Questions & explanations
1. Three farmers can form a cooperative to buy a tractor. Alone, each earns $100. Together, any two earn $250, and all three earn $400. What is the Shapley value for each farmer?
First, list all possible orders of joining. There are 6 orders. For each farmer, calculate their marginal contribution in each order. For farmer A: In order A,B,C: A joins first, contributes $100 (since alone $100), then B joins, total $250, so B contributes $150, then C joins, total $400, so C contributes $150. A's marginal is $100. In order A,C,B: similar, A contributes $100. In order B,A,C: B first $100, then A joins, total $250, so A contributes $150. In order B,C,A: B first $100, then C joins, total $250? Actually B and C alone: $100+$100=$200, but together $250, so C contributes $150? Wait, need correct: alone each $100, any two $250, so marginal of second player is $150. Then A joins third, total $400, so A contributes $150. In order C,A,B: C first $100, then A joins, total $250, so A contributes $150. In order C,B,A: C first $100, then B joins, total $250, so B contributes $150, then A joins, total $400, so A contributes $150. So A's marginal contributions: in 2 orders $100, in 4 orders $150. Average = (2*100 + 4*150)/6 = (200+600)/6 = 800/6 ≈ 133.33. Similarly for B and C. S
2. Two farmers and a transporter form a cooperative. Alone, each farmer earns $50, the transporter earns $0. Together, a farmer and transporter earn $80, both farmers together earn $100, and all three together earn $150. What is the Shapley value for the transporter?
List orders (3! = 6). For transporter T: In order T, F1, F2: T first alone $0, then F1 joins, total $80, so F1 contributes $80, then F2 joins, total $150, so F2 contributes $70. T's marginal = $0. In order T, F2, F1: similar, T's marginal $0. In order F1, T, F2: F1 first $50, then T joins, total $80, so T contributes $30, then F2 joins, total $150, so F2 contributes $70. T's marginal = $30. In order F1, F2, T: F1 first $50, then F2 joins, total $100, so F2 contributes $50, then T joins, total $150, so T contributes $50. T's marginal = $50. In order F2, T, F1: F2 first $50, then T joins, total $80, so T contributes $30, then F1 joins, total $150, so F1 contributes $70. T's marginal = $30. In order F2, F1, T: F2 first $50, then F1 joins, total $100, so F1 contributes $50, then T joins, total $150, so T contributes $50. T's marginal = $50. Average = (0+0+30+50+30+50)/6 = 160/6 ≈ 26.67. So transporter's Shapley value is about $26.67.
3. In a cooperative of four farmers, the Shapley value for each farmer is $25. If two farmers together contribute $60 to the total profit of $100, what can you infer about the other two farmers' contributions?
The total Shapley values sum to total profit, so $25 each * 4 = $100. If two farmers together contribute $60, their combined Shapley values are $50 (since each $25), but their actual marginal contributions might differ. The Shapley value is an average, so it's possible that in some coalitions they contribute more, in others less. The fact that their combined Shapley value is $50 while they contribute $60 together suggests that the other two farmers contribute less in some coalitions. However, the Shapley value is fair and considers all orders. This indicates that the two farmers are not the only high contributors; the other two also contribute significantly in some orders. The numbers show that the cooperative is balanced.
4. In a negotiation between a farmer and a buyer, each can choose to be 'tough' or 'cooperative'. If both are cooperative, they split the profit equally. If one is tough and the other cooperative, the tough one gets most of the profit. If both are tough, they get nothing. What is the Nash equilibrium?
A Nash equilibrium is a situation where no player can get a better outcome by changing their own choice alone. In this game, if both players are cooperative, each gets half the profit. But if one player switches to tough, they get most of the profit, so cooperative is not stable. If both are tough, they get nothing, and switching to cooperative alone would give the other player most of the profit, so tough is also not stable. Actually, the Nash equilibrium is when one player is tough and the other is cooperative, because neither can improve by changing alone. However, there are two such equilibria: (tough, cooperative) and (cooperative, tough). So the game has two Nash equilibria.
5. Two farmers can either cooperate to share a tractor or work alone. If both cooperate, each gets $100 profit. If one cooperates and the other works alone, the cooperator gets $20 and the loner gets $80. If both work alone, each gets $50. What are the Nash equilibria?
First, list the payoffs: (Cooperate, Cooperate): (100,100); (Cooperate, Alone): (20,80); (Alone, Cooperate): (80,20); (Alone, Alone): (50,50). A Nash equilibrium is where no player can improve by changing alone. Check (Cooperate, Cooperate): if Farmer 1 switches to Alone, they get 80 instead of 100, so worse. Similarly Farmer 2 gets 80 instead of 100, so worse. So (Cooperate, Cooperate) is a Nash equilibrium. Check (Alone, Alone): if Farmer 1 switches to Cooperate, they get 20 instead of 50, worse. So (Alone, Alone) is also a Nash equilibrium. The other two are not equilibria because a player would switch. So there are two Nash equilibria: both cooperate or both work alone.
6. Apply the concept of 'research spillover' to explain why one country's agricultural research can benefit another country.
Research spillover happens when knowledge from one country's agricultural research helps farmers in another country. For example, a rice variety developed in the Philippines to resist a disease can be grown in India if the climate is similar. The second country does not pay for the research but still gets the benefit. This is because scientific findings are often published and shared freely. International research centers like those in the CGIAR system spread improved seeds and methods worldwide. Spillover means that investing in research can have benefits beyond a country's borders. It encourages cooperation and reduces the need for each country to do all research alone.
7. Design a contract for a coffee cooperative that wants to finance its members' harvest. What key terms would you include?
The contract should state that the cooperative provides cash or inputs to each member before harvest. In return, the member agrees to deliver all their coffee cherries to the cooperative at a fixed minimum price. The contract should specify the quality standards, like bean size and moisture content. It should also include a repayment schedule, where the cooperative deducts the loan from the payment after delivery. To align incentives, the contract could offer a bonus if the coffee meets premium quality. It should also have a penalty if the member sells to another buyer. Finally, it should describe how disputes are resolved, such as through a local committee.
8. How can IPR in agriculture affect global food security?
IPR can affect food security by influencing who has access to improved seeds. If IPR makes seeds too expensive, poor farmers in developing countries may not afford high-yielding or stress-tolerant varieties, reducing their harvests. On the other hand, IPR can drive research into crops that benefit food security, like drought-tolerant maize. But if that research is patented, the seeds may be priced beyond reach. International agreements like the International Treaty on Plant Genetic Resources for Food and Agriculture try to ensure that important genetic resources remain accessible for breeding. Balancing IPR with access is crucial for global food security.
9. Compare ECR with a traditional supply chain where the retailer and supplier do not share information.
In a traditional supply chain, a retailer might order a large amount of a product based on guesswork, leading to too much stock or shortages. The supplier then produces based on those orders, not on actual demand. This often results in waste from unsold goods or lost sales when items are out of stock. With ECR, the retailer and supplier share real-time sales data and plan together. This allows them to match supply closely to demand. For example, a soft drink company can see exactly which flavors sell best at each store and deliver accordingly. ECR reduces inventory, waste, and costs, while traditional methods tend to have more inefficiency.
10. Give an example of how China's agricultural policies affect global markets.
China's large stockpiles of grains, built through price supports, can depress world prices when released. For example, in 2015-2016, China sold off old corn reserves at low prices, which reduced global corn prices. Also, China's import quotas for cotton limit its purchases, affecting global cotton demand. When China changes its policies, like reducing the minimum purchase price for rice, it can signal lower future imports, impacting exporting countries. Additionally, China's soybean imports (mostly from Brazil and the US) are huge, so any trade dispute or policy shift (like tariffs on US soybeans) can cause price volatility worldwide.
11. Compare the environmental requirements in the 2013 and 2021 CAP reforms.
The 2013 reform introduced mandatory greening practices like crop diversification and ecological focus areas, but these were often criticized as weak. The 2021 reform strengthens environmental ambition by introducing a new 'eco-scheme' that pays farmers extra for going beyond basic requirements. Eco-schemes are voluntary, but they offer higher payments for practices like organic farming, carbon sequestration, or precision agriculture. Unlike the 2013 greening, which was a condition for basic payments, eco-schemes are an additional incentive. The 2021 reform also links more payments to compliance with stricter environmental standards.
12. What is the main goal of Efficient Consumer Response (ECR) in food retailing?
Efficient Consumer Response (ECR) is a strategy where food retailers and suppliers work together to give consumers the best value. The main goal is to reduce costs and waste in the supply chain while making sure the right products are available when customers want them. This is done by sharing information and coordinating activities like ordering, delivery, and stocking. For example, a grocery store might share sales data with a dairy company so the company knows exactly how much milk to deliver each day. This cuts down on extra inventory and spoilage. ECR helps both the retailer and the supplier save money and keep customers happy.