Page 1 Chapter 2 Theor Theor Theor Theor Theory of y of y of y of y of Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods 1 . The consumer has to decide on how much of each of the different goods she would like to consume. Our objective here is to study this choice problem in some detail. As we see, the choice of the consumer depends on the alternatives that are available to her and on her tastes and preferences regarding those alternatives. To begin with, we will try to figure out a precise and convenient way of describing the available alternatives and also the tastes and preferences of the consumer. We will then use these descriptions to find out the consumerâ€™s choice in the market. Preliminary Notations and Assumptions A consumer, in general, consumes many goods; but for simplicity, we shall consider the consumerâ€™s choice problem in a situation where there are only two goods. 2 We will refer to the two goods as good 1 and good 2. Any combination of the amount of the two goods will be called a consumption bundle or, in short, a bundle. In general, we shall use the variable x 1 to denote the amount of good 1 and x 2 to denote the amount of good 2. x 1 and x 2 can be positive or zero. (x 1 , x 2 ) would mean the bundle consisting of x 1 amount of good 1 and x 2 amount of good 2. For particular values of x 1 and x 2 , (x 1 , x 2 ), would give us a particular bundle. For example, the bundle (5,10) consists of 5 units of good 1 and 10 units of good 2; the bundle (10, 5) consists of 10 units of good 1 and 5 units of good 2. 2.1 THE CONSUMERâ€™S BUDGET Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed 1 We shall use the term goods to mean goods as well as services. 2 The assumption that there are only two goods simplifies the analysis considerably and allows us to understand some important concepts by using simple diagrams. © NCERT not to be republished Page 2 Chapter 2 Theor Theor Theor Theor Theory of y of y of y of y of Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods 1 . The consumer has to decide on how much of each of the different goods she would like to consume. Our objective here is to study this choice problem in some detail. As we see, the choice of the consumer depends on the alternatives that are available to her and on her tastes and preferences regarding those alternatives. To begin with, we will try to figure out a precise and convenient way of describing the available alternatives and also the tastes and preferences of the consumer. We will then use these descriptions to find out the consumerâ€™s choice in the market. Preliminary Notations and Assumptions A consumer, in general, consumes many goods; but for simplicity, we shall consider the consumerâ€™s choice problem in a situation where there are only two goods. 2 We will refer to the two goods as good 1 and good 2. Any combination of the amount of the two goods will be called a consumption bundle or, in short, a bundle. In general, we shall use the variable x 1 to denote the amount of good 1 and x 2 to denote the amount of good 2. x 1 and x 2 can be positive or zero. (x 1 , x 2 ) would mean the bundle consisting of x 1 amount of good 1 and x 2 amount of good 2. For particular values of x 1 and x 2 , (x 1 , x 2 ), would give us a particular bundle. For example, the bundle (5,10) consists of 5 units of good 1 and 10 units of good 2; the bundle (10, 5) consists of 10 units of good 1 and 5 units of good 2. 2.1 THE CONSUMERâ€™S BUDGET Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed 1 We shall use the term goods to mean goods as well as services. 2 The assumption that there are only two goods simplifies the analysis considerably and allows us to understand some important concepts by using simple diagrams. © NCERT not to be republished income and the prices of the two goods, the consumer can afford to buy only those bundles which cost her less than or equal to her income. 2.1.1 Budget Set Suppose the income of the consumer is M and the prices of the two goods are p 1 and p 2 respectively. 3 If the consumer wants to buy x 1 units of good 1, she will have to spend p 1 x 1 amount of money. Similarly, if the consumer wants to buy x 2 units of good 2, she will have to spend p 2 x 2 amount of money. Therefore, if the consumer wants to buy the bundle consisting of x 1 units of good 1 and x 2 units of good 2, she will have to spend p 1 x 1 + p 2 x 2 amount of money. She can buy this bundle only if she has at least p 1 x 1 + p 2 x 2 amount of money. Given the prices of the goods and the income of a consumer, she can choose any bundle as long as it costs less than or equal to the income she has. In other words, the consumer can buy any bundle (x 1 , x 2 ) such that p 1 x 1 + p 2 x 2 = M (2.1) The inequality (2.1) is called the consumerâ€™s budget constraint. The set of bundles available to the consumer is called the budget set. The budget set is thus the collection of all bundles that the consumer can buy with her income at the prevailing market prices. EXAMPLE 2.1 Consider, for example, a consumer who has Rs 20, and suppose, both the goods are priced at Rs 5 and are available only in integral units. The bundles that this consumer can afford to buy are: (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1) and (4, 0). Among these bundles, (0, 4), (1,3), (2, 2), (3, 1) and (4, 0) cost exactly Rs 20 and all the other bundles cost less than Rs 20. The consumer cannot afford to buy bundles like (3, 3) and (4, 5) because they cost more than Rs 20 at the prevailing prices. 3 Price of a good is the amount of money that the consumer has to pay per unit of the good she wants to buy. If rupee is the unit of money and quantity of the good is measured in kilograms, the price of good 1 being p 1 means the consumer has to pay p 1 rupees per kilograms of good 1 that she wants to buy. Spoilt for Choice 9 Theory of Consumer Behaviour © NCERT not to be republished Page 3 Chapter 2 Theor Theor Theor Theor Theory of y of y of y of y of Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods 1 . The consumer has to decide on how much of each of the different goods she would like to consume. Our objective here is to study this choice problem in some detail. As we see, the choice of the consumer depends on the alternatives that are available to her and on her tastes and preferences regarding those alternatives. To begin with, we will try to figure out a precise and convenient way of describing the available alternatives and also the tastes and preferences of the consumer. We will then use these descriptions to find out the consumerâ€™s choice in the market. Preliminary Notations and Assumptions A consumer, in general, consumes many goods; but for simplicity, we shall consider the consumerâ€™s choice problem in a situation where there are only two goods. 2 We will refer to the two goods as good 1 and good 2. Any combination of the amount of the two goods will be called a consumption bundle or, in short, a bundle. In general, we shall use the variable x 1 to denote the amount of good 1 and x 2 to denote the amount of good 2. x 1 and x 2 can be positive or zero. (x 1 , x 2 ) would mean the bundle consisting of x 1 amount of good 1 and x 2 amount of good 2. For particular values of x 1 and x 2 , (x 1 , x 2 ), would give us a particular bundle. For example, the bundle (5,10) consists of 5 units of good 1 and 10 units of good 2; the bundle (10, 5) consists of 10 units of good 1 and 5 units of good 2. 2.1 THE CONSUMERâ€™S BUDGET Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed 1 We shall use the term goods to mean goods as well as services. 2 The assumption that there are only two goods simplifies the analysis considerably and allows us to understand some important concepts by using simple diagrams. © NCERT not to be republished income and the prices of the two goods, the consumer can afford to buy only those bundles which cost her less than or equal to her income. 2.1.1 Budget Set Suppose the income of the consumer is M and the prices of the two goods are p 1 and p 2 respectively. 3 If the consumer wants to buy x 1 units of good 1, she will have to spend p 1 x 1 amount of money. Similarly, if the consumer wants to buy x 2 units of good 2, she will have to spend p 2 x 2 amount of money. Therefore, if the consumer wants to buy the bundle consisting of x 1 units of good 1 and x 2 units of good 2, she will have to spend p 1 x 1 + p 2 x 2 amount of money. She can buy this bundle only if she has at least p 1 x 1 + p 2 x 2 amount of money. Given the prices of the goods and the income of a consumer, she can choose any bundle as long as it costs less than or equal to the income she has. In other words, the consumer can buy any bundle (x 1 , x 2 ) such that p 1 x 1 + p 2 x 2 = M (2.1) The inequality (2.1) is called the consumerâ€™s budget constraint. The set of bundles available to the consumer is called the budget set. The budget set is thus the collection of all bundles that the consumer can buy with her income at the prevailing market prices. EXAMPLE 2.1 Consider, for example, a consumer who has Rs 20, and suppose, both the goods are priced at Rs 5 and are available only in integral units. The bundles that this consumer can afford to buy are: (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1) and (4, 0). Among these bundles, (0, 4), (1,3), (2, 2), (3, 1) and (4, 0) cost exactly Rs 20 and all the other bundles cost less than Rs 20. The consumer cannot afford to buy bundles like (3, 3) and (4, 5) because they cost more than Rs 20 at the prevailing prices. 3 Price of a good is the amount of money that the consumer has to pay per unit of the good she wants to buy. If rupee is the unit of money and quantity of the good is measured in kilograms, the price of good 1 being p 1 means the consumer has to pay p 1 rupees per kilograms of good 1 that she wants to buy. Spoilt for Choice 9 Theory of Consumer Behaviour © NCERT not to be republished 10 Introductory Microeconomics 2.1.2 Budget Line If both the goods are perfectly divisible 4 , the consumerâ€™s budget set would consist of all bundles (x 1 , x 2 ) such that x 1 and x 2 are any numbers greater than or equal to 0 and p 1 x 1 + p 2 x 2 = M. The budget set can be represented in a diagram as in Figure 2.1. All bundles in the positive quadrant which are on or below the line are included in the budget set. The equation of the line is p 1 x 1 + p 2 x 2 = M (2.2) The line consists of all bundles which cost exactly equal to M. This line is called the budget line. Points below the budget line represent bundles which cost strictly less than M. The equation (2.2) can also be written as 5 1 21 22 p M xx pp =- (2.3) The budget line is a straight line with horizontal intercept 1 M p and vertical intercept 2 M p . The horizontal intercept represents the bundle that the consumer can buy if she spends her entire income on good 1. Similarly, the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on good 2. The slope of the budget line is 1 2 â€“ p p . Budget Set. Quantity of good 1 is measured along the horizontal axis and quantity of good 2 is measured along the vertical axis. Any point in the diagram represents a bundle of the two goods. The budget set consists of all points on or below the straight line having the equation p 1 x 1 + p 2 x 2 = M. 4 The goods considered in Example 2.1 were not divisible and were available only in integer units. There are many goods which are divisible in the sense that they are available in non-integer units also. It is not possible to buy half an orange or one-fourth of a banana, but it is certainly possible to buy half a kilogram of rice or one-fourth of a litre of milk. 5 In school mathematics, you have learnt the equation of a straight line as y = c + mx where c is the vertical intercept and m is the slope of the straight line. Note that equation (2.3) has the same form. Derivation of the Slope of the Budget Line The slope of the budget line measures the amount of change in good 2 required per unit of change in good 1 along the budget line. Consider any two points (x 1 , x 2 ) and (x 1 + ?x 1 , x 2 + ?x 2 ) on the budget line. a It must be the case that p 1 x 1 + p 2 x 2 = M (2.4) and p 1 (x 1 + ?x 1 ) + p 2 (x 2 + ?x 2 ) = M (2.5) © NCERT not to be republished Page 4 Chapter 2 Theor Theor Theor Theor Theory of y of y of y of y of Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods 1 . The consumer has to decide on how much of each of the different goods she would like to consume. Our objective here is to study this choice problem in some detail. As we see, the choice of the consumer depends on the alternatives that are available to her and on her tastes and preferences regarding those alternatives. To begin with, we will try to figure out a precise and convenient way of describing the available alternatives and also the tastes and preferences of the consumer. We will then use these descriptions to find out the consumerâ€™s choice in the market. Preliminary Notations and Assumptions A consumer, in general, consumes many goods; but for simplicity, we shall consider the consumerâ€™s choice problem in a situation where there are only two goods. 2 We will refer to the two goods as good 1 and good 2. Any combination of the amount of the two goods will be called a consumption bundle or, in short, a bundle. In general, we shall use the variable x 1 to denote the amount of good 1 and x 2 to denote the amount of good 2. x 1 and x 2 can be positive or zero. (x 1 , x 2 ) would mean the bundle consisting of x 1 amount of good 1 and x 2 amount of good 2. For particular values of x 1 and x 2 , (x 1 , x 2 ), would give us a particular bundle. For example, the bundle (5,10) consists of 5 units of good 1 and 10 units of good 2; the bundle (10, 5) consists of 10 units of good 1 and 5 units of good 2. 2.1 THE CONSUMERâ€™S BUDGET Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed 1 We shall use the term goods to mean goods as well as services. 2 The assumption that there are only two goods simplifies the analysis considerably and allows us to understand some important concepts by using simple diagrams. © NCERT not to be republished income and the prices of the two goods, the consumer can afford to buy only those bundles which cost her less than or equal to her income. 2.1.1 Budget Set Suppose the income of the consumer is M and the prices of the two goods are p 1 and p 2 respectively. 3 If the consumer wants to buy x 1 units of good 1, she will have to spend p 1 x 1 amount of money. Similarly, if the consumer wants to buy x 2 units of good 2, she will have to spend p 2 x 2 amount of money. Therefore, if the consumer wants to buy the bundle consisting of x 1 units of good 1 and x 2 units of good 2, she will have to spend p 1 x 1 + p 2 x 2 amount of money. She can buy this bundle only if she has at least p 1 x 1 + p 2 x 2 amount of money. Given the prices of the goods and the income of a consumer, she can choose any bundle as long as it costs less than or equal to the income she has. In other words, the consumer can buy any bundle (x 1 , x 2 ) such that p 1 x 1 + p 2 x 2 = M (2.1) The inequality (2.1) is called the consumerâ€™s budget constraint. The set of bundles available to the consumer is called the budget set. The budget set is thus the collection of all bundles that the consumer can buy with her income at the prevailing market prices. EXAMPLE 2.1 Consider, for example, a consumer who has Rs 20, and suppose, both the goods are priced at Rs 5 and are available only in integral units. The bundles that this consumer can afford to buy are: (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1) and (4, 0). Among these bundles, (0, 4), (1,3), (2, 2), (3, 1) and (4, 0) cost exactly Rs 20 and all the other bundles cost less than Rs 20. The consumer cannot afford to buy bundles like (3, 3) and (4, 5) because they cost more than Rs 20 at the prevailing prices. 3 Price of a good is the amount of money that the consumer has to pay per unit of the good she wants to buy. If rupee is the unit of money and quantity of the good is measured in kilograms, the price of good 1 being p 1 means the consumer has to pay p 1 rupees per kilograms of good 1 that she wants to buy. Spoilt for Choice 9 Theory of Consumer Behaviour © NCERT not to be republished 10 Introductory Microeconomics 2.1.2 Budget Line If both the goods are perfectly divisible 4 , the consumerâ€™s budget set would consist of all bundles (x 1 , x 2 ) such that x 1 and x 2 are any numbers greater than or equal to 0 and p 1 x 1 + p 2 x 2 = M. The budget set can be represented in a diagram as in Figure 2.1. All bundles in the positive quadrant which are on or below the line are included in the budget set. The equation of the line is p 1 x 1 + p 2 x 2 = M (2.2) The line consists of all bundles which cost exactly equal to M. This line is called the budget line. Points below the budget line represent bundles which cost strictly less than M. The equation (2.2) can also be written as 5 1 21 22 p M xx pp =- (2.3) The budget line is a straight line with horizontal intercept 1 M p and vertical intercept 2 M p . The horizontal intercept represents the bundle that the consumer can buy if she spends her entire income on good 1. Similarly, the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on good 2. The slope of the budget line is 1 2 â€“ p p . Budget Set. Quantity of good 1 is measured along the horizontal axis and quantity of good 2 is measured along the vertical axis. Any point in the diagram represents a bundle of the two goods. The budget set consists of all points on or below the straight line having the equation p 1 x 1 + p 2 x 2 = M. 4 The goods considered in Example 2.1 were not divisible and were available only in integer units. There are many goods which are divisible in the sense that they are available in non-integer units also. It is not possible to buy half an orange or one-fourth of a banana, but it is certainly possible to buy half a kilogram of rice or one-fourth of a litre of milk. 5 In school mathematics, you have learnt the equation of a straight line as y = c + mx where c is the vertical intercept and m is the slope of the straight line. Note that equation (2.3) has the same form. Derivation of the Slope of the Budget Line The slope of the budget line measures the amount of change in good 2 required per unit of change in good 1 along the budget line. Consider any two points (x 1 , x 2 ) and (x 1 + ?x 1 , x 2 + ?x 2 ) on the budget line. a It must be the case that p 1 x 1 + p 2 x 2 = M (2.4) and p 1 (x 1 + ?x 1 ) + p 2 (x 2 + ?x 2 ) = M (2.5) © NCERT not to be republished 11 Theory of Consumer Behaviour Price Ratio and the Slope of the Budget Line Think of any point on the budget line. Such a point represents a bundle which costs the consumer her entire budget. Now suppose the consumer wants to have one more unit of good 1. She can do it only if she gives up some amount of the other good. How much of good 2 does she have to give up if she wants to have an extra unit of good 1? It would depend on the prices of the two goods. A unit of good 1 costs p 1 . Therefore, she will have to reduce her expenditure on good 2 by p 1 amount. With p 1 , she could buy 1 2 p p units of good 2. Therefore, if the consumer wants to have an extra unit of good 1 when she is spending all her money, she will have to give up 1 2 p p units of good 2. In other words, in the given market conditions, the consumer can substitute good 1 for good 2 at the rate 1 2 p p . The absolute value 6 of the slope of the budget line measures the rate at which the consumer is able to substitute good 1 for good 2 when she spends her entire budget. Points Below the Budget Line Consider any point below the budget line. Such a point represents a bundle which costs less than the consumerâ€™s income. Thus, if the consumer buys such a bundle, she will have some money left over. In principle, the consumer could spend this extra money on either of the two goods, and thus, buy a bundle which consists of more of, at least, one of the goods, and no less of the other as compared to the bundle lying below the budget line. In other words, compared to a point below the budget line, there is always some bundle on the budget line which contains more of at least one of the goods and no less of the other. Figure 2.2 illustrates this fact. The point C lies below the budget line while points A and B lie on the budget line. Point A contains more of good 2 and the same amount of good Subtracting (2.4) from (2.5), we obtain p 1 ?x 1 + p 2 ?x 2 = 0 (2.6) By rearranging terms in (2.6), we obtain ? =- ? 2 1 12 x p xp (2.7) a ? (delta) is a Greek letter. In mathematics, ? is sometimes used to denote â€˜a changeâ€™. Thus, ?x 1 stands for a change in x 1 and ?x 2 stands for a change in x 2 . 6 The absolute value of a number x is equal to x if x = 0 and is equal to â€“ x if x < 0. The absolute value of x is usually denoted by |x|. A Point below the Budget Line. Compared to a point below the budget line, there is always some bundle on the budget line which contains more of at least one of the goods and no less of the other . © NCERT not to be republished Page 5 Chapter 2 Theor Theor Theor Theor Theory of y of y of y of y of Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour Consumer Behaviour In this chapter, we will study the behaviour of an individual consumer in a market for final goods 1 . The consumer has to decide on how much of each of the different goods she would like to consume. Our objective here is to study this choice problem in some detail. As we see, the choice of the consumer depends on the alternatives that are available to her and on her tastes and preferences regarding those alternatives. To begin with, we will try to figure out a precise and convenient way of describing the available alternatives and also the tastes and preferences of the consumer. We will then use these descriptions to find out the consumerâ€™s choice in the market. Preliminary Notations and Assumptions A consumer, in general, consumes many goods; but for simplicity, we shall consider the consumerâ€™s choice problem in a situation where there are only two goods. 2 We will refer to the two goods as good 1 and good 2. Any combination of the amount of the two goods will be called a consumption bundle or, in short, a bundle. In general, we shall use the variable x 1 to denote the amount of good 1 and x 2 to denote the amount of good 2. x 1 and x 2 can be positive or zero. (x 1 , x 2 ) would mean the bundle consisting of x 1 amount of good 1 and x 2 amount of good 2. For particular values of x 1 and x 2 , (x 1 , x 2 ), would give us a particular bundle. For example, the bundle (5,10) consists of 5 units of good 1 and 10 units of good 2; the bundle (10, 5) consists of 10 units of good 1 and 5 units of good 2. 2.1 THE CONSUMERâ€™S BUDGET Let us consider a consumer who has only a fixed amount of money (income) to spend on two goods the prices of which are given in the market. The consumer cannot buy any and every combination of the two goods that she may want to consume. The consumption bundles that are available to the consumer depend on the prices of the two goods and the income of the consumer. Given her fixed 1 We shall use the term goods to mean goods as well as services. 2 The assumption that there are only two goods simplifies the analysis considerably and allows us to understand some important concepts by using simple diagrams. © NCERT not to be republished income and the prices of the two goods, the consumer can afford to buy only those bundles which cost her less than or equal to her income. 2.1.1 Budget Set Suppose the income of the consumer is M and the prices of the two goods are p 1 and p 2 respectively. 3 If the consumer wants to buy x 1 units of good 1, she will have to spend p 1 x 1 amount of money. Similarly, if the consumer wants to buy x 2 units of good 2, she will have to spend p 2 x 2 amount of money. Therefore, if the consumer wants to buy the bundle consisting of x 1 units of good 1 and x 2 units of good 2, she will have to spend p 1 x 1 + p 2 x 2 amount of money. She can buy this bundle only if she has at least p 1 x 1 + p 2 x 2 amount of money. Given the prices of the goods and the income of a consumer, she can choose any bundle as long as it costs less than or equal to the income she has. In other words, the consumer can buy any bundle (x 1 , x 2 ) such that p 1 x 1 + p 2 x 2 = M (2.1) The inequality (2.1) is called the consumerâ€™s budget constraint. The set of bundles available to the consumer is called the budget set. The budget set is thus the collection of all bundles that the consumer can buy with her income at the prevailing market prices. EXAMPLE 2.1 Consider, for example, a consumer who has Rs 20, and suppose, both the goods are priced at Rs 5 and are available only in integral units. The bundles that this consumer can afford to buy are: (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1) and (4, 0). Among these bundles, (0, 4), (1,3), (2, 2), (3, 1) and (4, 0) cost exactly Rs 20 and all the other bundles cost less than Rs 20. The consumer cannot afford to buy bundles like (3, 3) and (4, 5) because they cost more than Rs 20 at the prevailing prices. 3 Price of a good is the amount of money that the consumer has to pay per unit of the good she wants to buy. If rupee is the unit of money and quantity of the good is measured in kilograms, the price of good 1 being p 1 means the consumer has to pay p 1 rupees per kilograms of good 1 that she wants to buy. Spoilt for Choice 9 Theory of Consumer Behaviour © NCERT not to be republished 10 Introductory Microeconomics 2.1.2 Budget Line If both the goods are perfectly divisible 4 , the consumerâ€™s budget set would consist of all bundles (x 1 , x 2 ) such that x 1 and x 2 are any numbers greater than or equal to 0 and p 1 x 1 + p 2 x 2 = M. The budget set can be represented in a diagram as in Figure 2.1. All bundles in the positive quadrant which are on or below the line are included in the budget set. The equation of the line is p 1 x 1 + p 2 x 2 = M (2.2) The line consists of all bundles which cost exactly equal to M. This line is called the budget line. Points below the budget line represent bundles which cost strictly less than M. The equation (2.2) can also be written as 5 1 21 22 p M xx pp =- (2.3) The budget line is a straight line with horizontal intercept 1 M p and vertical intercept 2 M p . The horizontal intercept represents the bundle that the consumer can buy if she spends her entire income on good 1. Similarly, the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on good 2. The slope of the budget line is 1 2 â€“ p p . Budget Set. Quantity of good 1 is measured along the horizontal axis and quantity of good 2 is measured along the vertical axis. Any point in the diagram represents a bundle of the two goods. The budget set consists of all points on or below the straight line having the equation p 1 x 1 + p 2 x 2 = M. 4 The goods considered in Example 2.1 were not divisible and were available only in integer units. There are many goods which are divisible in the sense that they are available in non-integer units also. It is not possible to buy half an orange or one-fourth of a banana, but it is certainly possible to buy half a kilogram of rice or one-fourth of a litre of milk. 5 In school mathematics, you have learnt the equation of a straight line as y = c + mx where c is the vertical intercept and m is the slope of the straight line. Note that equation (2.3) has the same form. Derivation of the Slope of the Budget Line The slope of the budget line measures the amount of change in good 2 required per unit of change in good 1 along the budget line. Consider any two points (x 1 , x 2 ) and (x 1 + ?x 1 , x 2 + ?x 2 ) on the budget line. a It must be the case that p 1 x 1 + p 2 x 2 = M (2.4) and p 1 (x 1 + ?x 1 ) + p 2 (x 2 + ?x 2 ) = M (2.5) © NCERT not to be republished 11 Theory of Consumer Behaviour Price Ratio and the Slope of the Budget Line Think of any point on the budget line. Such a point represents a bundle which costs the consumer her entire budget. Now suppose the consumer wants to have one more unit of good 1. She can do it only if she gives up some amount of the other good. How much of good 2 does she have to give up if she wants to have an extra unit of good 1? It would depend on the prices of the two goods. A unit of good 1 costs p 1 . Therefore, she will have to reduce her expenditure on good 2 by p 1 amount. With p 1 , she could buy 1 2 p p units of good 2. Therefore, if the consumer wants to have an extra unit of good 1 when she is spending all her money, she will have to give up 1 2 p p units of good 2. In other words, in the given market conditions, the consumer can substitute good 1 for good 2 at the rate 1 2 p p . The absolute value 6 of the slope of the budget line measures the rate at which the consumer is able to substitute good 1 for good 2 when she spends her entire budget. Points Below the Budget Line Consider any point below the budget line. Such a point represents a bundle which costs less than the consumerâ€™s income. Thus, if the consumer buys such a bundle, she will have some money left over. In principle, the consumer could spend this extra money on either of the two goods, and thus, buy a bundle which consists of more of, at least, one of the goods, and no less of the other as compared to the bundle lying below the budget line. In other words, compared to a point below the budget line, there is always some bundle on the budget line which contains more of at least one of the goods and no less of the other. Figure 2.2 illustrates this fact. The point C lies below the budget line while points A and B lie on the budget line. Point A contains more of good 2 and the same amount of good Subtracting (2.4) from (2.5), we obtain p 1 ?x 1 + p 2 ?x 2 = 0 (2.6) By rearranging terms in (2.6), we obtain ? =- ? 2 1 12 x p xp (2.7) a ? (delta) is a Greek letter. In mathematics, ? is sometimes used to denote â€˜a changeâ€™. Thus, ?x 1 stands for a change in x 1 and ?x 2 stands for a change in x 2 . 6 The absolute value of a number x is equal to x if x = 0 and is equal to â€“ x if x < 0. The absolute value of x is usually denoted by |x|. A Point below the Budget Line. Compared to a point below the budget line, there is always some bundle on the budget line which contains more of at least one of the goods and no less of the other . © NCERT not to be republished 12 Introductory Microeconomics Changes in the Set of Available Bundles of Goods Resulting from Changes in the Consumerâ€™s Income. A decrease in income causes a parallel inward shift of the budget line as in panel (a). An increase in income causes a parallel outward shift of the budget line as in panel (b). 1 as compared to point C. Point B contains more of good 1 and the same amount of good 2 as compared to point C. Any other point on the line segment â€˜ABâ€™ represents a bundle which has more of both the goods compared to C. 2.1.3 Changes in the Budget Set The set of available bundles depends on the prices of the two goods and the income of the consumer. When the price of either of the goods or the consumerâ€™s income changes, the set of available bundles is also likely to change. Suppose the consumerâ€™s income changes from M to M ' but the prices of the two goods remain unchanged. With the new income, the consumer can afford to buy all bundles (x 1 , x 2 ) such that p 1 x 1 + p 2 x 2 = M '. Now the equation of the budget line is p 1 x 1 + p 2 x 2 = M ' (2.8) Equation (2.8) can also be written as 1 21 22 â€“ p M' xx pp = (2.9) Note that the slope of the new budget line is the same as the slope of the budget line prior to the change in the consumerâ€™s income. However, the vertical intercept has changed after the change in income. If there is an increase in the income, i.e. if M' > M, the vertical intercept increases, there is a parallel outward shift of the budget line. If the income increases, the consumer can buy more of the goods at the prevailing market prices. Similarly, if the income goes down, i.e. if M' < M, the vertical intercept decreases, and hence, there is a parallel inward shift of the budget line. If income goes down, the availability of goods goes down. Changes in the set of available bundles resulting from changes in consumerâ€™s income when the prices of the two goods remain unchanged are shown in Figure 2.3. Now suppose the price of good 1 changes from p 1 to p' 1 but the price of good 2 and the consumerâ€™s income remain unchanged. At the new price of good 1, the consumer can afford to buy all bundles (x 1 ,x 2 ) such that p' 1 x 1 + p 2 x 2 = M. The equation of the budget line is p' 1 x 1 + p 2 x 2 = M (2.10) © NCERT not to be republishedRead More

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