Consider a market with a demand function: Q = 20 - p
Currently, there are ten firms operating. Each firm has the following variable cost:
V C(q) = q2 and the fixed cost for each firm is F = 4.

1. Find the cost function C(q), the marginal cost function MC(q), and the average cost function AC(q) for a representative firm.

2. What is the supply curve for a single firm? For the entire market?

3. What are the (short run) equilibrium price and quantity?

4. At the equilibrium price, what is output and profit for each firm? Do you expect the price to be stable, increase, or decrease?

5. What is the long-run price in this market? How much will each firm produce at this price? How many firms will there be in the industry?

6. Suppose the government decides to introduce a fixed tax of $5 for each firm. prepare down the profit maximization problem of the rep- resentative firm. What is the new short run equilibrium price and production? (Hint: No extra computation is needed.)