Question Three (15 Marks) There two hunters living in a village that has a park where they can hunt cutting grass to sell in the local market. The hunting ground is extensive it takes much skills to hunt down a single cutting glass. If they both sell 10 cutting grass each, cutting grass sells for 10,000 frs a piece in the market. When there are that many as 30 cutting glass in the market, the price per cutting grass falls to 8,000 frs a piece. When there are 40 cutting grass in the market, each sells for sooo frs. Given that it the effort (Skill) taken by each farmer to catch a cutting grass is 1,000 frs and 500 frs for any additional 10 caught. Required: i. Calculate the pay-offs of this two farmers ii. Is there a Nash equilibrium? iii. What will be the best outcome if the hunters had a hunters Union iv. What are the Advantages of the hunters union to the hunters v. Calculate and comment on the difference profits to the hunters, before and after collusion (3 Marks) (3 Marks) ( 6 Marks) ( 2 Marks) ( 1 Marks)

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Let's address each part of the question systematically.

### **i. Calculate the pay-offs of these two farmers**

**Given:**
- Both hunters sell **10 cutting grass each**, resulting in a total supply ($$ Q $$) of **20 cutting grass** in the market.
- **Price per cutting grass ($$ P $$)** when $$ Q = 20 $$ is **10,000 frs**.
- **Cost Structure:**
  - **1,000 frs** per cutting grass for the first **10**.
  - **500 frs** for any additional **10** caught.

**Calculations for Each Hunter:**

1. **Revenue:**
   $$
   \text{Revenue} = \text{Quantity Sold} \times \text{Price} = 10 \times 10,000 = 100,000 \text{ frs}
   $$

2. **Costs:**
   - Since each hunter catches **10 cutting grass**, the cost is:
     $$
     \text{Cost} = 10 \times 1,000 = 10,000 \text{ frs}
     $$

3. **Profit:**
   $$
   \text{Profit} = \text{Revenue} - \text{Cost} = 100,000 - 10,000 = 90,000 \text{ frs}
   $$

**Pay-off for Each Hunter:** **90,000 frs**

---

### **ii. Is there a Nash equilibrium?**

**Yes**, there is a Nash equilibrium in this scenario.

**Explanation:**
- **Nash Equilibrium** occurs when neither hunter can improve their payoff by unilaterally changing their strategy, given the other hunter's strategy.
- If both hunters choose to sell **10 cutting grass** each:
  - Any deviation (e.g., increasing or decreasing the number they sell) would not result in a higher profit for the deviating hunter.
  - Therefore, **selling 10 each** is the stable strategy where neither has an incentive to deviate.

---

### **iii. What will be the best outcome if the hunters had a Hunters Union**

**Best Outcome with a Hunters Union:**
- The hunters can **collaborate** to maximize their combined profits.
- By coordinating their total supply, they can manipulate the market price to a higher level.
- For instance, they might agree to limit the total supply to **20 cutting grass** to maintain the higher price of **10,000 frs** per piece, ensuring each hunter sells **10** and earns **90,000 frs**.

---

### **iv. What are the Advantages of the Hunters Union to the hunters**

**Advantages:**
1. **Increased Bargaining Power:**
   - Collective decision-making can lead to better pricing and terms in the market.
   
2. **Profit Maximization:**
   - By coordinating supply, they can prevent price drops caused by over-supply, ensuring higher profits.
   
3. **Cost Sharing:**
   - Potential to share costs related to hunting and market logistics, reducing individual expenses.
   
4. **Market Stability:**
   - A united front can stabilize prices and prevent aggressive competition that might harm profits.

---

### **v. Calculate and comment on the difference in profits to the hunters, before and after collusion**

**Before Collusion (Nash Equilibrium):**
- Each hunter sells **10 cutting grass**.
- **Profit per Hunter:** 90,000 frs.
- **Total Profit:** 180,000 frs.

**After Collusion (Union Agreement):**
- Each hunter still sells **10 cutting grass** to maintain the higher price.
- **Profit per Hunter:** 90,000 frs.
- **Total Profit:** 180,000 frs.

**Difference in Profits:** **0 frs**

**Comment:**
- In this specific scenario, collusion does not change the individual profits because the Nash equilibrium already has both hunters selling the optimal number (10) to maintain the higher price.
- However, collusion provides additional benefits such as ensuring stability and preventing any deviation that might disrupt the equilibrium.
**i. Each hunter earns 90,000 frs.** **ii. Yes, there is a Nash equilibrium where both hunters sell 10 cutting grass each.** **iii. If the hunters form a union, they can maintain the higher price of 10,000 frs per cutting grass, ensuring each earns 90,000 frs.** **iv. Advantages include increased bargaining power, profit maximization, cost sharing, and market stability.** **v. Before collusion, each hunter earns 90,000 frs. After collusion, the total profit remains the same at 180,000 frs, but the union ensures stability and potential cost-sharing benefits.

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