a.     If Betty bought one October 50 call option for $3 per share quoted price, then find her profit and loss at expiration. Your answer should be expressed in terms of per share quoted price.

To find Betty's profit or loss from buying a call option, we need to understand a few key concepts:

1. **Call Option:** A call option gives the holder the right, but not the obligation, to buy a stock at a specific price (called the strike price) on or before the option's expiration date.
  
2. **Quoted Price of the Option:** This is the price per share that Betty paid for the option. Since each option typically represents 100 shares, the total cost is $ \text{Quoted Price} \times 100 $. But for simplicity, we'll express the profit or loss per share.

3. **Strike Price:** This is the price at which Betty can purchase the stock if she exercises the option.

4. **Expiration Date:** This is the date on which the option expires.

### Given:
- Betty bought one October 50 call option.
- The quoted price of the option was $3 per share.

### Profit or Loss at Expiration:
Let's denote the stock price at expiration as $ S $.

- **If $ S \leq 50 $:** The option will expire worthless because the stock price is less than or equal to the strike price of $50. Betty wouldn't exercise the option because she can buy the stock cheaper in the open market.
  - **Loss:** Betty loses the premium she paid for the option.
  - **Loss per share:** $ \text{Loss} = -3 $ (since she paid $3 per share for the option).

- **If $ S > 50 $:** The option is "in the money," meaning it has intrinsic value. Betty would exercise the option to buy the stock at $50 and could potentially sell it at the market price $ S $.
  - **Profit per share:** $ \text{Profit} = (S - 50) - 3 = S - 53 $

### Summary of Profit/Loss per Share:

- **For $ S \leq 50 $:** $ \text{Loss} = -3 $ per share.
- **For $ S > 50 $:** $ \text{Profit} = S - 53 $ per share.

Thus, Betty's profit or loss depends on the stock price at expiration:

- If the stock price at expiration is **less than or equal to $50**, she loses $3 per share.
- If the stock price at expiration is **greater than $50**, her profit per share is $ S - 53 $.

Would you like any further details or explanations?

Here are 5 related questions to explore:
1. What is the break-even stock price for Betty at expiration?
2. How would the profit/loss change if Betty had bought two call options instead of one?
3. What would happen if the stock price at expiration was exactly $53?
4. How does the profit/loss differ if Betty had bought a put option instead of a call option?
5. How does the time until expiration affect the value of a call option?

**Tip:** When trading options, understanding the break-even point and potential scenarios at expiration is crucial for managing risk and maximizing profit.

Learn how to calculate profit and loss on a call option with a strike price of $50 and a quoted price of $3 per share. Understand the scenarios where Betty makes a profit or incurs a loss based on the stock price at expiration. Essential knowledge for investors and traders.

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