Suppose that there are 20 identical firms in a perfectly competitive market.

Each firm has a total cost function of TC = 50 + 0.2q2, where q is a firm's output

The market demand function is QD = 280 - 20P, where P is the price per unit of output and QD is total market demand.

1.1 (4 points) Derive the market direct supply equation (QS = f(P))

The market direct supply equation Qs = f(P) = _____________

1.2 (3 points) Calculate the short run equilibrium market price (P*) and total quantity (Q*) in the market. P* = $ __________ Q* = ___________ units.

1.3 (2 points) Determine the profit-maximizing quantity (q*) that each firm would produce. q* = ___________________ units.

1.4 (7 points) Determine the profit, the average total cost (ATC),

and the average variable cost (AVC) of the firm at its profit-maximizing quantity (q*).

The firm's profit (i) = $ ____________

The firm's ATC at q* = $ ____________

The firm's AVC at q* = $ ____________

The firm would:

a. shut down because its AVC at q* < P* < its ATC at q*.

b. shut down because P* < its AVC at q*.

c. continue producing because its AVC at q* < P* < its ATC at q*.

d. continue producing because P* > its ATC at q*.

4 1.5 (4 points) Draw the market supply curve. Calculate the firm's producer surplus and the market's producer surplus.

The firm's producer surplus = $ ____________

The market's producer surplus = $ __________

The direct market supply equation:

The inverse market supply equation: