2. The widget market is characterized by perfect competition. The "inverse" market demand is P = 30 – 0.05Q, while the market supply is Q=-100+20P. The firms are identical, and the cost structure of a typical firm is TC; = 200 + 5Q¡ + 0.5Q², with MC; = 5 + Qi a) How many (identical) firms are there currently in the market? b) Derive the competitive equilibrium for the market. c) Solve for the optimal output level for a typical firm.

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2. The widget market is characterized by perfect competition. The "inverse" market demand is P = 30 – 0.05Q,
while the market supply is Q=-100+20P. The firms are identical, and the cost structure of a typical firm is TC;
= 200 + 5Q; + 0.5Q?, with MC; = 5 + Qi
a) How many (identical) firms are there currently in the market?
b) Derive the competitive equilibrium for the market.
c) Solve for the optimal output level for a typical firm.
d) Solve for the profit level of a typical firm. Is this a short-run or long-run equilibrium? Or should the firms
simply fold? If they should fold, STOP!
e) Derive the long-run equilibrium output of a typical firm. What is the price? What is the profit now?
f) How many firms can this market support in the long-run (i.e. how many firms will there be in this long-run
equilibrium)?
g) What is the PS for the typical firm in the long-run?
Transcribed Image Text:2. The widget market is characterized by perfect competition. The "inverse" market demand is P = 30 – 0.05Q, while the market supply is Q=-100+20P. The firms are identical, and the cost structure of a typical firm is TC; = 200 + 5Q; + 0.5Q?, with MC; = 5 + Qi a) How many (identical) firms are there currently in the market? b) Derive the competitive equilibrium for the market. c) Solve for the optimal output level for a typical firm. d) Solve for the profit level of a typical firm. Is this a short-run or long-run equilibrium? Or should the firms simply fold? If they should fold, STOP! e) Derive the long-run equilibrium output of a typical firm. What is the price? What is the profit now? f) How many firms can this market support in the long-run (i.e. how many firms will there be in this long-run equilibrium)? g) What is the PS for the typical firm in the long-run?
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