Please imagine you are a smallholder farmer in Zambia with three sources of income: livestock, agriculture, and additional income-generating activities (paid labor, wood cutting, etc.). Earnings from all these sources amount to an average annual income of EUR 8,000.
Income from livestock rearing and miscellaneous activities account for 30% (EUR 2,400) and 10% (EUR 800) of your average annual income, respectively. Payouts from these activities, EUR 3,200 in total, are certain and will thus be disbursed to you at the end of the game in any event.
However, the remaining 60% (EUR 4,800 on average), your harvest-related income, heavily depends on weather conditions, rainfall in particular. Rainfall in a given year can only be either good for agriculture or bad, with each of these two states of the world occurring with the same probability (50%).If rainfall is insufficient, i.e. the bad state, your harvest-related payoff only amounts to 30% (EUR 2,400) of your average annual income. On the other hand, in the good state, with sufficient rainfall, your harvest income increases to 90% (EUR 7,200) of your average annual income.
Therefore, in a good year, your annual income reaches EUR 10,400. In a bad year, you only earn EUR 5,600. In this context, you are offered to insure against the bad state of the world, i.e. low rainfall.
For the price of 15% (EUR 1,200) of your average annual income, you can purchase an insurance policy against the bad state. This insurance pays out 30% (EUR 2,400) of your average annual income, if there is too little rainfall.Therefore, in a good year with insurance, your annual income amounts to EUR 9,200 only. In a bad year, if you opted to purchase insurance, your annual income is EUR 6,800.
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