). Combining the (in)equalities we see that as long as Vr is increasing over the interval [0, me](but remember that it may be decreasing in the first stage and increasing thereafter), but not as fast as Vu there is no inconsistency and it cannot be ruled out that m = 0 is indeed inefficient. Other cases can be analyzed

in a similar manner and are omitted. The result of possible inefficiency is easily extended to the nonweighted case for V_m, V_u, and V_w all behave in a similar way (namely increasing in the market size). ¥

Welfare Gains of Labeling with Heterogeneous Consumers

Diamonds are a girl’s best friend. But not only her’s: they are no less a rebel’s best friend. Rebel armies use guns to force labourers to dig holes and earn hundreds of millions of dollars by selling the ”blood stones”. To stop these activities, many countries have now signed to support a system of certificates for diamonds without a conflicting history. When does this lead to welfare gains?¹

5.1 Introduction

Implicit in the standard formulation of the fundamental welfare theorems is that the characteristics of commodities are observable to all market participants (Mas-Colell et al., [1995]). However, in many cases the consumer cannot observe all characteristics of a specific good, such as the safety or the quality level. Due to these informational asymmetries, the consumer is not willing to pay price premi-ums for different goods. No distinct markets can therefore exist for goods that are differentiated with respect to unobservable characteristics. As is well known, this can have dramatic consequences for the efficiency of the market mechanism.

Famous in this respect is the market for lemons as described by Akerlof [1970].

0This chapter is coauthored by Theo van de Klundert. We are thankful to Richard Nahuis and Sjak Smulders for helpful comments.

1See The Economist [2003] and BBC News [2000].

An in particular interesting class of goods where some characteristics are un-observable is that of goods with social externalities of production. For example, some production methods have damaging effects on the environment, involve child labour, or rely on what are perceived as unfair wages. These externalities are not taken into account by the producers and are therefore not reflected in the consumer price. And even though it seems that many consumers are in principle willing to pay premiums for the use of production methods that do not, or to a lesser extent, involve such social externalities, they cannot observe from the end product which production method has been used. Hence, goods with social externalities of production fall into the class of asymmetric information. As in the case of the lemons market, without improving the consumers’ information, there is little hope that the equilibrium will be efficient.

In this chapter, it is argued that goods with social externalities of production pose an even more severe problem to the efficiency of markets than most other goods with unobservable characteristics. In other cases where some characteristics are not directly observable, producers can often still signal them to the uninformed party. For example, the price, advertisements or warranties can sometimes provide a credible signal to the consumer that the product in question is of high quality (Tirole [1988]). However, such signaling strategies often do not exist for goods with social externalities of production (see the next section).

Lacking the possibilities of the usual market responses to informational asym-metries, the government can decide to intervene. One obvious way is to impose a standard on production methods. Under some circumstances this can be welfare improving. However, during recent years government regulation is increasingly relying on information provision to alter behavior (Magat and Viscusi [1992]).

One example is labeling. Labels are certificates issued by a third party that pro-vide credible information about the contents of a product. By now there exists a variety of such labels that concern, among other things, the environment, working conditions, fair trade, and child labour. Should they wish to do so, consumers can contribute to a reduction of social externalities by buying these labeled products.

The crucial difference between standards and labels is the fact that labels are voluntary. Firms can decide whether or not to apply for the label, and adjust their production technology conform the requirements. In contrast, standards imposed by the government are mandatory for all firms in the market. Labeling schemes therefore allow for more flexibility in the choice of production technology. This

has the advantage that labels serve the consumers’ needs better than standards when consumers are heterogeneous in their willingness to pay for reducing the social externality. The scope of differentiation is however limited by the costs of passing on informational contents to the consumers. These costs consist of designing the label, screening costs of the firm made by the third party, and the costs of information acquisition by the consumers, each of which can be significant.

Given this trade-off between flexibility and costs, the aim of this chapter is to examine under which conditions labeling is preferred over standards.

The setup is as follows. The next section first reviews background informa-tion concerning markets with asymmetric informainforma-tion and some of the aspects of labeling. In section 5.3, the model is described and a derivation of the welfare under imperfect information is given, together with the optimal standard and label technology. Section 5.4 presents the main proposition where a comparison is made between the welfare level under a standard and under a labeling policy.

The chapter ends with a discussion and conclusion.