Final answer:
Without the firm's production quantity, we cannot conclusively determine if the market is in long-run equilibrium. However, if the firm makes economic profits, this indicates the market is not in long-run equilibrium since profits should be zero in the long run due to market entry and exit.
Step-by-step explanation:
To determine if the market is in long-run equilibrium, we must consider whether firms in the market are earning zero economic profits. The condition for long-run equilibrium in a perfectly competitive market is when firms are producing at a level where the price (P) equals marginal revenue (MR), equals marginal cost (MC), and when price (P) also equals average cost (AC). In the scenario described, we need to use the provided total cost function (TC = 50 + 3Q + 2Q²) alongside the given price ($31) to determine if these conditions are met.
In long-run equilibrium, firms earn zero economic profits because any short-run economic profits or losses would lead to entry or exit from the market, driving the price to the point where P = AC. According to the information provided, the firm takes the price as given, which is characteristic of a perfectly competitive market. We are not given the exact quantity (Q) the firm is producing, and without this, we cannot calculate the average cost and subsequently determine the profit. However, if we consider an example with a quantity of 40 units and a price of $16, we see that the firm's total revenue at this output level ($640) exceeds its total cost ($580), resulting in economic profits of $60. This situation would not indicate long-run equilibrium since firms should be making zero economic profits in long-run equilibrium, and other firms would have the incentive to enter the market.
To conclude, without additional information on the firm's quantity produced at the given price we cannot securely state whether the market is in long-run equilibrium. However, the example provided suggests that if a firm is making economic profits, then the market is not in long-run equilibrium, as these profits would induce entry of new firms and eventually dissipate the profits until P = AC is restored.