"Consider a monopolist informal moneylender and competitive formal creditors who lend to farmers. Farmers use the loan in cultivation. They, without liquidity in spring, borrow to buy seeds ($200) which are indispensable for farming. Extra $50 credit to maintain irrigation system is helpful in cultivation but not "must". Well-maintained irrigation system increases the prospect of harvest. That is, we consider good harvest ($600) and bad harvest ($400), and the probability of good harvest is 0.8 (80%) with maintenance and 0.4 (40%) without maintenance. There is no outside option for farmers.
Both monopolist informal moneylender and competitive formal creditors determine interest rates so that there is no default in equilibrium and repayments fully cover funding cost. We assume that funding costs are 10% for both informal moneylender and formal creditors. There are no strategic defaults: farmers default on debts if and only if they do not have sufficient resources (money) in the harvest season. The informal moneylender has advantage in information: only informal moneylender can monitor maintenance of irrigation system and thus may provide extra $50 credit. Competitive formal creditors concern about rerouting of the extra $50 to non-production (consumption) purpose and thus do not provide $250 loan. That is, the informal moneylender can charge different interest rates for $250 loan (i250) and $200 loan (i200). On the other hand, formal creditors provide only $200 loan with interest rate of iF.
(a) When there is only monopolist informal moneylender, what are the interest rates for $250 loan (i250) and $200 loan (i200)?
(b) When there are only competitive formal creditors, what is the interest rate (iF)?
(c) When there are competitive formal creditors and a monopolist informal moneylender, what are the interest rates for $250 loan (i250) and $200 loan (i200) by the moneylender?