Final answer:
Short-run shutdown occurs when price falls below average variable cost; long-run exit happens when price is below average cost, at which point firms earn zero economic profits. Calculations for shutdown and zero-profit points depend on marginal and average costs. The number of firms in the industry will stabilize in long-run equilibrium.
Step-by-step explanation:
The conditions for shutting down in both the short run and the long run for the given cost functions are based upon the relationship between market price, average cost, and average variable cost. In the short run, a firm should continue producing as long as the market price is above the average variable cost, which we refer to as the shutdown point. If the price falls below this point, the firm should shutdown immediately. In the long run, a firm should exit the market if it cannot produce at a price that allows it to cover the average cost, therefore bringing economic profits down to zero. For the given cost functions, the calculation of shutdown points involves finding where the firm's marginal cost curve intersects with its average variable and average cost curves respectively.
To determine the number of firms in the long-run market, we look for where the market price is equal to the minimum average cost at the profit-maximizing output level, a point also known as the zero-profit point. At this point, no new firms have the incentive to enter the market, and existing firms do not have the incentive to leave. Therefore, in a perfectly competitive market, the long-run equilibrium will be achieved so that the number of firms serving the industry will stabilize such that each firm earns zero economic profits.