The Theory of Individual Economic Behavior (Ch. 4) Unit 3. The Theory of Individual Economic Behavior (Ch. 4)

Budget Constraint The maximum Q combinations of goods that can be purchased given one’s income and the prices of the goods.

Budget Constraint Variables I (or M) = the amount of income or money that a consumer has to spend on specified goods and services. X = the quantity of one specific good or one specific bundle of goods Y = the quantity of a second specific good or second specific bundle of goods Px = the price or per unit cost of X PY = the price or per unit cost of Y

Budget Line Equation Income = expenses I = PxX+PYY Y = l/PY – (Px/PY)X  straight line equation  vert axis intercept = I/PY  slope = dY/dX = -Px/PY

The Opportunity Set

Budget Line: Axis Intercepts & Slope Vertical Axis Intercept = I/PY = max Y (X = 0) Horizontal Axis Intercept = I/PX = max X (Y = 0) - Slope = PX/PY = ‘inverse’ P ratio = X axis good P/Y axis good P = Y/X

Budget Line Slope Equation: ¯Slope = ¯ rate at which y CAN be exchanged for x (holding $ expenses constant) = e.g. => 2y can be exchanged for 1x

Changes in the Budget Line Changes in Income - Increases lead to a parallel, outward shift in the budget line. - Decreases lead to a parallel, downward shift.

Changes in the Budget Line Changes in Price - A decrease in the price of good X rotates the budget line counter- clockwise. - An increase rotates the budget line clockwise.

Your Preferences? A: 1 drink, 1 pizza slice A: 1 movie, 1 dinner Lunch B: 1 drink, 2 pizza slices C: 2 drinks, 1 pizza slice Entertainment A: 1 movie, 1 dinner B: 1 movie, 2 dinners C: 2 movies, 1 dinner For each, indicate which of the following you prefer: A vs B, B vs C, A vs C

Utility Concepts Utility: satisfaction received from consuming goods Cardinal utility: satisfaction levels that can be measured or specified with numbers (units = ‘utils’) Ordinal utility: satisfaction levels that can be ordered or ranked Marginal utility: the additional utility received per unit of additional unit of an item consumed (U/ X)

An Understanding of Concepts Related to Indifference Curves and Utility Should Help One: Get along better with other people, by doing things that increase their utility. Make better business decisions that result in improved customer satisfaction and, thus, more sales. Understand what motivates people and why they behave the way they do, including how people are likely to respond to economic changes.

Utility Assumptions Complete (or continuous)  can rank all bundles of goods Consistent (or transitive)  preference orderings are logical and consistent Consumptive (nonsatiation)  more of a ‘normal’ good is preferred to less

More of a Good is Preferred to Less The shaded area represents those combinations of X and Y that are unambiguously preferred to the combination X*, Y*. Ceteris paribus, individuals prefer more of any good rather than less. Combinations identified by “?” involve ambiguous changes in welfare since they contain more of one good and less of the other.

Indifference Curve Analysis A curve that defines the combinations of 2 or more goods that give a consumer the same level of satisfaction. Marginal Rate of Substitution The rate at which a consumer is willing to substitute one good for another and stay at the same satisfaction level.

Investment Alternatives Fund Return Safety A 2.89% Hi B 6.59% Med C 7.29% Low

1. Ida Dontcare is indifferent regarding all three investment alternatives. U(A) = U(B) = U(C)

2. Ralph Returnman prefers C over B and prefers B over A. U(C) > U(B) > U(A)

3. Sally Safetyfirst prefers A over B and prefers B over C. U(A) > U(B) > U(C)

MRS & MU MRS = - slope of indifference curve = -Y/ X = the rate at which a consumer is willing to exchange Y for 1more (or less) unit of X U = 0 along given indiff curve = MUx(X)+MUY(Y) = 0 = - Y/ X = MUx/MUY = - slope = inverse MU ratio

Indifference Curve Shape Slope = MRS = marginal rate of substitution = Rate at which consumer is willing to exchange y for x = ΔY/ΔX Two ways to calculate: 1) Given utility function equation, derive inverse MU ratio =

=> Willing to exchange 2y for 1x 2) Given indifference curve equation, derive ¯dy/dx directly. e.g. 1) 2) => Willing to exchange 2y for 1x

Types of Goods & Utility Functions Normal Perfect Substitutes Perfect Complements

Normal Goods = goods for which a consumer’s willingness to exchange one good for another varies depending on Q’s of each Represented by U = xαYB

Perfect Substitutes (= a constant) = goods for which a consumer is willing to exchange one good for another at a constant rate.  Represented by U = αx + BY Equation of indifferent curve = (= a constant)

Perfect Complements = goods that are used in fixed or constant proportions with one another Represented by U = min [αX, βY] A consumer’s U = whichever is the least, αX or βY too much of one good without more of the other good will not increase one’s utility values where αX = βY lie along line (solve for Y) where Y = (α/β)X

Non ‘Goods’ & Indifference Curves 1 Good and 1 ‘Neutral’ 1 Good and 1 ‘Bad’

Utility Maximization Words Spend one’s income so as to get the most satisfaction possible Graph Go to the highest indifference curve that is within reach of the budget line Math Normal goods: point of tangency (equal slopes condition) between budget line and highest attainable indifference curve Perfect substitutes: corner solution normally; if slope of budget line flatter than slope of indifference curves => All X; else => All Y Perfect complements; pt. of intersection between budget line and line through vertex pts of indifference curves

Consumer Equilibrium (U Max) The equilibrium consumption bundle is the affordable bundle that yields the highest level of satisfaction.

Equal Slopes Condition (for consumer equilibrium) MUX/MUY = PX/PY MUX/PX = MUY/PY

Consumer Equilibrium (Perfect Substitutes)

Consumer Equilibrium (Perfect Complements)

Changes in Price Substitute Goods Complementary Goods An increase (decrease) in the price of good X leads to an increase (decrease) in the consumption of good Y. Complementary Goods An increase (decrease) in the price of good X leads to a decrease (increase) in the consumption of good Y.

Complementary Goods

Changes in Income Normal Goods Inferior Goods Good X is a normal good if an increase (decrease) in income leads to an increase (decrease) in its consumption. Inferior Goods Good X is an inferior good if an increase (decrease) in income leads to a decrease (increase) in its consumption.

Normal Goods

Figure 4-13. An increase in the price of good X leads to a substitution effect (A to B) and an income effect (B to C). Substitution effect – The movement along a given indifference curve that results from a change in the relative prices of goods, holding real income constant. Income effect – The movement from one indifference curve to another that results from the change in real income caused by a price change.

Individual Demand Curve An individual’s demand curve is derived from each new equilibrium point found on the indifference curve as the price of good X is varied.

Market Demand The market demand curve is the horizontal summation of individual demand curves. It indicates the total quantity all consumers would purchase at each price point.

A Classic Marketing Application

Variables: W = hrs/day worked (labored) L = hrs/day leisured (happy) Note: L = 24 – W P = hourly wage or ‘pay’ rate Q = consumer good quantity C = price per unit of Q N = nonlabor income

Constraint: expenses = income CQ = N + PW  Q = (N + 24P)/C – (P/C)L If C = 1, Q = (N + 24P) - PL

Intertemporal Choice Model Inter  between; temporal  time pds Time pds  current (0) or next yr (1) Variables: C0 and C1 = Q of goods consumed I0 and I1 = income levels P = price of consumer goods (P0 = P1) r = interest rate Objective (goal) = Max U = f(C0, C1) Constraint: PV of Income = PV of Expenses

Intertemporal Saving & Borrowing Facts If you save an extra $ (i.e. reduce current pd consumption by a $), you can INCREASE future pd consumption by the FV of the $. If you borrow a $ against your future income (i.e. agree to pay back a $ principal and interest), you can INCREASE current pd consumption by the PV of the $.

Math Summary of Intertemporal Choice Problem Max U (C0, C1) Subj. to PV of income = PV of expenses

Intertemporal Choice Problem Graph