Perfect Competition

In competitive markets there are:

1. Many buyers and sellers - individual firms have little effect on the price.
2. Goods offered are very similar - demand is very elastic for individual firms.
3. Firms can freely enter or exit the industry - no substantial barriers to entry.

Competitive firms have no market power. Recall that businesses are trying to maximize profits, and Profit = Total Revenue (TR) - Total Cost (TC).

Revenue in a Competitive Business

Businesses in competitive markets take the market price (P) as given (price takers). How much does the business receive for a typical unit is known as the "average revenue" (AR) and is equal to TR/Q = (P x Q)/Q = Price. So average revenue is equal to price, and is constant. How much additional revenue does the firm get if it sells one additional unit? To answer this question, we take a look at "marginal revenue" (MR) which is equal to the change in TR divided by the change in quantity. Note that this too is equal to price, so the marginal revenue is constant as well, and is equal to average revenue.

Profit Maximization

To maximize profit, we need to know the revenue and costs of the business. Profit is maximized when marginal revenue = marginal cost, and marginal cost is rising. To see why, recall that marginal revenue is the additional revenue from 1 additional unit. Marginal cost is the additional cost from 1 additional unit.
When MR > MC, revenue is increasing faster than costs and the firm should increase production. When MR < MC, revenue from the additional unit is less than additional cost, and the firm should decrease production. As such, A firm maximizes profits when MR = MC.
So what happens to output at various prices? Since MC is upward sloping, as price increases, quantity produced will increase too. As price falls, quantity produced falls. In each case, the marginal cost curve determines how much the firm is willing to produce at each price, so it translates into the supply curve.

Shutting Down a Company (temporary)

A company is considered to have shut down, if it temporary ceases production but keeps fixed capital. A company has exit the industry when it has made a permanent decision to leave the industry. The decision to temporarily shut down a business depends on a few factors. Recall that ATC = AVC + AFC. So average fixed cost is the vertical distance between average variable cost and average total cost.
Now if a business shuts down, its total revenue becomes zero, and its total cost equals the fixed cost. So the company should continue producing its product, as long as it covers its variable costs. This way, total revenue is greater than total variable cost, because losses are then less than TFC. Basically, shut down when P (AR = MR) < AVC, to minimize the losses and so the company's short-run supply curve = MC curve above AVC. The firm therefore produces where profit equals marginal cost.
Another way to put this is that sunk costs are sunk. Fixed costs are sunk, and therefore cannot be recovered by shutting down in the short run. The decision to continue producing depends on revenues and variable costs. If average revenue is greater than average variable cost, then the business should continue to produce. It is rational to continue producing, so long as AVC < P < ATC.

When to Leave An Industry (permanent)

A business should leave the industry when revenue is less than cost of operating in the long run. In other words, exit if total revenue is less than total cost (P < ATC). In competitive markets, a company will make zero economic profits in the long run. If companies are making more than zero economic profits, it will encourage other firms to enter the industry to share in these profits. In other words, enter if total revenue is greater than total cost (P > AC). If companies are making zero economic profits, there is no entry and no exit, which is a long run condition.