Partial and general equilibrium, law of demand and demand analysis

Elasticity and revenue

When the price elasticity of demand for a good is inelastic (|E_d| < 1), the percentage change in quantity demanded is smaller than that in price. Hence, when the price is raised, the total revenue of producers rises, and vice versa.

When the price elasticity of demand for a good is elastic (|E_d| > 1), the percentage change in quantity demanded is greater than that in price. Hence, when the price is raised, the total revenue of producers falls, and vice versa.

When the price elasticity of demand for a good is unit elastic (or unitary elastic) (|E_d| = 1), the percentage change in quantity is equal to that in price.

When the price elasticity of demand for a good is perfectly elastic (E_d is undefined), any increase in the price, no matter how small, will cause demand for the good to drop to zero. Hence, when the price is raised, the total revenue of producers falls to zero. The demand curve is a horizontal straight line. A banknote is the classic example of a perfectly elastic good; nobody would pay £10.01 for a £10 note, yet everyone will pay £9.99 for it.

When the price elasticity of demand for a good is perfectly inelastic (E_d = 0), changes in the price do not affect the quantity demanded for the good. The demand curve is a vertical straight line; this violates the law of demand. An example of a perfectly inelastic good is a human heart for someone who needs a transplant; neither increases nor decreases in price affect the quantity demanded (no matter what the price, a person will pay for one heart but only one; nobody would buy more than the exact amount of hearts demanded, no matter how low the price is).

In economics, the income elasticity of demand measures the responsiveness of the demand of a good to the change in the income of the people demanding the good. It is calculated as the ratio of the percent change in demand to the percent change in income. For example, if, in response to a 10% increase in income, the demand of a good increased by 20%, the income elasticity of demand would be 20%/10% = 2.

Thus far, we have dealt with the effect of a change in the price of a good on the same good's quantity demanded or supplied. Now we turn our attention to the impact on the demand for a good when consumer incomes change, holding prices constant. The business cycle describes alternating periods of economic growth, when incomes generally increase, and contraction (recession) which lead to a decrease in consumer incomes. A firm needs to understand income elasticity to see how changes in the macroeconomy translates into the demand for the good or service produced by the firm. Our consumption of some goods, such as luxuries, is very sensitive to changes in economic growth and consumer incomes. In contrast, necessities such as food and housing tend to be less affected by economic swings and the corresponding changes in consumer incomes.

There are three possibilities for a good's income elasticity:

1. 
   A good is income elastic if the income elasticity of demand is greater than 1. This implies that for a 1% change in income, demand for the good changes by more than 1%.
   
2. 
   A good is income inelastic if the income elasticity of demand is greater than 0 but less than 1. This implies that for a 1% change in income, demand for the good changes by less than 1%.
   
3. 
   A good is considered inferior if the associated income elasticity of demand is a negative number. In this case, if income increases, consumers actually buy less of the good.
   

Since Normal goods have a positive income elasticity of demand so as income rise more is demand at each price level. We make a distinction between normal necessities and normal luxuries (both have a positive coefficient of income elasticity).

Necessities have an income elasticity of demand of between 0 and +1. Demand rises with income, but less than proportionately. Often this is because we have a limited need to consume additional quantities of necessary goods as our real living standards rise. The class examples of this would be the demand for fresh vegetables, toothpaste and newspapers. Demand is not very sensitive at all to fluctuations in income in this sense total market demand is relatively stable following changes in the wider economic (business) cycle.
Luxuries
Luxuries are said to have an income elasticity of demand > +1. (Demand rises more than proportionate to a change in income). Luxuries are items we can (and often do) manage to do without during periods of below average income and falling consumer confidence. When incomes are rising strongly and consumers have the confidence to go ahead with “big-ticket” items of spending, so the demand for luxury goods will grow. Conversely in a recession or economic slowdown, these items of discretionary spending might be the first victims of decisions by consumers to rein in their spending and rebuild savings and household financial balance sheets.

Many luxury goods also deserve the sobriquet of “positional goods”. These are products where the consumer derives satisfaction (and utility) not just from consuming the good or service itself, but also from being seen to be a consumer by others.

Inferior goods have a negative income elasticity of demand. Demand falls as income rises. In a recession the demand for inferior products might actually grow (depending on the severity of any change in income and also the absolute co-efficient of income elasticity of demand). For example if we find that the income elasticity of demand for cigarettes is -0.3, then a 5% fall in the average real incomes of consumers might lead to a 1.5% fall in the total demand for cigarettes (ceteris paribus).

What to some people is a necessity might be a luxury to others. For many products, the final income elasticity of demand might be close to zero, in other words there is a very weak link at best between fluctuations in income and spending decisions. In this case the “real income effect” arising from a fall in prices is likely to be relatively small. Most of the impact on demand following a change in price will be due to changes in the relative prices of substitute goods and services.

The final type of elasticity is known as the cross-price elasticity and measures the responsiveness of our consumption of one good when the price of another good changes. The cross-price elasticity of two goods, say good A and good B, measures the percentage change in the quantity demanded of good A, when the price of good B changes by 1%. Cross-price elasticity's are given two categories: complements and substitutes.

• 
  Complements - Two goods that have a negative value for their cross-price elasticity are considered complementary goods such as compact disk (CD) players and compact disks. If the price of CD players increases then our consumption of CD's decreases, leading to a negative relationship between the two. Conversely, if the price of CD players falls (a negative coefficient), our consumption of CD's rises (a positive coefficient).
  
• 
  Substitutes - Two goods that have a positive value for their cross-price elasticity are considered substitutes such as gasoline prices and the demand for public transportation. If the price of gasoline rises, so does consumer demand for less expensive transportation alternatives such as public transportation (buses, subways).
  

Take the example of the airline industry and consider goods that are close substitutes. For example one good is the price of seat on American Airlines, the other good is the demand for seat on United Airlines, each on an identical flight route - say Boston to Washington DC. In the case of the airline industry, the cross-price elasticity of demand for airline tickets is very high, and firms respond immediately to fare changes. If one airline such as American initiates a fare war, competitors such as United quickly follow in reducing prices to prevent a loss of market share. Since there is a high cross-price elasticity, if American lowers its fare from Boston to Washington DC, and United keeps its fares constant, consumers quickly shift consumption towards the lower priced American tickets. The resulting decrease in the demand for United Airlines tickets is large

1.7 Other market forms

The supply and demand model is used to explain the behavior of perfectly competitive markets, but its usefulness as a standard of performance extends to other types of markets. In such markets, there may be no supply curve, such as above, except by analogy. Rather, the supplier or suppliers are modeled as interacting with demand to determine price and quantity. In particular, the decisions of the buyers and sellers are interdependent in a way different from a perfectly competitive market.

A monopoly is the case of a single supplier that can adjust the supply or price of a good at will. The profit-maximizing monopolist is modeled as adjusting the price so that its profit is maximized given the amount that is demanded at that price. This price will be higher than in a competitive market. A similar analysis can be applied when a good has a single buyer, a monopsony, but many sellers. Oligopoly is a market with so few suppliers that they must take account of their actions on the market price or each other. Game theory may be used to analyze such a market.

The supply curve does not have to be linear. However, if the supply is from a profit-maximizing firm, it can be proven that curves-downward sloping supply curves (i.e., a price decrease increasing the quantity supplied) are inconsistent with perfect competition in equilibrium. Then supply curves from profit-maximizing firms can be vertical, horizontal or upward sloping.