Eco 2- Choice and the Engel Curve PDF

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Chapter 7 : Consumer Choice How many choices do you make per day? Have you ever thought or even calculated how many different choices you make per day, or even per minute? If you really think about it, you may even make a number of choices at the same time. These choices range from : deciding on what time you should wake up in the morning or what you should have for breakfast or even if you feel like having breakfast. Choices may even include what you should bring with you to the next lecture or what you should wear. One can easily conclude that in our daily lives, we are all bombarded with a number of choices. In Economics, the main choice that we focus on is what a consumer should choose to consume. In the previous chapters (i.e. chapter 4-6), focus was placed on the consumption bundles that the consumer can afford to purchase (i.e. via the budget line) and the consumption bundles that a consumer is willing to consume (i.e. via the indifference curve). However, the question that needs to be asked is: How does a consumer make a choice? The answer is that the consumer will have to look at the consumption bundles he or she is willing to consume and the consumption bundles that he or she can afford to consume. This will be the focus of this chapter. In addition, consumer choice is affected by two main factors. They are: changes in money income and changes in price. This chapter will also examine how consumer choice is affected by changes in money income. How changes in price affect the consumer choice will be dealt with in the next chapter After reading this chapter, the learner should be able to: 1. Illustrate and explain how consumer choice is made. 2. Distinguish between the different types of goods 3. Understand how the income consumption curve is derived for a normal good and an inferior good. 4. Derive an Engel Curve for a normal good and an inferior good. 5. Illustrate and explain how a Backward Bending Engel Curve is derived. 7.1 Optimal Choice Allocation Figure 7.1.1 : Consumer Choice is found at A where the indifference curve is tangent to the budget line. Good Y

M1/Py1 D B B IC1 A IC2

C

IC1 E BL1 M1/Px1

Good X

As discussed earlier, when making a choice, a consumer needs to take into account the consumption bundles that he or she can afford and the consumption bundles that he or she is willing to consume. The consumption bundles that the consumer can afford are represented by the budget line. This implies that in determining what the consumer can afford, the consumer’s money income and the price of the good, need to be taken into account. The consumption bundles that the consumer is willing to consume are represented by the indifference curves (and consumer preferences). This implies that in determining what the consumer is willing to consume, the consumer needs to consider his or her indifference curves. Therefore, in order to make an optimal choice, the consumer’s budget line needs to be joined with their indifference curves. Figure 7.1 shows how the budget line is joined with the indifference curves in order to make an optimal choice. The consumer will optimize his or her choice at point A. This is where the indifference curve is tangent to the budget line. If two curves or a curve and a line are tangent, it means that the slopes of the curves and/ or lines are the same. Therefore, the slope of the budget line is equal to the slope of the indifference curve. This is expressed in the following equation:

MU x −P x =MRS= ………..(7.1.1) MU y Py In equation 7.1.1, the right hand side of the equation represents the slope of the budget line (BL 1) and the left hand side of the equation represents the slope of the indifference curve (IC 1). Optimal choice is made at point A or the point where the indifference curve is tangent to the budget line. However, if point A represents the optimal choice allocation, what can we say about point D, E, B or C? Can optimal choice be made at these points? To answer this, let us take each of these points and discuss whether they could possibly be an optimal choice allocation. Starting with point B, it is evident from figure 7.1.1 that even though point B lies on the highest indifference curve, it is greater than the budget line (BL1). This means that even though the consumer would be willing to consume at point B, thus, allowing the consumer to obtain the highest level of utility, the consumer unable to consume at point B. This is because with reference to the budget line (BL 1), point B lies in the area /region of infeasibility. Therefore, a choice cannot be made at point B. Let us now consider point C. This point is on the lowest indifference curve (IC1). The consumer can afford to consume at point C, as the budget line (BL1) is higher than the indifference curve. The consumer could choose to consume at point C. However, the consumer would most probably prefer to consume at point A. This is because point A lies on a higher indifference curve (IC2) and, thus, yields a higher level of utility than that of point C. Therefore, the consumer will choose to consume at point A rather than point C. What about point D and point E? Both point D and point E intersect the budget line (BL 1). This shows that the consumer is able to consume these consumption bundles. However, they will not constitute optimal choice for the consumer. This is because both point D and point E lie on a lower indifference curve (IC1) compared to point A. Consumers will most probably wish to rather consume at point A where the utility is greater and the consumer is on a higher indifference curve.

Box 7.1 : Consumer Choice: an Algebraic Interpretation Algebra can also be used to formulate the consumer’s choice problem. Before examining the algebraic interpretation, it is necessary to make the following assumptions: i. there are two goods (i.e. good X and good Y) ii. M denotes money income.

iii. iv.

Px denotes the price of good X. Py denotes the price of good Y.

In order to determine the optimal choice allocation, one needs to consider both the slope of the budget line and the slope of the indifference curve. Starting with the budget line, the budget line can be represented by the following equation: M= Px (X) + Py (Y)….. (7.1.2) Equation 7.1.2 implies that the consumer takes into account their money income and the price of good X and the price of good X when making a choice. In addition, the consumer is spending all of their money income on the respective goods. It is important to note that it is assumed that optimal choice occurs on the budget line. Therefore, only consumption bundles that lie on the budget line, are considered .Equation 7.1.2 reveals the consumption bundles that the consumer can afford. We now need focus on the consumption bundles that the consumer is willing to consume. It is, therefore, necessary to first look at the consumer’s utility function and then the slope of the indifference curve. The consumer’s utility function is represented by the following equation: U =u(X,Y) ….. ……….(7.1.3) Equation 7.1.3 indicates the utility derived from the consumption of both good X and good Y. It is important to note that

max =X .Y

In section 5.3, the slope of the indifference curve was defined.

X ,Y

In addition, it was concluded that the marginal rate of substitution (i.e. slope of the indifference curve) could be expressed as follows:

( )( )

−dY ∂ U ∂U = / dX ∂X ∂Y

……………(7.1.4)

The left hand side of equation 7.1.4 represents the slope of the indifference curve in terms of the quantity change in the consumption of good X and good Y. The right hand side of equation 7.1.4 is expressed in terms of the marginal utility of good X (i.e. (i.e.

∂U ) and the marginal utility of good Y ∂X

∂U ). Equation 7.1.4 indicates that the slope of the indifference curve (i.e. left hand side of ∂Y

the equation) is equal to the inverse relationship of the marginal utilities of the goods. In order to determine the optimal choice allocation, the consumer has to maximize equation 7.1.2 subject to equation 7.1.3 and 7.1. The first step is in this process is to re-look at equation 7.1.5 and determine the value of good Y. This is accomplished as follows: Px(X) +Py(Y) =M……………………(7.1.5) Py(Y) =M-Px (X) ……………………(7.1.6) Y=

M −P x (X ) ……………………………..(7.1.7) Py

Equation 7.1.7 can be expressed as follows:

Y=

M Px − X ………….………(7.1.8) Py P y

In order to determine the optimal choice allocation, equation 7.1.8 is substituted into equation 7.1.3. This results in the following equation:

max X . X

(

)

Px M Px − X = .(X . M −X 2 ) ………….(7.1.9) Py Px Py P y

Equation 7.1.9 is then re-written as follows:

M 2 M 2 M 2 ¿ −( ¿ + X . −X ) 2 Px Px 2 Px ¿ ……….(7.1.10) M 2 max X X . −X =¿ Py X

(

)

However, it is important to take note that:

M 2 M 2 ¿ +X . −X Px 2 Px M 2 −X ¿ 2 Px M 2 ¿ −¿ 2 Px M 2 ¿ −(¿)=¿ 2 Px ¿ max X ¿ X

As a result, optimal choice is expressed as follows:

M 2 −X¿ 2 Px ………………………………………(7.1.11) min ¿ X

What can we conclude from this? The optimal choice allocation can be solved by: X=

M 2 PX

and Y =

M 2 PY

7.2 The Corner Solution An interior solution – an optimal choice allocation that consists of the consumption of more than one good.

A corner solution – an optimal choice allocation that consists of the consumption of only one good.

In section 7.1, the optimal choice allocation was determined by an allocation where the indiffernce is tangent to the budget line.It was also noted that the optimal choice allocation point represented a combination of the consumption of good X and good Y. This type of optimal choice allocation is

referred to as an interior solution.However, what happens if the consumer decides to consume only one of the goods. For example, Sikelela can decide to spend her income on the consumption of food and/ or clothing. If Sikelelwa spent all her income on say 10 items of clothing and 5 items of food, this would represent an interior solution as described in the previous section. What would happen if Sikelelwa spent all of her income of clothing? What would her optimum choice look like? Sikelelwa’s choice would be represented by a corner solution. This is illustrated in the figure 7.2 below. Place figure here 7.2 here

In figure 7.2 above, clothing is on the vertical axis and food is on the horizontal axis. Sikelelwa spends her entire money income on clothng. This is shown by point A in figure 7.2 above. It is important to note that with a corner solution, the indifference curve touches the budget line BL 1 at point A. As a result no food is consumed. Only clothing is consumed. Therefore, Sikelela spends all of her money income on clothing and spends none of her money income on food. In the corner solution the indifference curve touches the budget line. This is different from the interior solution as there is no tangency between the indiffereence curve and budget line. This implies that the slope of the indifference curve and budget line are not equal to each other.Is a corner solution an optimal choice allocation ? The answer is no. This is because that by the indifference curve merely touching the indifference curve, there is no form of tangency. Does there have to be tangency? The answer to this is yes. In order for a choice allocation to be optimal, there must be tangency between the indifference curve and the budget line. Hence, the slope of the indifference curve and the budget line must be equal (i.e. (-px/py) = MRSxy). If this condition does not hold, the choice allocation is not an optimal allocation. 7.3 ) Different Types of Goods A normal good - a good that the consumer will consume more of as the consumer’s money income increases. An inferior good - a good that the consumer will consume more of as the consumer’s money income increases. A Giffen good - a special type of inferior good that defies the Law of Demand.

In order to examine the effects of a change in the consumer’s money income (which is dealt with in section 7.4 and 7.5) or the price of a good (which will be dealt with in chapter 8) on the optimal choice allocation, we need to identify what type of good we are dealing with. The types of goods that we will be discussing are: normal goods, inferior goods, Giffen goods and Veblen goods. It is important to note here that when changes in money income are examined, reference is only made to

normal goods and inferior goods. However, when the effects of changes in price of a good are examined, reference is only made to normal goods, inferior goods and Giffen goods. What are these different types of goods? A normal good is a good that the consumer will consume more of as the consumer’s money income increases. Examples of normal goods are: red meat, pizza, dvd’s, playstation games. As the consumer’s money income increases, the consumer will consume more of these goods. As the consumer’s money income decreases, the consumer will consumer will consume less of these goods. For example, Natasha is currently earning R 2000 a month. Since Natasha’s money income is relatively low, she shops for clothing at the “Cheap-Cheap Store” (a clothing store where the average price of clothing items is R 20). In addition, Natasha mainly eats bread, potatoes and pilchards. Natasha receives a promotion and now earns R 20 000 per month. Will she still shop at the “Cheap-Cheap Store”? Will Natasha still mainly eat bread, potatoes and pilchards? The answer is no. When Natasha’s money income increases, she will most probably afford to purchase more expensive clothing and food items. Natasha will probably purchase her clothes from an exclusive boutique and her main meals will consist of more expensive food items such as red meat, prawns and exclusive pizzas. An inferior good is a good that the consumer will consume less of as the consumer’s money income increases. Examples of inferior goods include: pilchards, maize, paraffin, matches, a t-shirt purchased for R20 at a clothing store. As the consumer’s money income increases, the consumer will purchase less of these goods (because the consumer is consuming more normal goods). If the consumer’s money income decreases, the consumer will consume more inferior goods. This is probably because these are the only goods that the consumer can afford. It is important to note that an inferior good is not necessarily a bad good. Remember that a bad good is a good that will cause the consumer’s utility to decrease as more of the good is consumed. This is not the case with an inferior good. The consumer does enjoy consuming an inferior good and the consumer’s utility will probably increase if he or she consumed potatoes or maize. What distinguishes an inferior good from other goods is that fact that it is a good that is predominantly consumed at low levels of income. For example, Linda is currently a student majoring in Economics. Her meals mainly consist of Kwik-kwik noodles (a simple noodle meal that costs R1 per packet). Linda places the Kwik-kwik noodles in a mug, adds hot water and then seasons with the meal with inexpensive tomato sauce (which costs R 2 per bottle). In this example, the Kwik-kwik noodles and the inexpensive tomato sauce are inferior goods. This is because as a student, Linda’s money income is very low. However, when Linda graduates with her Honours Degree in Economics and starts working at Bank X, her meals mainly consist of steak, lamb chops and gourmet vegetables. This shows that as Linda’s money income increases, she will consume more normal goods (i.e. steak, lamb chops and gourmet vegetables) and less inferior goods (i.e. Kwik-kwik noodles and inexpensive tomato sauce). If Linda is retrenched due to downsizing at Bank X, her money income will decrease. As a result, she will probably go back to consuming more inferior goods and less normal goods. This is not to say that the inferior goods are bad goods because Linda still enjoys eating the Kwik-kwik noodles and inexpensive tomato sauce. It is important to note that a bad good is only a good that will decrease the consumer’s utility if the consumer consumes more of that good that he or she dislikes. In no way is Linda’s utility decreasing because she consumes more inferior goods at a lower level of income. An important feature of normal goods and inferior goods is that they both obey the Law of Demand. You will remember that as we discussed in the previous chapter, the Law of Demand states that if price increases, the quantity of demand of the good will decrease. Similarly, if the price of the good decreases, the quantity demanded of the good will increase. Although both the normal and inferior good obey the Law of Demand, there are goods that will defy the Law of Demand. These goods are:

Giffen goods and Veblen goods. A Giffen good is defined as a special type of inferior good that defies the Law of Demand. Therefore, if the price of a Giffen good increases, the quantity demanded of the good will increase. Similarly, if the price of a Giffen good decreases, the quantity demanded of the good will decrease. A Giffen good is a staple good and it is also a good that has very few substitutes. We will continue our discussion of Giffen goods when we deal with changes in the price of goods in chapter 8. 7.3 ) The Engel Curve An Engel Curve - shows how the consumption of a good may change due to changes in money income.

An Income Consumption Curve - shows how the consumption of good X and the optimal choice allocation may change due to changes in money income.

An Engel Curve shows how the consumption of a good may change due to changes in money income. An Engel Curve is derived from an Income Consumption Curve. An Income Consumption Curve shows how the consumption of good X and the optimal choice allocation may change due to changes in money income. Before, examining the derivation of an Engel Curve for a normal good and an inferior good, it is necessary to first analyze what is meant by an Income Consumption Curve and, thus, how changes in money income will affect the optimal choice allocations. It is important to note in this section that changes in money income have nothing to do with the Law of Demand. This is because both Engle Curves and Income Consumption Curves only focus on changes in money income. 7.3.1) The Income Consumption Curve for a Normal Good and an Inferior Good An Income Consumption Curve shows how the consumption of good X and the optimal choice allocation may change due to changes in money income. This section will focus on the derivation of the income consumption curve for a normal good and an inferior good. Figure 7.3.1 below illustrates an income consumption curve for a normal good.

Insert figure 7.3.1.1 here

vc

Figure 7.3.1.1 reveals the derivation of the Income Consumption Curve for a normal good. An increase in money income will cause the budget line (BL 1) to shift parallel to the right to BL 2. Since good X is a normal good, consumption of the good will increase from x 1 to x2. A further increase in money income will cause the budget line to shift to the right from BL 2 to BL3. Since good X is a normal good, consumption of the good will increase from x 2 to x3. An additional increase in money income will cause the budget line to shift to the right from BL 3 to BL4. Since good X is a normal good, consumption of the good will increase from x 3 to x 4. Points A, B, C and D are joined by an income consumption curve. This curve joins the combinations of good x and good y as money income increases. The income consumption curve for a normal good is positively sloped. What will the income consumption curve for an inferior good look like? Figure 7.3.2 below illustrates an income consumption curve for an inferior good. Insert figure 7.3.1.2 here

Figure 7.3.1.2 reveals the...