Final answer:
Given the available information and the correction of the cost equation to TC=49+4q, an oligopolistic market is implied with three firms serving the total market demand of 30,000 units at the optimal production level of 10,000 units each at the lowest cost.
Step-by-step explanation:
To determine the number of firms that will serve the market in the long run under perfect competition, we must look at the market demand and the long-run average cost curve for firms. The student's cost equation TC=49-4q seems incorrect, as total cost typically increases with quantity, not decreases. It may be a mistake, as the total cost should have a positive relationship with the quantity produced. If we correct this to TC=49+4q and assume that the marginal cost (MC) is constant at $4 (since TC increases by 4 for each additional unit q), then the firm will supply where price equals marginal cost (P=MC) in perfect competition, if we assume P=$500 (using demand q=530-4p, at P=$500, q=30).
Assuming a large number of firms serve the market initially, firms will enter and exit the market until they can no longer make a normal profit. In the long run, supply will equal demand, and each firm will produce at the minimum of their long-run average cost curve. If we reference the scenario where the bottom of the long-run average cost curve is at 10,000 units, but the total quantity demanded at that price point is less, the market could end up with fewer firms. Specifically, if the total demand is 30,000 units and each firm can optimally produce 10,000 units at the lowest cost, the market will have three firms in an oligopoly setting, as each firm supplies one-third of the total market demand.