Let's go step by step through the problem: --- ### (a) What can Farmer John do to ensure his profitability? Is this a long or a short hedge? **Step 1: Identify the risk** - Farmer John is worried that wheat prices will fall by harvest time in September. - If the price falls, he will get less money for his crop. **Step 2: Hedging strategy** - To protect against falling prices, Farmer John can **sell September wheat futures contracts** now. - This locks in a selling price for his wheat in September. **Step 3: Type of hedge** - Since Farmer John is a seller of wheat and is hedging against a price decrease, this is a **short hedge** (selling futures contracts). #### **Explanation:** A short hedge is used when you have (or expect to have) the commodity and want to protect against falling prices by selling futures contracts. --- ### (b) Compute Farmer John’s net wealth change due to the drop in wheat prices, assuming he hedged his anticipated production and his final yield was 60,000 bushels. #### **Step 1: Quantity to hedge** - Anticipated production = 60,000 bushels - Each futures contract = 5,000 bushels - Number of contracts to hedge = 60,000 / 5,000 = **12 contracts** #### **Step 2: Initial futures price (August 10)** - September wheat futures price = **$2.52 per bushel** #### **Step 3: Final cash price at harvest (September)** - Spot (cash) price = **$1.70 per bushel** #### **Step 4: Futures market action** - At harvest, close out the futures position by buying back the contracts at the new futures price. - Let's assume the futures price also drops to $1.70 per bushel (in practice, it may be slightly different, but often converges to spot at expiration). #### **Step 5: Calculate gains/losses** **A. Cash market loss:** - Farmer John sells his wheat at $1.70 per bushel. - Loss per bushel compared to the earlier price ($2.25): $2.25 - $1.70 = **$0.55 loss per bushel** (compared to August 10 spot, but he’s concerned with the drop from $2.25 to $1.70). **B. Futures market gain:** - He sold futures at $2.52; buys back at $1.70. - Gain per bushel = $2.52 - $1.70 = **$0.82 gain per bushel** - Total gain = $0.82 x 60,000 = **$49,200 gain from futures** #### **Step 6: Calculate total cash received (cash market + futures gain)** - Cash received from selling wheat: $1.70 x 60,000 = **$102,000** - Add futures gain: **$49,200** - **Total net cash = $102,000 + $49,200 = $151,200** #### **Step 7: Compare to initial break-even** - At $2.25 per bushel: $2.25 x 60,000 = **$135,000** - By hedging, Farmer John actually ends up with more than his break-even amount because of the favorable movement in the futures hedge. --- ## **Final Answers:** ### a) **Farmer John should sell September wheat futures contracts to lock in his selling price and protect against a price drop. This is called a short hedge.** ### b) **If the cash price drops to $1.70 per bushel at harvest and Farmer John hedged his entire anticipated production of 60,000 bushels, his net wealth increases by $16,200 compared to his break-even point (he receives $151,200 total, compared to the $135,000 from selling at $2.25 per bushel).** --- ## **Summary Explanation:** - By using a short hedge (selling futures), Farmer John effectively locks in the higher futures price, offsetting losses from a drop in the cash price. The gain from the futures contract compensates for the lower cash price at harvest, ensuring his profitability.