APPLIED ECONOMICS FOR BUSINESS MANAGEMENT

Lecture # 2

• Review

• Go over Homework Sets #1 & #2

• Consumer Behavior

APPLIED ECONOMICS FOR BUSINESS MANAGEMENT

Lecture Outline:

• Review • Homework Sets #1 & #2 • Consumer Behavior

Consumer Behavior:

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

Consumer Behavior3 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.


(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.


(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 BehaviorWhat is utility?

Utility is the satisfaction which a good or service yields.


(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 BehaviorLaw 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.

PreferencesExample:

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.


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


(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 FunctionThe 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 y1 and y2, 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:

then

Utility Function

Indifference CurveThese 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.

Commodity combinations on yield greater satisfaction than any combination on .Likewise any combination on yields greater utility than any combination on .

Indifference Curve

An indifference curve map can be shown as follows:

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 .

As more are given up, the consumer must be compensated with less . So additional units of are worth more to the consumer.

Concavity

If the indifference curve had this shape:

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 y2 than point B.

Utility Function

Let Take total differential:

Loss in utility from giving up

Gain in utility from consuming

more

Indifference Curve

Recall for an indifference curve, Note: points along this indifference curve yield a constant amount of satisfaction

RCS

gain = loss keep utility constantAlso,

We call the slope of the indifference curve, the rate of commodity substitution (RCS).

The RCS measures the substitution of for as we move down along the indifference curve.

The RCS shows substitutability of for . RCS

So

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:

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 ,

If income and and , then how are the axes point determined?Budget Constraint

Budget ConstraintLikewise 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:

Take total differential:Note: Since and are given,

Budget Constraint

Another way to show this:

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.


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 andsuch that his/her utility is maximized subject to his/her income or budget constraint.


Given andMax utility subject to the budget constraint:where λ is the Lagrange multiplier 1st order condition:


Rearranging terms:


Recall andSoSo the critical values are those values of andsuch 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 2nd order condition:

Suppose that a consumer has the following utility function:where and are two commodities

Example

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

Orcritical values: , and

2nd order condition:

Expand by 1st 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 . 2nd order conditions to verify utility max subject to budget constraint

Expand by 1st row:

critical values represent a rel max

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

If consumer spent all income on

If consumer spent all income on

Documents

APPLIED ECONOMICS FOR BUSINESS MANAGEMENT