Consider the decision-making of farmers in a poor rainfed agricultural area of India. Suppose that there are two possible outcomes at the end of each growing season depending on the amount of rainfall: the good outcome generates revenue of $100, the bad outcome generates $50. Due to historical reasons associated with the British colonizers’ treatment of wealthy landowners, fixed rent contracts are $30 in region A and $20 in region B. Suppose that all land sizes are identical and the only input to production is labor, and the cost of labor (inclusive of opportunity costs) is fixed at $30.
(a) Suppose that there is a 70% chance of good rainfall. What is the expected income under fixed rent contracts for a tenant in region A? in region B? What about expected profits?
(b) Now suppose that there has been a dramatic increase in factory jobs in nearby towns leading to an increase in the (opportunity) cost of labor on the farm to $60. Will tenants in region A still accept the fixed rent contracts? in region B? What is the maximum fixed rent rate that tenants will accept in each region?
(c) Going back to the original assumptions, what sharecropping rule (i.e., what value of α) will make landlords indifferent between fixed rent and sharecropping contracts? Use the resulting α* to show that tenants will prefer fixed rent instead of sharecropping in the case of good rainfall but sharecropping in the case of bad rainfall.
(d) Going back to the original assumptions, now suppose that irrigation canals are widely available and reduce farmers’ dependence on rainfall. Conceptually, this lowers the chance of a bad outcome by 10%. How would your answers to (a) and (b) change? Discuss the intuition for this result.
(e) Suppose that landlords adopt a small dose of altruism and decide to offer limited liability contracts in which they will return 50% of the rental payment at the end of a bad rainfall season. What is the new expected income under fixed rent contracts for a tenant in region A? in region B? What are the implications for contract choices?