Final answer:
The price of the product in long-run equilibrium would be equal to the cost at the lowest point of the firm's long-run average cost curve. However, if market demand is very close to or less than the quantity at the lowest LRAC, the market might become a monopoly.
Step-by-step explanation:
If a firm’s total cost (TC) function is given as TC=10,000+200Q+5Q², where Q represents output, and the market is in a long-run equilibrium, the price of the product would be equal to the minimum point of the long-run average cost (LRAC) curve. In a perfectly competitive market, firms produce where price equals marginal cost (MC) and where the MC curve intersects the LRAC at its lowest point. Assuming the firm is perfectly competitive and the market is in equilibrium, the firm would produce at a quantity that minimizes the LRAC.
The LRAC can be found by dividing the TC by Q, resulting in LRAC = (10,000 / Q) + 200 + 5Q. To find the quantity that minimizes LRAC, we calculate the first derivative of the LRAC function with respect to Q, set it to zero, and solve for Q. This gives us the quantity that the firm would produce at the lowest cost per unit in long-run equilibrium. Given the TC function, we can then plug this Q into the marginal cost function (the first derivative of TC with respect to Q) to find the price.
However, if the bottom of the LRAC is at a quantity of 10,000 units and the total market demand at this quantity is only slightly higher or lower, it could lead to different market structures, such as a monopoly, if the total demand is substantially lower than the bottom of the LRAC. In such a case, there might be only one firm in the market able to produce at that level without incurring losses, deterring entry of other firms.