Demand Curves Relate the Quantity Demanded to the Price of a Good

Demand

Demand curves relate the quantity demanded to the price of a good.

To understand demand curves consider the following: Let there be six people labeled A, B, C, D, E, and F. Each person can buy a good, and each person values the good differently. The amount they value the good (the marginal benefit) is given in the table below. Note the amount one values a good can be thought of as the maximum one would be willing to pay for the good.

This same information can be displayed graphically below.

Demand Schedule

First, notice that a person will only buy if the marginal benefit is greater than or equal to the price of the good. That is, a person buys if

Marginal Benefit ≥ Price

Knowing, this we can create the following table:

This captures the simple idea that if the price is reduced more will be purchased. This is simply because as the price falls, more people will find that the marginal benefit exceeds the price, and hence they will buy. For instance when the price is 5, only A and B buy since they are the only ones for whom Marginal Benefit ≥ Price. But as the price falls to 4, person C now has Marginal Benefit ≥ Price, and so he now buys.

Also notice that for any price we pick, the “last unit” purchased will have a marginal benefit equal to that price. For instance, at the price of 4, three units are purchased. At any higher price the third unit will not be purchased. Hence 4 is the maximum price that C will pay for that unit, hence it is the marginal benefit of the good.

From Demand Schedule to Demand Curve

If we plot the first and third columns of table 2 we have a demand curve, shown below.

As one can see the demand curve is nothing more than the earlier figure that orders the units from those valued the most to those valued the least. In fact, is simply a marginal benefit “curve”.

Marginal Benefit

Given the demand curve is created from the marginal benefit of the goods, it should be possible to find marginal benefit from a demand curve.

Recall our earlier conclusion:

The marginal benefit of the last unit produced is equal to the price.

For Example:

• Suppose the price is 6. One unit is consumed. It is consumed by person A. What is the marginal benefit of the first unit consumed? 6
• Suppose the price is 5. Two units are consumed. The second is consumed by person B. What is the marginal benefit of second unit consumed? 5
• Suppose the price is 4. Three units are consumed. The thrid is consumed by person C. What is the marginal benefit of the third unit consumed? 4

** Thus notice that the height of demand curve at some particular quantity, which is the most that a person will pay for that unit, is the marginal benefit of that unit to the person that consumes it.

This is summarized in Table 3:

Total Benefit

The total benefit is the sum of all marginal benefits. For example, from the above table one can see the total benefit of three units consumed is 6+5+4=15. This is summarized in Table 4 below:

Now if we return to the bar graph of the demand curve, we will see the same information is captured there. Recall the height of the demand curve (one of the bars) tells one the marginal benefit of that unit. Since the total benefit is just the sum of marginal benefit, we simply add up the heights of the demand curves; or the height of the bars. This gives us the area under the demand curve.

** The total benefit of a given number of units purchased is the area under the demand curve up to that number of units.

Continuously Downward Sloping Demand

While the bar graph is useful to understand demand, it is not very useful for using the demand curve. Generally, we will use a demand curve that is continuously downward sloping, as in the graph below:

Finding marginal and total benefit on the graph

Recall our two statements on marginal and total benefit:

** The marginal benefit of a unit is the height of demand curve at some particular quantity.

** The total benefit of a given number of units purchased is the area under the demand curve up to that number of units.

We can find this on a graph as follows: In the following graph, at a price of 10, 75 units are purchased. The marginal benefit of the 75th unit is 10, while the total benefit is the area under the demand curve up to 75.

Why do demand curves slope downward?

Substitution Effect:

This is the main reason. As price rises, people will switch to consuming something else. For example, if the price of Coke rises, people switch to Pepsi. If the price of pizza rises, people switch to hamburgers. Note that the greater the substitutes, the greater the switching, and hence the more responsive is quantity demanded to price changes.

Demand Curve Questions

Consider the following graph.

Questions:

2.1What is the marginal benefit of the 100th unit? What is the total benefit of all 100 units?

The marginal benefit of the 100th unit is 2. The total benefit of all 100 units is the area under the demand curve up to unit 100.

2.2Suppose the good in question is beef. As the price of beef rises from 2 to 4, the quantity of beef demanded falls from 100 to 50. What do you suppose is happening to the amount of chicken being purchased as the price of beef rises from 2 to 4?

As the price of beef rises it seems reasonable that people will switch to chicken (i.e. the substitution effect). The important thing to notice here is that this switch in consumption from beef to chicken is due not to a directive from a central planning committee, but simply to the price increase. Hence we can say the price increase has “signaled” consumers to consume less beef and more chicken. Just as prices are responsible for allocating resources as (captured on the supply curve), prices are also responsible for allocating final goods to consumers (as captured on the demand curve).

2.3At the price/quantity combination 100/2 demonstrate that the people who value the good the most will get the good.

This is simply seen be recalling that the demand curve orders those who value the good the most to those who value it the least. Hence at the price of 2, those on the upper portion of the demand curve (those who value the 100 units the most) will be the ones that decide to purchase the good.

Shifts in Demand

Increase (decrease) in demand is when more (less) is demanded at any given price.

Graph of an Increase

Notice at the price of 14 the amount demanded increased from 25 to 40. This is captured by a rightward shift of the demand curve.

Graph of a Decrease

Notice at the price of 20 the amount demanded decreased from 350 to 250. This is captured by a leftward shift of the demand curve.

Causes of Shifts in Demand:

1. Income changes.
2. Normal Goods…As income increases, the demand for the good rises.
3. Inferior Goods (e.g. old cars, bread)…Consider goods that are typically consumed by poor people because they are inexpensive. As income rises, at least some of the poor will experience a rise in income and their consumption of these goods will decline as they switch to higher quality goods. Hence demand for such goods will fall.
4. Changes in Price of Alternative Goods
5. Substitutes…Consider two soft drinks; say Coke and Pepsi. These are considered substitutes for each other. Now suppose we are considering the demand for Coke. As the price of Pepsi rises, people will switch from Pepsi to Coke. Hence the demand for Coke rises. In general, as the price of a substitute good rises the demand for good in question rises.
6. Complements…Consider two goods that people tend to consume together. For example, if one wants to take a holiday in Salalah in August, then flights to Salalah and hotel rooms in Salalah are complements. Now suppose we are considering the demand for hotel rooms in Salalah. If the price of a flight to Salalah rises, then the price of a holiday in Salalah rises, hence the demand for hotel rooms in Salalah will fall. In general, when the price of a complementary good rises, the demand for the good in question will fall.
7. Tastes/Preferences (e.g. fashion; food): Normally we assume tastes are constant. That is, most of our explanations about what we observe are not based on differences in tastes, but other things, like difference in income, prices, etc. The problem is, because tastes are unobservable, you can explain everything by saying tastes have changed over time, or tastes are different between countries. Some this becomes a “catch-all” category for things that do not fit neatly in our other categories.
8. Expectations: If people expect the price of a good to rise in the future, you may buy more today, store it in inventory, and consume it in the future. Hence current demand rises for the good in question.

Review Questions on Demand

1. Draw a demand curve and pick a quantity. Show the marginal benefit of that particular unit. Show the total benefit of all those units.
2. When the price of a good rises, the quantity of the good demanded falls. Why is that? That is, what behavior is being captured?
3. What is a change in demand? How is this different from a change in quantity demanded?
4. What would cause an increase in demand? What would cause a decrease in demand?

This section of notes is for the following part of the course outline.

1. Microeconomics: Markets as a Method of Social Cooperation
2. Supply and Demand Model of a Market
3. Opportunity Costs and Supply

Supply

Supply refers to the amount of goods offered for sale at various prices. To understand supply we must first understand the condition under which a seller would offer any unit for sale.

Recalling our self-interest assumption, a seller will only sell a good if the price received exceeds the marginal cost of producing that unit. For instance, if the marginal cost of a unit is R.O. 5, then the seller must receive a price greater than or equal to R.O. 5 to be willing to sell the good. In general we can say that for a seller to sell a particular unit it must be the price of the good is greater than or equal to the marginal cost of that unit. We can write this condition mathematically as

P ≥ MC.

Alternatively we can show it using the bar graph as we used earlier. Let the height of the bar represent the marginal cost of a good, expressed in OMR, and then we can say for any price line higher than the bar, the good will be sold.

Now, let us assume there are many possible sellers of this good, but they all have different marginal costs. In particular, suppose there are six possible sellers of this good, A, B, C, D, E, and F. Let us suppose there marginal costs are as follows:

Now recall, any given producer sells a unit if P ≥ MC. Hence we can summarize the decisions to produce in the following table:

If the price is 3, only person A has a MC less than or equal to price. Hence only one unit is produced. If the price is 4, then both A and B have a MC less than or equal to the price. Hence two units are produced. If the price is 5, then A, B, and C have MC less than or equal to the price, thus 3 units are produced. Etc.

In the above table, the first and third columns make up what is known as the supply schedule. It tells one at alternative prices what will be the amount offered for sale.

This same information can be displayed in graphically. The graph below shows the various units produced by A-F and their associated marginal costs.

As in the table above, and remembering that no one sells a unit unless P ≥ MC, we can graphically find the amount of goods produced for any given price. For instance suppose the price is 5. Then the only ones producing are those that have a marginal cost less than or equal to 5. The graph below shows this is the units produced by A, B, and C.

Clearly A, B, and C are produce the three units that have a marginal cost less than or equal to the price of 5. Or one could say, the bars representing the marginal cost of the units is less than the price line. So at the price of 5, the amount supplied will be 3.

Similarly, if the price is 6, the amount supplied is 4. This is shown in the graph below, where persons A, B, C, and D produce their unit.

Since A produces the first unit, B produces the second unit, etc., we can write the above graph as

Now what we have is the supply curve. Notice it is simply the graph of our supply schedule. It tells one at alternative prices the total amount supplied.

From the Bar Graph to a Continuously Upward Sloping Supply Curve

The bar graphs above are useful for explaining the relationship between costs and supply. However, we now want to transition to a graph that is continuously upward sloping. The reason for this is though the above graph is useful for introducing the concept of supply it is not very realistic to have cost of each additional unit jumping up, instead of going up gradually. Hence to capture the idea that costs for additional units rise gradually first let us “push” the bars together as in the graph below.

Now notice if we connect these bars with a straight line we have the following graph.

Below we draw this same graph without any bars. This is the standard way of drawing a supply curve.

Though the supply curve looks different from the bar graph, the same information is contained. Higher prices lead to more units being produced. For example in the graph below, when the price rises from 10 to 15, the amount of goods produced rises from 50 to 80.

Prices as Signals

Notice that as the price rises (falls), more (fewer) goods are produced. But consider this increase in goods produced. When the price rises causing producers to produce more of a good, where do the resources to produce these extra units come from? They must be taken away from other goods. Hence more of one good necessarily means less of other goods. Thus a price increase (decrease) causes a reorganization of the economy. The first of the three big questions (What to Produce?) is ultimately decided by this signaling role of prices.

The Second Big Question

The second big question is “How to Produce?”. The answer we gave to this question was to produce in the lowest cost manner possible. From the supply curve we can see that this is precisely what happens.

Now let us pick a price/quantity combination. Suppose the price is five and three units are produced. We know from the above table the total cost of those three units is simply 3 + 4 + 5 = 12. This can also be found in the graph below by adding up the marginal cost of the first three units, which is given by the height of the supply curve for each unit. Adding these three bars (marginal costs) together gives us the black area in the graph below.

It is simply the area under the supply curve. So in general we can say

The total cost of a given number of units is the area under the curve up to that particular unit.

From the Bar Graph to a Continuously Upward Sloping Supply Curve

The bar graphs above are useful for explaining the relationship between costs and supply. However, we switch now to using continuously upward sloping supply curves, as in the graph below. On the vertical axis we have alternative prices, and on the horizontal axis we have the quantity offered for sale at alternative prices.

Though the supply curve looks different from the bar graph, we find marginal and total cost in an identical way. The height of the curve at some quantity is the marginal cost of the last unit produced, and the area under the curve is the total cost of that quantity. For example, in the graph below at the price of 10, 50 units are produced. So the marginal cost of the 50th unit is 10. The total cost is the area labeled as TC.