Consumption Theory: Consumer Choice and Economic Constraints

Consumer's Choice

In economic theory, consumer choices are defined by two sets of elements:

Economic Constraints

Consumer decisions are constrained by their economic resources, specifically their income. By considering the prices of goods and their disposable income, consumers can determine which combinations of goods they can afford to purchase.

Consumer's Preferences

Preferences indicate a consumer's desires by determining which combination of goods, among all those that can actually be purchased, will be preferred in relation to the satisfaction of needs.

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Economic Constraints

• Assuming a consumer has an income of Y and needs to purchase two goods - good A and good B - knowing their respective prices PA and PB.

... Then the consumer has a variety of combinations of goods to choose from. For instance:

Good B A C B Good A Sports Economics - Consumer Choice 3

Economic Constraints Budget Line

• By joining the points representing all possible purchase alternatives given by a complete use of the income, we obtain the segment AB which represents the budget line of the consumer:

Good B A C B Good A Sports Economics - Consumer Choice 4

Economic Constraints on Expenditure

• For an individual consumer, income is a constraint because it represents the maximum expenditure that can be made to purchase these two goods A and B.
• The budget constraint of the consumer can be represented as follows:

Y = PA * A + PB * B = S where A and B represent the number of unit consumed of good A and good B.

• The above formula implies that the total expenditure (S) required to purchase goods A and B at the price PA and PB should not exceed the value of income (Y).

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Economic Constraints and Feasibility

V

• Allocations of goods, beyond the budget line (i.e., point F) are not feasible for the consumer as they exceed the consumer's income.
• Purchases for which consumers leave part of their income unused, represented by points inside the possibility constraint (i.e., point D) are feasible but not efficient.
• The set of baskets accessible using the full income (i.e., point E), represented by the points along the straight line, are feasible and efficient.

Good B Fo Do E Good A Sports Economics - Consumer Choice 6

Economic Constraints (V) Budget Constraint Rewritten

• By applying some simple algebraic steps, the budget constraint can be rewritten as follows:

Y B = − A PB PA PB . Where -- represents the vertical intercept and -A represents the PB PB slope of the budget constraint Sports Economics - Consumer Choice 7

Economic Constraints and Maximum Quantities

V

• The intercepts of the budget line on the axes identify the maximum quantities that can be purchased of each of the two goods.
• To calculate this quantity for good B, for instance, simply substitute A with 0 in the equation of the budget line and solve for B.

Good B Y/PB Y/PA D Good A Sports Economics - Consumer Choice 8

Economic Constraints and Slope

V

• The ratio of the two prices determines the slope of the budget constraint.

− PA PB . The budget line has a negative slope because, given a fixed income, a consumer can only purchase more of one good by reducing the quantity of the other.

• Therefore, the slope of the budget line represents the opportunity cost of one good in terms of the other.

Good B PA − PB Good A Sports Economics - Consumer Choice 9

Economic Constraint Changes (I)

. The budget constraint is changed if one of the two determining factors changes:

• Income
• Prices of goods
• An increase in income results in a rise in purchasing power, allowing the consumer to purchase more of both goods at the same prices. Geometrically, an increase in income causes the budget line to shift rightward. And viceversa, a decreasing in income reduces consumer's purchasing power so that the consumer can purchase less of both goods and the budget line shifts leftward.

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Economic Constraint Changes with Income

An increase of income Good B A reduction of income Good B Good A Good A Sports Economics - Consumer Choice 11

Economic Constraint Changes (I) with Price

• Assuming ceteris paribus income, an increase in the price (PA), leads to a decrease in the demand for good A. As a consequence, see the graph on the left, the ratio:

• PA increases, while the ratio PA Y decreases PB

• And similarly, when the price (PB) increases, then the demand for good B decreases and the ratio:

• PA decreases, while the ratio Y increases PA

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Economic Constraint Changes with Price

An increase of PA An increase of PB Good B Good A Y Y PA PA Good B Y PB Y PB Good A Sports Economics - Consumer Choice 13

Consumer's Preferences

• Consumers' choices are the result of not only budget constraints, but also of consumer's preferences
• How does a consumer choose between the various consumption alternatives available?
• In analysing consumer preferences, economics uses an ordinal approach.

. This means that an individual is able to construct a ranking between the various consumption options Sports Economics - Consumer Choice 14

Consumer's Preferences Ordinality

• The hypothesis underlying consumer's preferences is:
• Preferences are ordinal this implies that:

If preferences were cardinal, it would be possible to assign a numerical value to each basket and order them accordingly. However, since they are ordinal, it is only possible to rank them in order. Sports Economics - Consumer Choice 15

Consumer's Preferences Axioms

• The axioms of consumer's preferences are:

1. Completeness: A consumer should be able to order all available alternatives, meaning that he/she may decide if he/she prefers the basket A or basket B or is indifferent between A and B.
2. Transitivity: Given three baskets, if A is preferred to B, and B is preferred to C, then A should be preferred to C. This means that preferences of a consumer are consistent.
3. Monotonicity: The consumer should prefer a larger quantity of a good to a smaller quantity, meaning that more of a good is better.

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Consumer's Preferences and Utility Function

V

• The previous assumptions allow us to write a consumer's preferences in the form of a utility function:

Ui = U (A, B, ... , Z)

. This means that an individual can exchange baskets in terms of composition while maintaining their level of utility: indifference curve. Sports Economics - Consumer Choice 17

Indifference Curve: Construction (I)

• Given a series of baskets, we may compare them with respect to basket A1 and say:
• Basket A1 is preferred to baskets B1 and B2

. Baskets C1 and C2 are preferred to basket A1

· Baskets A2 and A3 are indifferent to basket A1

Good B + C2 A3 · C1 · A1 . B1 A2 B2 Good A Sports Economics - Consumer Choice 18

Indifference Curve: Construction (II)

• Combining the indifferent baskets gives an indifference curve

. This curve indicates all combinations of Good A and Good B between which the consumer is indifferent

Good B C2 A3 · C1 A1 . B1 A2 B2 Good A Sports Economics - Consumer Choice 19

Indifference Curve: Construction and Preferences

Good B Preferred baskets Not Preferred baskets Indifferent baskets Good A

• The consumer prefers baskets above the indifference curve to those on the curve

. The consumer prefers the baskets on the curve to those below the curve

. The consumer is indifferent to all baskets on the curve Sports Economics - Consumer Choice 20

Indifference Curve: Characteristics (I)

• Indifference curves have two main characteristics:

1) They are decreasing: negative slope 2) They are convex towards the origin of the axes: diminishing marginal rate of substitution

• As a consequence ....
• Indifference curves cannot intersect as they represent different levels of utility, and any intersection would violate preference axioms.

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Indifference Curve: Characteristics (II) Negative Slope

• Negative slope: An indifference curve has a negative slope because it represents the union of baskets with constant utility. To maintain consumer's utility at a constant level, an increase in the consumption of Good A always results in a decrease in the consumption of the other good (Good B).

Good B A B Good A Sports Economics - Consumer Choice 22

Indifference Curve: Characteristics Convexity

• Convexity: According to the diminishing slope of an indifference curve, as the consumer moves from left to right along the indifference curve, he/she will gradually be willing to give up less and less of Good B in order to have an additional unit of Good A.

Good B - - Good A Sports Economics - Consumer Choice 23

Marginal Rate of Substitution (MRS)

• The Marginal Rate of Substitution (MRS) measures the number of units of one good that a consumer is willing to forego in order to obtain an additional unit of the other good, while maintaining the same level of satisfaction/utility.
• The MRS is equal to the ratio of the quantity changes of the two goods along the indifference curve.

ΔΒ MRS = LA Good B Z ABZ ΔΑΖ Y ABY ΔΑΥ Good A Sports Economics - Consumer Choice 24

Indifference Curve Maps

• Baskets on the same indifference curve provide the same level of satisfaction, indicating equal total utility
• Baskets on different indifference curves provide varying levels of total utility.
• Each indifference curve is associated with a different utility index, which can be ordered to obtain a bundle of indifference curve defined as:

MAP OF INDIFFERENCE CURVES. Sports Economics - Consumer Choice 25

Indifference Curve Maps and Utility Levels

• Indifference curves cannot intersect as they represent different levels of utility

Good B

. Curves that are further away from the axis origin are preferred over those that are closer to it.

U4 U3 U2 U. Good A Sports Economics - Consumer Choice 26

A Consumer Optimum (I)

Good B

• Among the available baskets within the budget set, which is the one the consumer will choose?
• The consumer will choose the basket that allows him/her to reach the highest indifference curve, the one furthest from the origin of the axes

Good A Sports Economics - Consumer Choice 27

A Consumer Optimum (II)

• The optimal choice for the consumer is the combination of goods where the budget constraint is tangent to the indifference curve.

. Therefore, the slopes of the budget line and the indifference curve are equal at the point of optimum.

• The slope of the budget line reflects the ratio between prices, while the slope of the indifference curve corresponds to the MRS:

PA PB = MRS Sports Economics - Consumer Choice 28