Environment

The economy is composed of M isolated markets. Each market m is populated by Im farmers and Jm traders. Interactions between the two agents can occur under two alternative contracts. In spot markets, the trader and farmer transact only at harvest time. This contract can be viewed as the benchmark model, with no interlinkages. In interlinked transactions (ILT), a trader provides credit before harvest and then purchases output from the farmer at harvest, unless the farmer chooses to default.

Traders are homogeneous. Farmer i in market m is endowed with an amount of land li. This varies across farmers. If the farmer does not receive credit, the land produces quantity qim, which we will write as qi to reduce notation. If the farmer receives credit, the land is assumed to produce qi(1+r). We can also interpret qi as quality-adjusted quantity. In this case, which is particularly relevant for our setting, credit allow farmers to improve quality of their output, through post-harvesting processing. We assume farmers and traders are risk-neutral and maximize their (expected) profits. We now discuss the payoff structure under the two tyes of contracts

Spot Markets

Spot market prices in market m, pS

m, are equal to the wholesale price over a constant markdown,

pS_m = wm

µ , µ≥1 (3.3)

The mark down is a reduced form capturing both trading costs proportional to value and any market power the trader may have. The utility of farmer i farmer transacting on the spot market is:

uS_im = pSqi = wm

µ qi (3.4)

On the spot market, we assume that each trader has an equal probability to secure cocoa from a given farmer in market m equal to 1/Jm. Therefore, the expected utility for trader j

transacting with farmer i in market m is: vS_jim= 1 Jm (wm−pSm)qi = 1 Jm µ−1 µ wmqi (3.5) Interlinked Transactions

In interlinked transactions, a trader provides credit before harvest, and subsequently purchases output at a pre-determined price. We assume that traders and farmers are randomly matched and that only one trader can offer credit to a given farmer.11 In order to provide credit, the trader incurs a fixed cost f . This can be interpreted as the minimum amount of screening and monitoring that trader needs to undertake, independent of the amount of credit outlay (for a review of these issues, see Banerjee, 2002). We assume that if the two parties enter an interlinked transaction, the trader provides a fixed amount of credit per each bag denoted by c. As we mentioned above, this raises the farmer output by a factor(1+r).

In addition to the impact of credit on production levels, we assume that the farmer marginal utility from consuming (part of the) loan c before harvest is cF = λ·c, with λ ≥ 1. This is a reduced form for the increased utility of the farmer from extra pre-

harvest consumption, which is assumed to be weakly larger than the trader’s utility cost of disbursing the loan. One way to think about this is that the farmer experiences a higher marginal utility per unit of income relative to the trader in the pre-harvest season.

After receiving credit, the farmer decides whether to stick to the terms of the contract or to undertake a strategic default. If the farmer respects the contract, he receives a farmer- specific contract price pC_im. We describe how this price is determined in equilibrium in section 3.4.2. When he does not default, the utility of farmer i under ILT is

uCN_im = (pC_im(1+r) +cF)qi (3.6) 11_{This is consistent with anecdotal evidence in our setting that farmers mostly receive advances from one}

trader. However, we note that the static nature of the game obviously neglects the relational component of credit provision, which is potentially very relevant for our setting.

and the utility for trader j in an ILT contract with farmer i is

vCN_jim = ((wm−pCim)(1+r) −c)qi− f (3.7) Note here that the trader’s utility no longer includes the term 1/Jm, since in the interlinked transaction contract, he is now certain to get the farmer’s output (if the contract is enforced).

The benefit of strategic default for the farmer depends on the underlying contracting institutions in market m. Specifically, we assume that, if the farmer defaults, he loses a share

γimof his output. He then sells(1−γim)qi(1+r)on the spot market. The parameter γimis a reduced form measure of contracting institutions capturing market characteristics that could shape the cost of default, including trader monitoring costs, proximity to law enforcement, and social norms specific to farmer i. Thus, another benefit of the credit provision for the trader, in addition to the higher quantity to purchase, is that the credit contract “locks in" the farmer’s supply by imposing a penalty γ to the farmer if he side-sells to other traders.12

In the strategic default scenario, the utility of farmer i in the ILT contract is uCD_im =pS_m(1−γim)(1+r) +cF  qi =  wm µ (1−γim)(1+r) +cF  qi, (3.8) while the utility of trader j is

vCD_jim = −c·qi− f (3.9)