Chapter 2: Modeling Individual Choice zPurposes of Chapter zVenture into microeconomics. zExamining the economic decision process of consumers, a key component.

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Chapter 2: Modeling Individual Choice zPurposes of Chapter zVenture into microeconomics. zExamining 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 zRationality – the behavior of economic units (i.e. individuals, firms, government) reflects the pursuit of an underlying goal.

The “Underlying Goals” in Rational Economic Behavior zBased upon values, what the economic unit (consumer, firm, government) holds to be important. zVaries across different units. zTypically includes one or more constraints, reflecting scarcity. zGenerally phrased in terms of “maximizing” or “minimizing,” possibly subject to (constraint).

Individual Choice in Buying Goods:Theory zIndividuals want to be as happy as possible. zIndividuals gain happiness from the consumption of goods. zThe more consumption the better, at least to a satiation point. zThe happiness we gain becomes less and less as we consume more and more of any good.

Individual Choice in Buying Goods:Model zUtility – happiness that individuals feel (measured in “utils”). zUtility – caused by levels of the various goods that we consume. zUtility Function – A explicit relationship which specifies the level of utility based upon the amounts of all the goods that we consume.

Marginal Utility zMarginal Utility (MU) -- the change in utility (U) resulting from a change in the quantity of an individual good (Q) consumed. zIn mathematical terms, MU = ΔU/ΔQ.

Positive and Diminishing Marginal Utility zThe more consumption the better, i.e. Q   U ,  Positive Marginal Utility zThe 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 zSuppose I get utility from consuming coffee (and other goods). zSuppose 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 zCeteris Paribus – Latin term, meaning “all else constant,” or in the context of theories and models, “all other causes constant”. zFundamental concept in theories and models: most behavior has multiple causes. zOne 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 Goods zMy utility is determined by consumption of a number of goods (call it n goods). zNotation: Q 1 = quantity consumed of good 1, Q 2 = quantity consumed of good 2, etc. MU 1 = marginal utility of good 1, MU 2 = marginal utility of good 2, etc.

Condition for Maximizing Utility, No Scarcity of Goods zI can have as much as I want of any good for free. zThen to maximize utility, I should choose to consume quantities of each good until each of their marginal utilities equals zero. zIn mathematical notation: I choose quantities of goods so that MU 1 = MU 2 = MU 3 = … = MU n = 0.

Maximizing Utility With Scarcity and Finite Budget zScarcity  every good as a price. zNotation: P 1 = price of good 1, P 2 = price of good 2, etc. zA related issue: finite budget: I have so much I can spend. zAlso called Budget Constraint.

Maximizing Utility: Scarcity and Finite Budget zThen 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. MU 1 /P 1 = MU 2 /P 2 = … = MU n /P n.

An Example zSuppose my world has two goods, steak dinners (S) and bottled water (W), and I get similar utility from consumption of each one. zThe price of a steak dinner (P S ) equals \$25, while the price of bottled water (P W ) equals \$1.

Maximizing Utility Subject to Budget Constraint zI should seek to consume quantities of steak dinners and water so that I spend my entire budget and MU S /P S = MU W /P W, or equivalently MU S /\$25 = MU W /\$1.

The Solution zThus, 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. zDiminishing 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 zThe Production Function – A relationship for the individual firm that specifies how inputs (natural resources, labor, and capital) are combined to produce output. zCapital – physical capital (machines) and human capital (skills, innate and acquired).

Marginal Product of Labor zMarginal Product of Labor (MP N ) -- the change in output (Q) resulting from a change in the amount of labor employed (N), ceteris paribus on the other inputs. zIn mathematical terms, MP N = ΔQ/ΔN.

The Law of Diminishing Returns zThe 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 zSuppose King David’s (a Marshall Street eatery) employs labor and other inputs (e.g. food, electricity, cooking machines) to produce lunches. zSuppose 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) MP N 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? zAssumption: King David’s seeks to maximize profits. zTherefore, not enough information for them to make this decision. zNeed 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 Employment zIncreased usage of inputs, ceteris paribus, imply more output, i.e. N   Q ,  Positive Marginal Product of Labor. zThe Law of Diminishing Returns has set in, i.e. N   MP N ,  Diminishing Marginal Product of Labor.

Additional Complexities in the Economic Decision Process zRealistically, life places complexities that influence the rational economic decisions of both consumers and firms. zHere, we just introduce two of them and motivate how they can be influential.

Complexity #1 – The Present Versus The Future zConsumers: Should I buy and/or work now or later (existence of interest on savings, investment in human capital)? zFirms: Should I expand my physical capital by buying this machine (trading current costs versus future benefits)?

Intertemporal Decisions zIntertemporal Decisions – rational economic plans for consumers and firms in assessing the future along with the present. zMechanisms for weighing the present versus the future. yThe Discount Rate yPresent Value

The Discount Rate zThe Discount Rate – the rate, in percentage terms, that we are willing to trade off money received one year from now versus money received today. zEquivalent amounts received today and in the future are worth more today – need to discount future amounts.

The Discount Rate: An Example zSuppose 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. zYour discount rate = [(\$360  \$300)/(\$300)]x100% = 20%

Characteristics of the Discount Rate zConsumers – depends upon different individual’s utility or preferences. yHigh Discount Rate: devalues the future sharply, “wants it now”. yLow Discount Rate: more willing to forego the present for the future. zFirms – the market interest rate is their ultimate discount rate.

Present Value zPresent Value – an explicit formula for converting the value of dollars received in future years to their current value equivalents. zHugely important in many aspects of financial world (interest rates).

Complexity #2 – Risk and Uncertainty zKey Issue: future is unknown, affects economic decisions. zRisk – unknown events to which we can attach a probability. zUncertainty – absolutely un-thought of events which may end up occurring. zUncertain events which in fact occur will convert into risky events.

Incorporating Risk in Economic Decisions zWe develop expectations of unknown events – our best guess of what we think will happen, then we act upon those (right or wrong). zWe practice risk aversion – of different events with the same expected return, we prefer less risk.

Conclusions – Economic Decisions zIntertemporal issues and risk/uncertainty place complexities on the rational decisions of consumers, firms, and even government zWe won’t use them explicitly here, the basics still tell us a lot. zWe covered the decision rule for consumers, for firms we got the process started.

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