Chapter 2: Modeling Individual Choice

Purposes of Chapter

Venture into microeconomics.Examining the economic decision

process of consumers, a key component of the economic decision process of firms, and several complexities in modeling human behavior.

Another Economic Fundamental: Rationality

Rationality – the behavior of economic units (i.e. individuals, firms, government) reflects the pursuit of an underlying goal.

The “Underlying Goals” in Rational Economic BehaviorBased upon values, what the economic

unit (consumer, firm, government) holds to be important.

Varies across different units.Typically includes one or more

constraints, reflecting scarcity.Generally phrased in terms of

“maximizing” or “minimizing,” possibly subject to (constraint).

Individual Choice in Buying Goods:TheoryIndividuals want to be as happy as

possible.Individuals gain happiness from the

consumption of goods.The more consumption the better, at least

to a satiation point. The happiness we gain becomes less and

less as we consume more and more of any good.

Individual Choice in Buying Goods:Model

Utility – happiness that individuals feel (measured in “utils”).

Utility – caused by levels of the various goods that we consume.

Utility Function – A explicit relationship which specifies the level of utility based upon the amounts of all the goods that we consume.

Marginal Utility

Marginal Utility (MU) -- the change in utility (U) resulting from a change in the quantity of an individual good (Q) consumed.

In mathematical terms,

MU = ΔU/ΔQ.

Positive and Diminishing Marginal Utility

The more consumption the better, i.e. Q U, Positive Marginal Utility

The happiness we gain becomes less and less as we consume more and more of any good

i.e. Q MU, Diminishing Marginal Utility

Utility and Marginal Utility: An Example

Suppose I get utility from consuming coffee (and other goods).

Suppose my utility from coffee, holding consumption of all other goods constant, looks as follows.

My Utility From Coffee (All Other Goods Constant) Coffee (Cups) Utility (Utils) 0 0 1 100 2 185 3 245 4 295 5 325 6 340 7 340 8 320

My Marginal Utility From Coffee (All Else Constant) Coffee (Cups) Utility Marginal Utility 0 0 -- 1 100 100 2 185 85 3 245 60 4 295 50 5 325 30 6 340 15 7 340 0 8 320 -20

Ceteris Paribus

Ceteris Paribus – Latin term, meaning “all else constant,” or in the context of theories and models, “all other causes constant”.

Fundamental concept in theories and models: most behavior has multiple causes.

One can only look sensibly at responses to changes in one cause at a time, therefore one needs to hold others constant.

Utility and Marginal Utility: Multiple GoodsMy utility is determined by consumption

of a number of goods (call it n goods).

Notation:

Q1 = quantity consumed of good 1,

Q2 = quantity consumed of good 2, etc.

MU1 = marginal utility of good 1,

MU2 = marginal utility of good 2, etc.

Condition for Maximizing Utility, No Scarcity of GoodsI can have as much as I want of any good

for free.Then to maximize utility, I should choose to

consume quantities of each good until each of their marginal utilities equals zero.

In mathematical notation: I choose quantities of goods so that

MU1 = MU2 = MU3 = … = MUn = 0.

Maximizing Utility With Scarcity and Finite BudgetScarcity every good as a price.Notation:

P1 = price of good 1,

P2 = price of good 2, etc.

A related issue: finite budget: I have so much I can spend.Also called Budget Constraint.

Maximizing Utility: Scarcity and Finite Budget

Then to maximize utility subject to being within my budget constraint, I should choose to consume quantities of each good according to two conditions.

(1) I spend my entire budget. (2) The “marginal benefit-cost ratio” is equal across all goods, i.e.

MU1/P1 = MU2/P2 = … = MUn/Pn.

An Example

Suppose my world has two goods, steak dinners (S) and bottled water (W), and I get similar utility from consumption of each one.

The price of a steak dinner (PS) equals $25, while the price of bottled water (PW) equals $1.

Maximizing Utility Subject to Budget Constraint

I should seek to consume quantities of steak dinners and water so that I spend my entire budget and

MUS/PS = MUW/PW, or equivalently

MUS/$25 = MUW/$1.

The Solution

Thus, I should choose my consumption of steak dinners and water where the marginal utility of steak dinners is 25 times the marginal utility of water.

Diminishing marginal utility for both steak dinners and water I should consume a small amount of steak dinners and a lot of water.

Behavior of the Firm: The Production Function

The Production Function – A relationship for the individual firm that specifies how inputs (natural resources, labor, and capital) are combined to produce output.

Capital – physical capital (machines) and human capital (skills, innate and acquired).

Marginal Product of Labor

Marginal Product of Labor (MPN) -- the change in output (Q) resulting from a change in the amount of labor employed (N), ceteris paribus on the other inputs.

In mathematical terms,

MPN = ΔQ/ΔN.

The Law of Diminishing Returns

The Law of Diminishing Returns – as a firm uses more and more of a given input such as labor, ceteris paribus on the other inputs, there will come a time when the marginal product of labor will decrease (i.e. Diminishing Marginal Product of Labor).

Production and Marginal Product: An Example

Suppose King David’s (a Marshall Street eatery) employs labor and other inputs (e.g. food, electricity, cooking machines) to produce lunches.

Suppose their production function with labor, ceteris paribus on the other inputs, looks as follows.

King David’s Production Function Labor Input (People) Output (Lunches) 0 0 1 10 2 25 3 50 4 70 5 86 6 95 7 101 8 104 9 93

King David’s Marginal Product of Labor Labor Input (N) Output (Q) MPN 0 0 -- 1 10 10 2 25 15 3 50 25 4 70 20 5 86 16 6 95 9 7 101 6 8 104 3 9 93 -11

So How Much Should King David’s Produce and Employ?

Assumption: King David’s seeks to maximize profits.

Therefore, not enough information for them to make this decision.

Need additional information on: -- cost per unit of each input

-- price of their output -- market structure, or degree of competitiveness with other lunch eateries

The “Relevant Region” of Production and EmploymentIncreased usage of inputs, ceteris paribus,

imply more output, i.e. N Q, Positive Marginal Product of Labor.

The Law of Diminishing Returns has set in, i.e. N MPN,

Diminishing Marginal Product of Labor.

Additional Complexities in the Economic Decision Process

Realistically, life places complexities that influence the rational economic decisions of both consumers and firms.

Here, we just introduce two of them and motivate how they can be influential.

Complexity #1 – The Present Versus The Future

Consumers: Should I buy and/or work now or later (existence of interest on savings, investment in human capital)?

Firms: Should I expand my physical capital by buying this machine (trading current costs versus future benefits)?

Intertemporal Decisions

Intertemporal Decisions – rational economic plans for consumers and firms in assessing the future along with the present.

Mechanisms for weighing the present versus the future. The Discount Rate Present Value

The Discount Rate

The Discount Rate – the rate, in percentage terms, that we are willing to trade off money received one year from now versus money received today.

Equivalent amounts received today and in the future are worth more today – need to discount future amounts.

The Discount Rate: An Example

Suppose you have a choice between $300 today and a higher amount next year. Suppose as well that you decide that you’re indifferent between $300 today and $360 next year.

Your discount rate = [($360 $300)/($300)]x100% = 20%

Characteristics of the Discount Rate

Consumers – depends upon different individual’s utility or preferences. High Discount Rate: devalues the future

sharply, “wants it now”. Low Discount Rate: more willing to forego

the present for the future.Firms – the market interest rate is their

ultimate discount rate.

Present Value

Present Value – an explicit formula for converting the value of dollars received in future years to their current value equivalents.

Hugely important in many aspects of financial world (interest rates).

Complexity #2 – Risk and UncertaintyKey Issue: future is unknown, affects

economic decisions.

Risk – unknown events to which we can attach a probability.

Uncertainty – absolutely un-thought of events which may end up occurring.

Uncertain events which in fact occur will convert into risky events.

Incorporating Riskin Economic Decisions

We develop expectations of unknown events – our best guess of what we think will happen, then we act upon those (right or wrong).

We practice risk aversion – of different events with the same expected return, we prefer less risk.

Conclusions – Economic DecisionsIntertemporal issues and

risk/uncertainty place complexities on the rational decisions of consumers, firms, and even government

We won’t use them explicitly here, the basics still tell us a lot.

We covered the decision rule for consumers, for firms we got the process started.