1. Goals and Plans in Farmers’ Crop-Growing Decisions Howard C. Kunreuther kunreuther@wharton.upenn.edu Operations and Information Management (OPIM) Dept. Risk Management and Decision Processes Center The Wharton School, University of Pennsylvania http://opim.wharton.upenn.edu/risk kunreuther@wharton.upenn.edu http://opim.wharton.upenn.edu/risk Conference in Honor of Gavin Wright Stanford University September 26, 2008

2. Outline of Talk 1.East Pakistan and 19 th Century South 2.Safety-First and Gambling Models of Farmers’ Behavior 3.Goals and Plans in Decision Making 4.Policy Implications 5.Summary and Future Research

3. 1. East Pakistan and 19 th Century South Question: How much acreage to plant with cash crop and food crop? –East Pakistan: jute (cash crop) / rice (food crop) –19 th Century South: cotton (cash crop) / corn (food crop) Answer: Large and small farmers allocate most of their land to CASH crop Middle income farmers plant mostly FOOD crop Question: WHY? 3

4. 1. East Pakistan and 19 th Century South Cash crop is risky choice for subsidence farmers –Food crop: need to consider yield variance –Cash crop: need to consider yield and price variance Cash crop has slightly higher expected return than food crop Comparisons of standard deviations of crop returns –Ratio of jute/rice: 2 to 3 –Ratio of cotton/corn: 4 to 5 4

5. 1. East Pakistan and 19 th Century South Why do large and small farmers follow a similar pattern that differs from middle income farmers? –Large: Get higher return from cash crop. Not concerned about high variance in returns –Small: Only chance of getting out of debt or feeding their family was if they reaped a high yield from cash crop –Middle: Were able to ensure they had enough to eat by growing food crop (Safety-first strategy) 5

6. 2. Safety-First Model of Farmers’ Behavior x and y are random variables representing returns per acre for cash crop and food crop respectively m : fraction of acreage devoted to cash crop Maximize E[mx + (1-m)y] (1) subject to constraint Probability { [mx + (1-m)y] } ≤ Z* ≤ α* (2) where Z* = critical yield per acre producing minimum tolerable consumption α* = risk level farmer is willing to tolerate 6

7. 2. Safety-First Model of Farmers’ Behavior Subsidence Farmers in 19 th Century South (1860) Subsistence farmers in 1860 had sufficient acreage so they had a low value of α* and devoted most of their land to corn so as to meet constraint (Safety-first behavior) 7

8. 2. Gambling Model of Farmers’ Behavior Subsistence Farmers in 19 th Century South (1880) Subsistence farmers in1880s had decrease in farm size so there was no allocation of acreage that satisfied constraint given by (2) They now want to maximize chance of achieving Z* Objective function becomes: Minimize α' = Probability { [mx + (1-m)y] } < Z* Farmer is forced to gamble on cash crop to have any chance of achieving Z* 8

9. 3. Goals and Plans in Decision Making Examined anomalies in insurance purchasing behavior 30 years later –Difficult to explain using utility theory or prospect theory –Dave Krantz and I proposed constructed model of choice that highlights importance of goals and plans that could explain insurance anomalies This model can incorporate farmers’ multiple goals in crop growing decisions and explain behavior where standard models cannot 9

10. Comparison between utility theory and goals/plans theory Utility theory weights utilities (could be multi-attributes) by probabilities n U(strategy i) = ∑ p j u ij j=1 Plan/goal formulation evaluates plans in terms of values of the goals and weights associated with each goals n U(plan i) = ∑ w ij v j j=1

11. Subjective multi-attribute utility theory (SEMAUT) 11

12. Plan/Goal Structure for Decision Making 12

13. Advantage of goals/plans model over E(U) model Using multi-attribute utility to integrate goals is a complex process Goal/plan framework drops artificial compounds and elicits simple goals directly Highlights importance of goals by assigning decision weights to each goal 13

14. Plan /Goal Framework for Farmers’ Crop-Growing Decisions Two Plans Plan 1: ¾ acreage with cotton and ¼ with corn Plan 2: ¾ acreage with corn and ¼ with cotton Return from crops Corn and Corn: certain yield Cotton: P(Price per bushel)(high.2; average.5; low.3) Goals 1. Obtaining a high financial return 2. Having enough food for the family 3. Reducing his debt 14

15. Assigning Weights to Goals in Illustrative Example Weights assigned to each goal are determined by probabilities associated with high, average or low price of cotton per bushel and its ability to satisfy the particular goal in question Example: Goal 1: Achieving high financial return in 1860 Plan 1: w 11 =.7 (Price of cotton is high or medium) Plan 2: w 21 =.2 (Price of cotton is high) 15

16. Plan/goal matrix for small farmer in 1860 16

17. Decision by farmers to choose Plan 2 in 1860 Plan 2 met Goals 2 and 3 with certainty but did not do as well with respect to Goal 1 Associated values of these goals (v 2 and v 3 ) assumed to be high relative to goal 1 ( v 1 ) 17

18. Plan/goal matrix for small farmer in 1880 18

19. Decision by farmers to choose Plan 1 in 1880 Farmer has decreased acreage for planting cotton and corn Plan 1 meets Goals 1, 2 and 3 with probability.7 (High or medium price of cotton) Plan 2 meets Goals 1, 2 and 3 with probability.2 (High price of cotton) 19

20. Policy Implications Incentivizing Farmers to Adopt New Technologies Green Revolution -- Norman Borlaug High Yield Rice/Corn were not adopted by farmers Principal reasons: Concerned with meeting subsistence goal Uncertainty about yields from new crop Desire to maintain status quo 20

21. Policy Implications Incentivizing Farmers to Adopt New Technologies Policy Implications Guarantee farmers same return as last year on high yield crops (Mexico) Low interest loans to help poor farmers (Grameen bank in Bangladesh) Clifton R. Wharton, Jr. 21

22. Conclusions and Future Research Gavin helped me appreciate importance of goals in decision-making under uncertainty. Understanding central role of goals and plans suggests policies that may not be obvious using standard economic theory. Open Q: What strategies have worked and not worked in the past? This is a project for economic historians like Gavin Wright to undertake. 22