perfect competition market analysis

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 (πi) = $ ____________
• 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*.
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: