APPLIED ECONOMICS FOR BUSINESS MANAGEMENT Review Lecture

APPLIED ECONOMICS FOR BUSINESS MANAGEMENT • Review Lecture # 2 • Go over Homework Sets #1 & #2 • Consumer Behavior

Lecture Outline: • Review • Homework Sets #1 & #2 • Consumer Behavior

Consumer Behavior: Recall from introductory economics, for competitive markets, the interaction of demand supply determines market price. Let’s examine demand first.

Consumer Behavior 3 Characteristics of Consumer Behavior: (i) consumers spend everything they earn on goods and services. Note: savings and investments are considered to be goods which provide services, such as, increasing one’s wealth or taking precautions against future uncertainties. Money income is spent on: food, clothing, shelter, medicine, entertainment, savings, ………. etc.

Consumer Behavior 3 Characteristics of Consumer Behavior: (i) consumers spend everything they earn on goods and services. (ii) consumers prefer more to less. However, consumers do not buy infinite quantities of goods because they have a limited amount of money income.

Consumer Behavior 3 Characteristics of Consumer Behavior: (i) consumers spend everything they earn on goods and services. (ii) consumers prefer more to less. So consumers have a constraint, an income or budget constraint, which limits the number of commodities/services they can purchase while trying to maximize their utility or satisfaction derived from these commodities/services.

Consumer Behavior What is utility? Utility is the satisfaction which a good or service yields.

Consumer Behavior 3 Characteristics of Consumer Behavior: (i) consumers spend everything they earn on goods and services. (ii) consumers prefer more to less. (iii) Another noticeable feature of consumer behavior is that income is not spent on only a single item, rather a variety of goods and services are purchased. The reason for this behavior is the law of diminishing marginal utility.

Consumer Behavior Law of Diminishing Marginal Utility The law of diminishing marginal utility states that as individuals consume additional units of a specific commodity, consumption of other goods and services unchanged, the amount of satisfaction derived from each additional unit of that good decreases. Note: total utility or satisfaction increases but the additional utility (called marginal utility) declines.

Preferences In a given time period, the individual or household will consume a variety of commodities and will express a preference in consuming these items. The objective of the consumer is to maximize utility for a given level of income. In order to attain this objective, the consumer must be able to rank different commodity bundles.

Preferences Example: Let A, B, and C represent different commodity bundles. Notation: A & B are indifferent.

Ordering Preferences We have the following postulates (rules) for ordering preferences: (i) Consumers have the ability to rank commodities. For any given set of commodities, the consumer is able to determine which commodity bundle provides the most satisfaction.

Ordering Preferences We have the following postulates (rules) for ordering preferences: (i) Consumers have the ability to rank commodities. (ii) Antisymmetry in ordering i. e. , if (iii) Transitivity in ordering i. e. , if

Ordering Preferences (i) Consumers have the ability to rank commodities. (ii) Antisymmetry in ordering i. e. , if (iii) Transitivity in ordering i. e. , if These 3 postulates are the necessary and sufficient conditions for the consumer to be able to order preferences.

Utility Function The analysis of consumer behavior is greatly facilitated by the use of an utility function. Consider the following utility function: where U = utility = commodities

Utility Function We assume that the utility function is continuous. This means that for any level of y 1 and y 2, we can determine a level of utility or satisfaction. Also, this utility function is twice differentiable, i. e. , first and second order direct and cross partials exist (need this to derive optimal consumption bundles).

Utility Function If (where utils is the measure of satisfaction), this can be achieved by various combinations of and . For instance, if the exact utility function can be written as:

Utility Function then

Indifference Curve These combinations of and yield a given level of satisfaction (i. e ). So the indifference curve for can be graphed as follows: An indifference curve is a curve or a locus of point which shows combination of commodities that yield the consumer the same amount of satisfaction or utility.

Indifference Curve An indifference curve map can be shown as follows: Commodity combinations on yield greater satisfaction than any combination on . Likewise any combination on yields greater utility than any combination on .

Indifference Curve Characteristics of indifference curves: 1. Downward sloping to the right. 2. Convex to the origin (or concave upward). 3. Cannot intersect one another.

Indifference Curve What does downward to the right imply? Examine the previous graph: giving up for more . What about convex to the origin? Concave upward.

Concavity This also shows that as more are given up, the consumer must be compensated with increasing additions of .

Concavity We often call this feature: diminishing marginal utility (MU). Additional units of are worth less in terms of . So we have diminishing MU of .

Concavity If the indifference curve had this shape: As more are given up, the consumer must be compensated with less . So additional units of are worth more to the consumer.

Indifference Curve Indifference curves cannot intersect one another: Cannot have this case. Why? Reason #1: For point A, what level of satisfaction? 22 or 25 utils?

Indifference Curve Reason #2: Point C has greater satisfaction than point B, however, point C consumes less y 2 than point B.

Utility Function Let Take total differential:

Indifference Curve Recall for an indifference curve, Note: points along this indifference curve yield a constant amount of satisfaction Gain in utility from consuming more Loss in utility from giving up

RCS gain = loss keep utility constant Also, We call the slope of the indifference curve, the rate of commodity substitution (RCS).

RCS The RCS shows substitutability of for . So The RCS measures the substitution of for as we move down along the indifference curve. or negatively sloped indifference curve. The RCS is often called the marginal rate of substitution (MRS). and are used interchangeably.

Budget Constraint Money income is a constraint to consumer purchases – a consumer has a limited amount of income. In the sample case of two commodities, if the consumer spends his/her income in purchasing and , we have the following budget line:

Budget Constraint If income and , then how are the axes point determined? Another way of asking the question: What are the maximum quantities of and that can be purchased by this consumer given commodity prices and his/her budget of $100? By spending all his/her income on ,

Budget Constraint Likewise if he/she spend all of the income on then he/she could purchase So we know two points on the budget line

Budget Constraint Using these two points, we can find the slope of the budget line:

Budget Constraint Another way to show this: Take total differential: Note: Since and are given,

Consumer Equilibrium Consumer equilibrium occurs where the budget constraint is tangent to the indifference curve. At point E, the indifference curve is tangent to the budget line, i. e. , the slope of the indifference curve is equal to the slope of the budget line.

Consumer Equilibrium Another way of saying this is the rate at which the consumer is willing to substitute for is equal to the rate at which the market permits the substitution of for . In other words, E is where: The rational consumer desires to purchase and such that his/her utility is maximized subject to his/ her income or budget constraint.

Consumer Equilibrium Given and Max utility subject to the budget constraint: where λ is the Lagrange multiplier 1 st order condition:

Consumer Equilibrium Rearranging terms:

Consumer Equilibrium Recall and So So the critical values are those values of and such that the indifference curve is tangent to the budget constraint (i. e. , point E or the consumer equilibrium point)

Marginal Utility of Income What is λ? which is the change in utility due to a change in income. So, λ is the marginal utility of income ( ) For the 2 nd order condition:

Example Suppose that a consumer has the following utility function: where and are two commodities Assume also that the consumer has a budget of $100 to spend on and . The market prices for and are: and

Find the consumer equilibrium point where he/she maximizes utility subject to the budget constraint. Solving these two equations for λ:

Also, Substituting the value of

Or critical values: , and

2 nd order condition: Expand by 1 st row:

So what does the solution look like graphically…. and

So if all income is spent on purchasing , the maximum amount of the commodity purchased =

If all income is spent on purchases , then the maximum amount purchased = The consumer maximizes utility subject to his income or budget constraint at point E.

What is the level of consumer satisfaction or utility at point E ?

Now, suppose the increases to , ceteris paribus (all other things constant). Determine the new consumer equilibrium level for and . Redo the optimization procedure:

So critical values: , and . 2 nd order conditions to verify utility max subject to budget constraint Expand by 1 st row: critical values represent a rel max

Graphically, we can show what has happened. increases from to

If consumer spent all income on