# Computing the Optimal Price for an API Call in Tokens

Given Parameters:

* Token's Current Market Price = $0.01/token
* Total tokens = 100,000,000
* Base Gas Fee = $0.07 (7 cents)
* Gas Fee Growth is Linear: It will be $0.07\*n where n is the number of images.
* Current demand at $0.01/token = 10 users/day
* Demand follows an inverse relation with price change.
* Minimum token price for an API call = 1 token
* Maximum token price for an API call = 1000 tokens

**Let's Compute the Optimal Price:**

```
import numpy as np

TOKEN_PRICE = 0.01
BASE_GAS_FEE = 0.07

def demand(price_in_tokens):
    """
    Model the demand based on token price using the inverse relationship.
    """
    price_change_percent = (price_in_tokens * TOKEN_PRICE - TOKEN_PRICE) / TOKEN_PRICE * 100
    change_in_demand = price_change_percent / 100 * 10  # 10 users is the initial demand
    return 10 - change_in_demand

def compute_cost_in_tokens(n):
    """
    Compute the cost efficiency for a given batch size in tokens.
    """
    total_fee = BASE_GAS_FEE * n
    return total_fee / TOKEN_PRICE / n

def compute_profit(price_in_tokens):
    """
    Compute the net profit for a given token price.
    """
    costs = [compute_cost_in_tokens(n) for n in range(1, 101)]
    avg_cost = np.mean(costs)
    revenue = price_in_tokens * demand(price_in_tokens)
    return revenue - avg_cost

def find_optimal_token_price(min_price, max_price):
    """
    Evaluate different token prices to find the most profitable one.
    """
    profits = [compute_profit(price) for price in np.linspace(min_price, max_price, 1000)]
    optimal_price = np.argmax(profits) * (max_price - min_price) / 1000 + min_price
    return optimal_price

# Sample usage:
min_token_price = 1  # minimum price in tokens
max_token_price = 1000   # maximum price in tokens

optimal_token_price = find_optimal_token_price(min_token_price, max_token_price)
print(f"Optimal price for the API call in tokens: {optimal_token_price:.2f}")
```

Run the above Python code to get the most optimal token price for the API call.