THE LAW OF DEMAND

For most goods, consumers are willing to purchase more units at a lower price than at a higher price. The inverse relationship between price and the quantity consumers will buy is so widely observed that it is called the law of demand. The law of demand is the rule that people will buy more at lower prices than at higher prices if all other factors are constant. This idea of the law of demand seems to be a pretty logical and accurate description of the behaviour we would all expect to observe and for now, this will suffice.

The law of demand states that consumers are willing and able to purchase more units of a good or service at lower prices than at higher prices, other things being equal. Have you ever thought about why the law of demand is true for nearly all goods and services? Two influences, known as the income effect and the substitution effect, are particularly important in explaining the negative slope of demand functions. The income effect is the influence of a change in a product’s price on real income, or purchasing power. If the price of something that we buy goes up and our income will go farther and we can purchase more goods and services (including the goods for which price has fallen) with a given level of money income. The substitution effect is the influence of a reduction in a product’s price on quantity demanded such that consumers are likely to substitute that good for others that have thus become relatively more expensive.

The concept of demand is often depicted in a graphic model as a demand curve. A demand curve is a graphic illustration of the relationship between price and the quantity purchased at each price. When plotting a graph for demand, the price is measured along the vertical axis and the quantities that would be purchased at various prices are measured along the horizontal axis. The demand curve shows the relationship between the own price of a good and the quantity demanded of it. Any change in own price causes a movement along the curve as shown in Figure-1. In this case, a rise in price from P1 to P2 results in a fall in quantity demanded from Q1 to Q2 i.e. a move from B* to A* in the figure.

demand-curve

The same information can also be given in a table or demand schedule, such as Table -1, or by an equation for the demand function such as the following:

P = 100 – 0.25Q

where P is price and Q is quantity. The advantage of the equation is that it is compact to work with, and modern managers in both the private and public sector rely on such functions with increasing frequency. 

demand-schedule

THE MARKET DEMAND CURVE

The market demand curve is the total of the quantities demanded by all individual consumers in an economy (or market area) at each price. Economic theory supports the proposition that individual consumers will purchase more of a good at lower prices than at higher prices. If this is true of individual consumers, then it is also true of all consumers combined. This relationship is demonstrated by the example in Figure-2, which shows two individual demand curves and the market demand that is estimated by adding the two curves together. 

market-demand-curve

A market demand curve is the sum of the quantities that all consumers in a particular market would be willing and able to purchase at various prices. If we plotted the quantity that all consumers in this market would buy at each price, we might have a market demand curve such as the one shown in Figure-2. The market demand curve in Figure -2 shows that at a price of Rs. 15, the market demand would be 4 for the first consumer and 2 for the second consumer, giving a total of 6 units as market demand. Analogously, at Rs. 10.00 the total market demand is 13 units.

Another way of showing the derivation of the market demand curve is through equations representing individual consumer demand functions. Consider the following three equations representing three consumers’ demand functions:

Consumer 1: P = 12 – Q1

Consumer 2: P = 10 – 2Q2

Consumer 3: P = 10 – Q3 

You should substitute some value of Q (such as Q = 4) in each of these equations to verify that they are consistent with the data in Table-2. Now, add these three demand functions together to get an equation for the market demand curve. Be careful while doing this. There is sometimes a temptation to just add equations without thinking about what is to be aggregated. In Table 2, it is easy to see that the quantities sold to each consumer at each price have been added. For example, at a price of Rs. 6, consumer number 1 would buy six units (Q1 = 6), consumer number 2 would buy two units (Q2 = 2), and consumer number 3 would buy four units (Q3 = 4). Thus, the total market demand at a price of Rs. 6 is 12 units (6 + 2 + 4 = 12). The important point to remember is that the quantities are to be added; not the prices. To add the three given demand equations, we must first solve each for Q because we want to add the quantities (that is, we want to add the functions horizontally, so we must solve them for the variable represented on the horizontal axis). Solving the individual demand functions for Q as a function of P (for consumers 1, 2 and 3), we have—

Q1 = 12 P

Q2 = 5 0.5P

Q3 = 10 P

Adding these equations results in the following:

Q1 + Q2 + Q3 = 27 2.5P

And letting QM = Q1 + Q2 + Q3 where QM is market demand.

QM = 27 2.5P

QM is the total quantity demanded.

This is the algebraic expression for the market demand curve. We could solve this expression for P to get the inverse demand function:

P = 10.8 – 0.4QM

Now, check to see that this form of expressing the market demand is consistent with the data shown in Table-2. 

derivatives-of-market-demand-schedule

The market demand curve shows that the quantity purchased goes up from 12 to 22 as the price falls from Rs. 6.00 to Rs. 2.00. This is called a change in quantity demanded. As the price falls, a greater quantity is demanded. As the price goes up, a smaller quantity is demanded. A change in quantity demanded is caused by a change in the price of the product for any given demand curve. This is true of individual consumers’ demand as well as for the market demand. But what determines how much will be bought at each price? Why are more televisions bought now than ten years ago, despite higher prices? Why are more paperback books bought today than in previous years, even though the price has gone up? Questions such as these are answered by looking at the determinants of demand. 

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