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Institute of Lifelong Learning,University of Delhi
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Introduction o 1.1 demand and Supply o 1.1.Supply o 1.1.3 Equilibrium o 1.2.1 Elasticity of Demand o Summary o Exercise o Glossary
The quantity of a good an individual is willing to buy over a specific time period is a function of the price of the good, the individual’s money income,and the prices of other goods. In simple mathematical language it can be expressed as:
Qd x = f (P x , I, Po) (1.1)
where Qd x = the quantity of good X demanded by the individual, over the specific time period,
f = a function of, or depends on, P x = the price of good X, I = the money income of individual, Po = the prices of other goods. In any particular situation if we keep factors other than own price as constant, we can derive the individual’s demand function for the good as
follows :
where, the ‘bar’ on top of Iand Po means that they are kept constant. Equation (1.2) can also be written as Qd x = f (P x ) cet. par. (1.3)
where, cet. par. = ‘ceteris paribus’ means everything else held constant.
Eqn(1.3) implies that the quantity of good X demanded by an individual over a speific time period is a function of the price of that good, while holding constat everything else that affects the individual’s demand for the good.
Eqn(1.3) is a ‘general’ functional relationship between quantity demanded of the good X at various alternative prices of X, ceteris paribus. We can also take a ‘specific’ demand function. For example,
Qd x = 32 – 4P x cet. par. is a specific functional relationship indicating precisely how Qd x depends on P x. That is, by substituting various prices of good X into this specific demand function, we get the particular quantity of good X demanded by the individual per unit of time at these various prices. Thus, we get the individual’s demand schedule.
In general, the individual’s demand schedule for a good is a table giving us the quantity demanded of the good at various alternative prices of the good, keeping constant the prices of other goods and money income and tastes of the consumer. The graphic representation of the individual’s demand schedule gives us that person’s demand curve.
In the previous example where the demand function for an individual for good X is given as Qd x = 32 – 4P x , if we substitute various prices of X into the demand function we will get the individual’s demand schedule as given in Table 1.1.
Table 1.
P x (in Rs.) 8 7 6 5 4 3 2 1 0
Qd x 0 4 8 12 16 20 24 28 32
Plotting each pair of values as a point on a graph and joining the resulting points, we get the individual’s demand curve for good X. In Fig. 1.1 it is shown as dx
Figure 1.1: Linear Demand Curve
The individual buys the good X only when price falls below Rs. 8. At a price of Rs. 7 she buys 4 units of X. As the price falls further, she purchases more of X because they are becoming less expensive. At a price of Re1, she buys 28 units. However, even at a price of Rs.0 she would not take more than 32 units because additional units of X may result in a storage and disposal problem for the consumer. This is called the ‘saturation point’ for the individual. So the maximum quantity that the individual will ever demand of good X per time period is 32 units.
In drawing the demand curve d x in fig. 1.1.1, we assume complete divisibility, so that price and quantity demanded can both change by infinitely small steps. This enables us to draw a demand curve by joining the points A, B, C, D... I by a continuous, smooth line. Another point to be noted about the construction of the demand curve is that the independent variable, price, is measured on the vertical axis, and the dependent variable, quantity, on the horizontal axis which contradicts the mathematical principle of drawing a curve. But this is a convention which economists follow so that they can draw the demand curve of the consumers and the cost curves of the firms on the same set of axes. The demand curve drawn this way is also called the inverse demand curve.
In the given example,the demand curve for the good X is a straight line and is of the form of
Qd x = a – b P x , (1.4)
Where ‘a’ (32) is the quantity intercept and ‘–b′ (–4) is the slope, i.e., When we plot the demand curve, we actually plot the inverse demand curve which is given as:
Px = α – β Qdx, (1.5)
Where is the price intercept and is the slope of the inverse demand curve and equals
In our example, α = (32/4) = 8, is the price intercept, and –β = -(1/4), is the slope of the inverse demand curve.
Px (in Rs.) 0 1 2 4 5
Qdx (in units) ∞ 100 50 25 20
The demand curve derived will be non-linear. In fact, it will be a rectangular hyperbola, i.e., it will be asymptotic to both the axes and the areas of the rectangles formed under the curve will be equal to each other.
In the given figure, dx is a demand curve which is a rectangular hyperbola. Area of the rectangle OP 1 AQ 1 =area of OP 2 BQ 2 =area of OP 3 CQ 3 =area of OP 4 DQ 4 =100.
The individual’s demand curve for a good represents a maximum boundary of the individual’s intentions. For the various alternative prices of a good, the demand curve shows the maximum quantity of the good the individual intends to purchase per unit of time. For various alternative quantities of a good, the demand curve shows the maximum prices the individual is willing to pay. For example, in fig.1.2 point E on the demand curve indicates two things. First, if the price is given as Rs.50, the individual will buy maximum 5 units of good Y Second, the maximum price that the individual will be willing to pay to buy 5 units of Y is Rs.50.
1.1.1 (b) Movements Along vs. Shifts in Demand
When there is a change in the price of one good, other things remaining constant, the quantity demanded of that good changes and the consumer moves along the same demand curve. The movement along the same demand curve for a good is known as the change in the quantity demanded the good which occurs due to a change in the own price, ceteris paribus.
For example, in Table 1.2, when price of Y falls from say Rs.50 to Rs.40, the quantity demanded of Y rises or expands from 5 units to 8 units and the consumer moves from point E to point F on the same demand curve ‘dy’.
However, when any of the ‘ceteris paribus’ conditions changes holding own price of the good constant, the entire demand curve ‘shifts’ either to the right or to the left. A rightward shift is called an increase in demand (rather than an increase in the quantity demanded), and this shows that at any given price of the good, the consumer buys more of the good. Similarly, with a leftward shift the consumer buys less of the good at any given price. This is known as a decrease in demand.
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Increase in Demand
Case Studie
Reducing the Quantity of Tobacco Demanded
The Government in an effort to control the spread of Oral Cancer is contemplating two policy options to bring about reduction in tobacco (Gutka) consumption. One option is to tax the tobacco manufacturers thereby increasing the price and thus reducing/ contracting the demand for tobacco. Alternatively the Government can make use of public service announcements, health warnings on tobacco products, restrictions on advertisements of tobacco products etc. These measures would shift the demand curve of tobacco products to the left implying a decrease in the demand for tobacco products.
Shifts in the demand curve occur due to changes in income of the consumer or in the prices of other goods or in the tastes of the consumer. When consumer’s money income increase, while everything else remains constant, the consumer’s demand for a good usually increases so that the consumer demands more of the good at the same price of the good. These goods are referred to as normal goods. For example, with an increase in the consumer’s income, the consumer’s demand for ‘mango’ may increase even though price of ‘mango’ has not changed. This will lead to a rightward shift of the consumer’s demand curve for mango. Similarly, a decrease in income will lead to a leftward shift of the consumer’s demand curve.
Sometimes, with a rise in individual’s income the demand for certain goods may fall. These goods are known as inferior goods. For example, with a rise in income consumer may demand less of potatoes and switch over to better quality vegetables or fruits.
In fig. 1.4, d1 represents the demand curve for coke when price of one pizza was Rs.100. At that time the consumer was consuming 5 bottles of coke at a price of Rs.10/bottle. When price of pizza rises to Rs.150/unit, the demand curve for coke shifts leftward to the position d2 and at the same price of coke (which is Rs.10/bottle), the consumer reduces the demand to 3 bottles. This happens, because with an increased price of pizza, consumption of both pizza as well as coke, falls. The opposite will happen if price of pizza falls.
Figure 1.4: Shift In Demand Curve
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1.1.1 (c) Substitutability and Narrowness of Definition
When a consumer buys a number of goods, it is possible for her to substitute other goods for a particular good if its price rises. But the ability to substitute away from a good increases with the narrowness of its definition. That is, the more narrowly a good is defined; more substitutes are available for it, where as, the more broadly a good is defined, less will be availability of its substitutes.
For example, food is a broader category than fruits and fruit is a broader category than mango. As other goods in the individual’s consumption basket are very poor substitutes of food, so with a rise in the price of food, the consumer will find it difficult to substitute
it with anything else. Whereas, if the good in question is fruit, then meat, milk,
vegetables etc. are substitutes for fruits. So a rise in the price of fruits may induce the consumer to substitute fruits by meat or milk or vegetables. Mango is even more narrowly defined than fruits. Because other fruits like orange, banana and apple are more close substitutes of mango than is milk for fruits, so with a rise in the price of mango, the consumer immediately will switch over to other fruits.
1.1.1 (d) The Market Demand for a Product
The market demand for a good gives the alternative quantities of the good demanded per time period, at various alternative prices, by all the individuals in the market. The market demand for a good, therefore, depends on all the factors that determine the individual’s demand and also on the number of buyer of the good in the market.
In particular, if there are 100 identical buyers in the market for good X, having the same demand function Qdx = 32 – 4 Px, the market demand function will be simply given by 100 Qdx, i.e.,
QDx = 100 Qdx = 3200 – 400 Px, (1.6) where QDx is the market demand function. The market demand schedule can be derived by substituting various prices of X into this demand function. Market demand curve will be a graphical presentation of the market demand schedule. Table 1.3 gives us the market demand schedule and fig. 1.5 gives the market demand curve.
Table 1.
P x (in Rs.) 8 7 6 5 4 3 2 1 0
QD x 0 400 800 1,200 1,600 2,000 2,400 2,800 3,
Plotting each pair of values as a point on a graph and joining the resulting points, we get the market demand curve. In fig. 1.5 Dx gives us the market demand curve for good X.
Figure 1.5: Market Demand Curve
In practice, individuals have different preferences and so they have different demand functions for the same good X. In this case of people having different demand curves for the same good, we can derive the market demand curve by horizontally adding up the individual demand curves.
Solved Problem
Question: Suppose that a good is demanded by just two consumers A and B. Their demand curves are
qa = 80-8P qb = 40-10P
i) Derive the individual demand schedules.
ii) Plot the individual demand curves and the market demand curve on the same set of axes.
Solution: i) Individual Demand Schedule for A
Price (in Rs.) 0 1 2 3 4 5 6 7 8 9 10 Quantity (in units) 80 72 64 56 48 40 32 24 16 8 0
Individual Demand Schedule for B
Price (in Rs.) 0 1 2 3 4
Quantity (in units) 40 30 20 10 0
(ii)
Plotting the individual demand schedule of A and B we get the demand curves dada’ and dbdb’ respectively. The market demand curve, daCD, is a horizontal summation of the two individual demand curves. Its price-intercept is at Rs.10 because if the price is Rs. or more there is no demand by both the consumers of the good and hence, the market demand is zero. From the demand schedule of B it is clear that for any price greater than or equal to Rs.4, B’s demand for the good is zero. Thus the market demand curve will merge with A’s demand curve between the price Rs.10 and Rs.4. For any price below Rs.4 we can obtain the market demand by adding the demand by A and B both. For example, at price Rs. 2, A’s demand is 64 units and B’s demand is 20 units and the market demand is 64+20=84 units. In the given figure Pea+Peb=PE. At zero price the market demand is maximum 120 units.
Supply curves describe the seller’s desire to make the good available. The quantity of a good that an individual firm is willing to supply over a specific time period is a function of the price of the good and the cost of production. In order to derive the firm’s supply curve of a good, we just vary the price of the good, factors influencing the cost of production being held constant. The factors which influence cost of production are (i) the prices of the factors of production which have helped in the production of the good, (ii) technology and (iii) for agricultural goods, climate and weather conditions. A single firm’s supply curve of a good shows the alternative quantities of the good that the firm is willing to supply over a specific period of time at various alternative prices for the good, while keeping the above constant.
In simple mathematical language this functional relationship can be expressed as follows :
or, Qsx = g (Px) cet. par. (1.7´)
Where Qsx = the quantity supplied of good X by the single producer, over the specific time period,
g = a function of,
Tech = technology,
Pi = the price of inputs,
Fn = features of nature such as climate and weather conditions.
The bar on top of the last three factors indicate that they are kept constant. Equation (1.7) or (1.7´) is a general functional relationship. In order to derive a single firm’s supply schedule and supply curve, we must get that firm’s specific supply function.
For example, let a single firm’s supply function for good X be
Qsx = – 50 + 25 Px. If we substitute various prices of X into the above supply function we will get the individual supply schedule as given in Table 1.5.
Figure 1.8:Shift In Supply Curve
1.1.2 (c) The Market Supply of a Product
The market or aggregate supply of a good gives the alternative amounts of the good supplied per time period at various alternative prices by all the producers of this good in the market. In addition to all the factors that influence individual producer’s supply, the market supply depends also on the number of producers of the good in the market.
If all the producers face identical cost conditions such that they have the same supply functions then the market supply function can be derived simply by multiplying the individual supply function by the number of producers in the market. In the previous example, if there are 100 identical producers in the market having the supply function Qsx = – 50 + 25 Px, then the market supply function will be given by QSx = 100 × Qsx = – 5,000 + 2,500 Px
The market supply schedule will be given by Table 1.6.
Table 1.6 Market Supply Schedule
P x (in Rs.) 10 9 8 7 6 5 4 3 2 Qd y 2,000 17,500 15,000 12,500 10,000 7,500 5,000 2,500 0
The market supply curve is simply a graphical presentation of the market supply schedule which can be drawn very much in the same way as fig. 1.7, only the scale on the horizontal axis will have to change.
When individual producers face different cost conditions they will face different supply functions and supply curves. In this case the market supply curve will be given by the horizontal summation of the individual supply curves of all the firms in the market. Let Table 1.7 give the supply schedules of the three producers of good X in the market.
Table 1. P x (in Rs.)
Quantity supplied (per time period) Firm 1 Firm 2 Firm 3 5 4 3 2 1 0 15 12 5 0 0 0
25 20 15 10 0 0
30 25 18 12 5 0
The individual supply curves of the three firms are drawn on the same set of axes in fig. 1.9 as sx^1 , sx^2 and sx^3. The market supply curve is given by Sx (OEDCBASx) which is a horizontal summation of sx^1 , sx^2 & sx^3. Various points on the market supply curve are obtained by adding up the quantities supplied by the individual producers at different price levels. For example, at price Rs.5 (or P 5 ) the quantity supplied by firm 1 is P 5 A 1 (15), by firm 2, P 5 A 2 (25) and by firm 3 it is P 5 A 3 (30). So the total quantity supplied in the market at P 5 price is P 5 A 1 + P 5 A 2 + P 5 A 3 = P 5 A (70 units). The market supply curve merges with Firm 3’s supply curve till price rises from Re.0 to Re1 and after that it
becomes a horizontal sum of s^1 x, s^2 x & s^3 x.
Figure 1.9:Derivation Of The Market Supply Curve
1.1.3 Equilibrium
Equilibrium is said to exist when opposing forces are in balance. In the market for a particular good, demand and supply are like two opposing forces. The market is in equilibrium at the price where the amount that is demanded equals the amount supplied. This price is called the equilibrium price and the quantity demanded and supplied at this price the equilibrium quantity. Market equilibium is shown graphically in Fig.1.10.
In fig.1.10 Dx is the market demand curve and Sx the market supply curve. They intersect at point E. Only at price OP, the quantity demanded is equal to the quantity supplied which is equal to OQ. At any price higher than OP* supply exceeds demand and any price below OP, demand exceeds supply and they are not in balance. So the equilibrium price is OP and the equilibrium quantity OQ*.
where the numerator gives the proportionate change in the quantity demanded of X and the denominator gives the proportionate change in the price of X.
Equation (1.8) can also be written as
For infinitesimally small change in quantity and price the formula for price elasticity will be
where is the inverse of the slope of the demand curve at a point where price is Px and quantity demanded of the good is Qx. Equation (1.10) can, therefore, be written as :
and it gives us the formula to measure elasticity at a point on the demand curve.
To measure elasticity between two points on the demand curve we may use the formula given by equation (1.9). But while applying this formula to measure elasticity between two points on a demand curve we would get different results depending on whether we move from higher price to the lower price or from the lower price to the higher one. For example, suppose we want to measure elasticity between points D & F on the market demand curve Dx given in fig.1.5 which is reproduced in fig. 1.11. If we let the price fall from Rs.5 to Rs3 and move from D to F on the demand curve Dx, then elasticity will be
Whereas, if we let the price rise from Rs.3 to Rs.5 and move from point F to point D on the same demand curve Dx, then elasticity will be
Thus, though we are measuring elasticity between the same pair of points on a demand curve we are getting different results depending on whether we are moving from a higher to a lower point or from a lower to higher point. This problem arises because the elasticity of demand tends to vary from one point to another on the demand curve, and for a large change in price and quantity we need an average value over the entire range. Thus, when we deal with large changes in price and quantity, we should use the following Arc Elasticity formula.
where P 1 and P 2 are the prices between which we want to find out the elasticity. Following this formula, the elasticity between the points D and F on the demand curve
Dx in fig.1.11 will be
II. Graphical Presentation of Elasticity
Graphically the price elasticity at a point on a linear demand curve is shown by the ratio of the segments of the line to the right and to the left of the particular point. It can also be described as the ratio of the lower segment to upper segment. Let us look at the linear demand curve given in fig.1.11.
Figure 1.11: Demand Curve
