We now move to the equilibrium problem, asking, when will shoe prices be high, low, and of what quantity? The answers depend on the market supply and demand curves taken together. Consumer and Producer surplus are also key concepts to the measure of gains 

7.1  The Supply Function

From Firm Supply to Market Supply: The Short Run

For a competitive (price-taking) firm, the price of its product is identical to its Marginal Revenue. The key proposition is that profit is maximized by setting output so that Marginal Cost equals price:  
\(MC = P = MR\).
The supply curve shows how a firm's output responds to different levels of price (running along its MC curve). The no-shutdown condition dictates zero output whenever the market price is less than the minimum of Average Variable Cost in the short run. In the long run, this applies to Average Total Cost. We can show this below in the graph:
Now we turn to understanding the influence of the input prices on supply. For example, if one firm decides to expand output and hire more, there probably isn't an impact on the wage. But if the whole industry begins to expand, wages will definitely go up, increasing the costs of production for every firm. Thus, the industry supply curve is the horizontal summation of the individual firm supply curves though steeper (less elastic) to allow for the input price effect:
The short-run supply curve of an industry is the horizontal sum of the firms' supply curves, but only after allowing for the input-price effect that raises Marginal Cost curves as industry output rises. The input-price effect reduces the magnitude of the supply response to changes in output price, making the industry supply curve steeper than it would otherwise be. 
The elasticity of supply is the proportional change in quantity supplied divided by the proportional change in price:
\(k \equiv \frac{\frac{\Delta Q}{Q}}{\frac{\Delta P}{P}} \equiv \frac{\Delta Q}{\Delta P} \cdot \frac{P}{Q}\)
While the elasticity of demand is normally negative (price increase means quantity demanded declines) the elasticity of supply is usually positive. 

Long-Run and Short-Run Supply

Long-run versus short-run is really a matter of degree: how permanent the price change is, how fixed the various inputs are, and how cohesive the industry is. Recall that for a firm to remain in business in the long run, the price must be greater than the minimum of the Long-Run Average Cost curve. From that point, the firm's supply curve follows the Long-Run Marginal Cost curve:
The industry long-run supply curve also has the additional element of entry-exit effect. In the long-run, every firm must be earning non-negative economic profit (\(P \geq LRAC\)). Firms that do not meet this condition go out of business, and conversely, if there are profit opportunities within the industry we will see new entrants. 
Supply tends to be more elastic in the long run. The biggest reason is that responses to changes in price will be larger since the inputs are more changeable. 

External Economies and Diseconomies

In examining an industry's response to changes in demand, it is useful to distinguish between (1) the influences that are internal to the separate firms and (2) those that are internal to the industry as a whole but external to the separate firms. 
Internal influences that limit individual firms' responses to a price change are summarized by their short-run and long-run cost functions, whose rising shapes reflect internal diseconomies of scale. The "input-price" effect is an external diseconomy of scale, and in general, these are pecuniary (monetary). A technological external influence is usually an economy of scale, since all firms could benefit from sharing this knowledge and infrastructure. 
In conclusion, the internal effects (how changes in a firm's output affect its own costs) must be diseconomies in the neighborhood of equilibrium, since the firm's optimum requires that Marginal Cost slope upward. The external effects (how changes in industry output influence firms' cost functions) are of two types -- pecuniary and technological. Pecuniary effects will usually be diseconomies since rising industry output tends to raise the input prices faced by individual firms. Technological externalities can be either, because increases in industry output may have favorable effects upon the production functions of the individual firms. 

7.2  Firm Survival and the Zero-Profit Theorem

Competition tends to reduce economic profit to zero. This is due to the fact that profit opportunities induce new entrants, who in turn grow industry output, lower product prices, and raise input prices. Entry stops when no firm outside the industry can earn a profit within it, called the marginal firm. For such a marginal firm, economic profit (excess of revenues over the best alternative foregone) is zero. But in the long-run equilibrium, all firms earn zero economic profit. 
This zero economic profit will be due to the fact that if one firm has a superior resource (labor, land, tech, etc.) firms will bid for it until its marginal profit equals the marginal cost. Thus while accounting profit may be high, there is usually a trend towards zero economic profit, stemming from downward pressure on product prices and upward pressure on input prices, in the long run for firms.  

7.3  The Benefits of Exchange: Consumer and Producer Surplus

One of the most important principles of economics is the fundamental theorem of exchange: Trade is mutually beneficial. The proof is self-explanatory; parties will only agree to a voluntary exchange if they subjectively view it as beneficial. We turn now to answer the question: how much does each side gain from trade? 
Consumer surplus measures the advantage to buyers of being able to buy a certain quantity at a certain price, when they would have been willing to pay higher prices. The concept of demand price (height of the demand curve at any quantity) is useful here-- the demand price is the equivalent marginal value to an individual. Thus, consumer surplus is the area under this curve, minus the area under the price paid. Similarly, the supply price is the height of the supply curve, minus the portion under the prices above the equilibrium price. 

An Application: The Water-Diamond Paradox

Water is more valuable than diamonds in the sense that consumers' aggregate willingness to pay (total area under the demand curve is greater). However, the supply of water is so enormous that the market value is small. For diamonds, demand is small but supply is smaller still-- hence a high price.  

An Application: Benefits of an Innovation

A quality-improving innovation shifts the demand curve upward, rising the equilibrium price and quantity. The combined CS and PS will become larger, though the gain is largest for the producer.

7.4  Transaction Taxes and Other Hindrances to Trade

The adverse effects of hindrances to trade are best quantified in terms of consumer or producer surplus.  Hindrances to trade affect CS and PS in two ways: transfers of surplus from one group to another, and deadweight losses caused by the reduced amount of exchange. 

Transaction Taxes

An "add-on" tax requires distinguishing between the gross price paid by the buyers (higher) and the net price (lower) received by the sellers. Both the buyer and seller are worse off than before from a reduction in their surpluses. See below the effects of a transaction tax: 

Supply Quotas

While taxes reduce trade by driving a wedge between the gross and net price, a supply quota involves an order from government to supply a fixed amount to the market. Under this measure, the quota both raises the price and reduces the quantity exchanged:
 

Price Ceilings and Shortages

Legislation that sets the price of a good below its market-clearing level creates a shortage, when goods are unavailable to people even willing to pay the price for them. The classic example for this is a city with rent control. Consumers may seem to gain by the abnormally low price, but it also means that resources are not allocated as efficiently to the highest valuing users, and the quality often falls:
We often see that consumers who cannot buy desired commodities owing to price ceilings often give rise to competition on other margins: waiting, political influence, bribes, and so forth.