Suppose that farmers in Small Village may use their land to cultivate either traditional green beans, for which transfer costs to the external market are moderate, or supermarket carrots, for which...

1. Suppose that farmers in Small Village may use their land to cultivate either traditional green beans, for which transfer costs to the external market are moderate, or supermarket carrots, for which transfer costs to the external market are initially very high. The external market price for a kilogram of supermarket carrots is significantly higher than the external market price for a kilogram of traditional green beans. There is no local demand for supermarket carrots.

1. Draw two well-labeled diagrams depicting the Small Village markets for green beans and supermarket carrots, with the market for green beans in autarky equilibrium and local farmers producing no supermarket carrots.

1. Suppose that joint investments by supermarkets and NGOs reduce the transfer costs associated with exporting supermarket carrots to the external market (while leaving transfer costs on exports of traditional green beans unchanged). Depict in your diagram a reduction in transfer costs large enough to induce farmers in Small Village to begin producing and exporting supermarket carrots. What happens to the effective local price for supermarket carrots?

1. What might happen to the local supply schedule for traditional beans in response to the changed conditions in the market for supermarket carrots? As a result of this change, what is likely change in the price of green beans in the local market?

1. Consider two potential buyers of health insurance. Each maximizes expected utility, and each experiences utility in any state of the world that depends on his consumption expenditure (in pesos) C and his level of health H. Each knows that he will be hit by a health shock with probability 0.5. If not hit by a health shock, he will enjoy C = 100 and H = 100. When hit by a health shock, his health will fall to zero if he does not obtain care, but his health can be maintained at 100 if he purchases health care for 100 pesos (causing his consumption expenditure to fall to zero). Potential Buyer A’s utility function is:

and Potential Buyer B’s utility function is:

1. Which potential buyer is risk neutral? Which is risk averse? How can you tell?

1. Show that in the absence of insurance, both potential buyers would choose to obtain health care if hit by the health shock (rather than suffer the health loss associated with the shock).

1. What is the highest premium Potential Buyer A would just be willing to pay for the health insurance contract? What is the highest premium Potential Buyer B would pay? Why is one willing to pay more than the other?

Game Theory

1. Consider a small rural area inhabited by just two small farmers, Farmer A and Farmer B. The farmers must each choose whether or not to make investments that would allow them to produce a higher-value crop. If either farmer continues cultivating traditional crops, he earns a profit of 0. To switch to cultivating a higher-value crop, he must incur an investment cost of 10. Having made the investment, he will obtain revenue of 20 if an urban-based food processing company decides to set up a trucking route to collect produce in his area, but he earns no revenue if the food processing company does not do this. Both farmers know that the food processor will set up local crop collection if and only if both farmers invest in producing the high-value crop. If only one farmer invests or if neither farmer invests, neither farmer will have an opportunity to sell his higher-value product to the processor. If both farmers invest, the processor will certainly collect their produce and pay them each 20.

1. Fill in the following table of payoffs to describe the game these two farmers are faced with, assuming their payoffs are equal to any revenue they receive from the food processor less any investment costs they undertake. Solve for any possible equilibria.

1. Does Farmer A have a dominant strategy? Explain.

1. What does the structure of this game imply about the kinds of activities an NGO might experiment with to encourage a shift to high-value crop production in this area?