Determine the optimal quantity to produce qm the price you

Question

You are the manager of a business in a monopoly market with the following inverse demand function

In addition, assume your production technology is described by the total cost function

C(q) = 500 + 10q

1. Determine the optimal quantity to produce (q^M), the price you should charge for your product (p^M), and compute the profit of your business.
2. Provide an intuitive explanation of market power. What is market power? How do we measure the market power of a business? Compute the market power of your business.