To determine the price you should charge for your product, we need to follow these steps:

1. Review the demand function:

The demand function is given by:

$P = 20 - 2Q$

Where:

• $P$ is the price.
• $Q$ is the quantity demanded.

2. Review the cost function:

The total cost (TC) function is:

$TC = 100 - 2Q^3 - 100Q + 34Q^2$

From the information, I assume that in question 2a, you have already found the profit-maximizing level of output, denoted by $Q^*$. Once we know the optimal quantity $Q^*$, we can plug this value into the demand function to find the price.

3. Use the optimal quantity to determine the price:

Once we have $Q^*$ (which is the profit-maximizing quantity), substitute $Q^*$ into the demand equation $P = 20 - 2Q^*$ to find the price $P^*$.

Would you like me to proceed with the calculations if you provide the profit-maximizing quantity from question 2a? Or if you want, I can help determine the profit-maximizing output from scratch.

---

Here are some questions to expand your understanding:

1. How do you derive the marginal cost from the total cost function?
2. How is the profit-maximizing quantity determined using marginal revenue and marginal cost?
3. How does a change in the total cost function impact the profit-maximizing output?
4. How would you calculate profit from the demand and cost functions after determining the price?
5. What are the implications of increasing fixed costs on the optimal price?

Tip: The profit-maximizing output occurs when marginal revenue equals marginal cost (MR = MC).