Chapter 2: Modeling Individual Choice

1. 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.

2. Another Economic Fundamental: Rationality • Rationality – the behavior of economic units (i.e. individuals, firms, government) reflects the pursuit of an underlying goal.

3. The “Underlying Goals” in Rational Economic Behavior • Based 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).

4. Individual Choice in Buying Goods:Theory • Individuals 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.

5. 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.

6. 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.

7. 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

8. 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.

9. 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

10. My Marginal Utility From Coffee (All Else Constant) Coffee (Cups)UtilityMarginal 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

11. 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.

12. Utility and Marginal Utility: Multiple Goods • My 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.

13. Condition for Maximizing Utility, No Scarcity of Goods • I 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.

14. Maximizing Utility With Scarcity and Finite Budget • Scarcity  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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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).

20. 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.

21. 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).

22. 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.

23. 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

24. 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

25. 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

26. The “Relevant Region” of Production and Employment • Increased 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.

27. 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.

28. 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)?

29. 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

30. 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.

31. 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%

32. 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.

33. 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).

34. Complexity #2 – Risk and Uncertainty • Key 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.

35. 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.

36. Conclusions – Economic Decisions • Intertemporal 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.