Final answer:
Long-run equilibrium occurs when firms in a perfectly competitive market earn zero economic profits. To determine if the market is in long-run equilibrium, we compare the market price with the average total cost of the firms. In this case, we calculate the average total cost and compare it to the market price of $21.
Step-by-step explanation:
In a perfectly competitive market, long-run equilibrium occurs when all firms in the market earn zero economic profits and there are no incentives for firms to enter or exit the market. To determine if the market is in long-run equilibrium, we need to compare the market price with the average total cost (ATC) of the firms in the market.
In this case, each firm has a cost function of c(q) = 10 + q + 2/3q². The ATC can be calculated by dividing the total cost by the quantity produced: ATC = (10 + q + 2/3q²) / q.
If the market price is equal to the ATC, firms in the market are earning zero economic profits, indicating long-run equilibrium. However, if the market price is lower than the ATC, firms would be making losses and may exit the market. On the other hand, if the market price is higher than the ATC, firms would be making positive economic profits, attracting new firms to enter the market.
To determine whether the market is in long-run equilibrium, we need to calculate the ATC and compare it to the market price of $21.