Suppose that there are 8 identical firms in a perfectly competitive market. Each firm has a total cost function TC = 80 + 0,4Q² where Q is a firm's output. The market demand function is Qd = 96 - 2P, where P is the price per output unit and Qd is total market demand.

1. Derive the market direct supply function (Qs).
2. Determine the short-run equilibrium market price (P*) and Total Quantity (Q*).
3. Determine the firm's profit-maximizing quantity (Q*).
4. Determine the total profit, the average cost (ATC), and the average variable cost (AVC) of the firm at its profit-maximizing quantity (Q*).
5. What is the inverse market supply function?
6. What is the firm's producer surplus?
7. What is the market's producer surplus?