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© Consumer Equilibrium Key Points * Cardinal vs. ordinal utility and how they measure satisfaction. * The law of diminishing marginal utility and its role in stopping consumption. + Single-commodity and two-commedity equilibrium conditions. + Budget-line shifts and rotations, and how they affect the optimal bundle. © Consumer Basics Consumer - any individual or group of people who purchases goods or services to satisfy wants and achieve satisfaction (utility). « A consumer can be one person or a collection of people. + Consumption yields full satisfaction only when the need is completely met. © Utility Concepts @ Cardinal (Alfred Marshall) Utility Utility measured in imaginary units called utils; allows numeric comparison of satisfaction levels. + Example: © First slice of pizza > 20 utils © Second slice > 16 utils © Third slice > 10 utils © Fourth slice > 4 utils @ Ordinal (Marginal) Utility Focuses on the rank order of preferences; does not assign numeric values. + Introduced by Hicks & Allen. + Uses marginal utility (MU) to capture extra satisfaction from one additional unit. lal Total and Marginal Utility Quantity (Units) Total Utility (TU) Marginal Utility (MU = ATU/AQ) 1 20 20 2 36 (20+16) 16 3 46 (36+10) 10 4 50 (46+4) 4 5 50 (no change) 0 (point of saturation) 6+ \ (negative) negative (diminishing) * Total Utility (TU) = sum of utils from each consumed unit. * Marginal Utility (MU) = additional utility from the next unit: —_A MU=5 + Point of Saturation occurs when MU = 0; beyond this, MU becomes negative. ‘\ Law of Diminishing Marginal Utility (First Law of Consumer Choice) As aconsumer continues to consume more units of a commodity, the marginal utility from each additional unit declines. « Illustrated with samosa example: ° First samosa > high satisfaction (16 utils) « Rational Consumer: e Able to compare utilities and prices. © Chooses the bundle that maximizes satisfaction. « Fixed Income: © Income level does not change during the decision period. « No Change in Quality: © All units of a good are identical in quality; only quantity varies. * Continuous Consumption: ° No large time gaps between consumption of successive units. // Graphical Insight + TUcurve rises steeply at first, then flattens, reaching a maximum (saturation point). « MU curve starts high, declines with each unit, crosses the price line at equilibrium, then falls to zero and becomes negative. « Key points on the graph: 0 MU=P > equilibrium. eo MU =0 > saturation point. ° Negative MU > over-consumption, loss of satisfaction. | Practical Illustrations « Pizza slices - utility values illustrate diminishing returns. + Samosa binge - after a few, extra samosas cause discomfort (negative MU). + Water bottles - each successive bottle provides less additional thirst relief. These examples reinforce how real-world consumption aligns with the theoretical concepts of utility, marginal utility, and consumer equilibrium. 42 Dual-Commodity Consumer Equilibrium (Two-Good Case) Consumer equilibrium with two goods occurs when the consumer allocates income such that the marginal utility per rupee spent on each good is identical. « Equilibrium condition MUx, _, MUy Py 39 Py « When this equality holds, the consumer cannot increase total utility by shifting spending from one good to the other. Example: Apples (X) and Bananas (Y) Quantity of X MU_X Quantity of Y MU_Y (apples) (bananas) 1 20 1 16 2 14 2 12 3 12 3 8 + At the third bundle (3 apples, 3 bananas), the marginal utilities are both 12, so if the prices are equal (e.g., %1 per unit), the condition B_R 17 1 is satisfied - the consumer is at the equilibrium point. + Notice that quantities differ across goods; the equality is about ratios, not absolute quantities. // Indifference (Difference) Curves & Preference Mapping An indifference curve (called a difference curve in the lecture) is the collection of all consumption bundles that give the consumer the same level of satisfaction. + Key properties discovered in the transcript: 1. Non-intersection - two distinct indifference curves never cross. If they did, a bundle would provide two different utility levels attractive. * This leads to indifference curves that are convex, ensuring that the optimal consumption point (where a budget line just touches a curve) is unique. ® Budget Constraint & Budget Set The budget line shows all combinations of two goods that exhaust the consumer’s income. « Algebraic form Px X34+;PyY;s;1 where (I) is total income. + Budget set: the collection of all affordable bundles, i.e., all points on or below the budget line. Visual Description from Lecture + Points on the line (e.g., ((5\text{ apples},0)) or ((0,4\text{ bananas}))) represent full expenditure. + Points inside the line (e.g., ((2\text{ apples}, 1\text{ banana})) when (I) is larger) represent partial spending - the consumer still has leftover money. Example with Numbers « Income (I = 220) * Prices: (P_X = %1) (apple), (P_Y = 22) (banana) e Budget line: (1\cdot X + 2\cdot Y = 20) © Intercepts: = (X)-intercept (Y =0): (X = 20) apples = (Y)-intercept (X =0): (Y = 10) bananas * Any bundle like ((12\text{ apples},4\text{ bananas})) lies on the line because (12 + 2-4 = 20). + A bundle ((8\text{ apples},3\text{ bananas})) lies inside the set, costing (8 + 2.3 = 14 < 20). Relationship Between Indifference Curves and the Budget Line « The optimal consumption bundle is where the budget line is tangent to the highest reachable indifference curve. « Tangency condition (derived from equality of slopes): MUx _ MUy =k Po = Re <— MRSxyy = Pe « At this point, the consumer cannot improve utility by either: 1. Shifting spending between goods (would break the equality). 2. Changing the total amount spent (would move to a lower indifference curve). yf Key Takeaways (Bullet Summary) + Dual-commodity equilibrium requires equal marginal utility per rupee across goods. + Indifference curves (difference curves) map equal-utility bundles; they are non-intersecting, higher = better, and convex due to diminishing MRS. + Monotonic preferences drive consumers to favor larger quantities; convexity reflects desire for balanced consumption. * The budget line ((P_X X + P_Y Y =1)) delineates affordable bundles; the budget set includes all points on or below it. + Optimal choice occurs at the tangency of the budget line and the highest attainable indifference curve, satisfying both the equilibrium condition and the MRS-price ratio equality. ‘\ Slope of the Budget Line Definition - The slope of the budget line is the market rate of exchange between the two goods, i.e. the amount of good Y that must be given up to obtain one more unit of good X. Rotation (Pivot) of the Budget Line (Price Changes) Rotation - A pivot of the budget line around the intercept of the good whose price stays fixed, triggered by a change in the price of the other good. 1. Price of Good X falls ((P_X\downarrow)) + New slope: (-\frac{P_X*{\text{new}}}{P_Y}) becomes flatter (numerically smaller). « The line rotates outward to the right because the consumer can now buy more X for the same amount of Y. 2. Price of Good X rises ((P_X\uparrow)) + Slope steepens (more negative). « The line rotates inward to the left, reflecting fewer affordable X units. 3. Symmetric cases for Good Y + A fall in (P_Y) pivots the line outward upward (more Y affordable). + Arise in (P_Y) pivots it inward downward. Numeric pivot example (price change only) * Original: (P_X = 2), (P_Y = 2), (I = 20) > (;2X + 2Y = 20) > intercepts (X=10), (Y=10). + (P_X) drops to (1) (Y price unchanged): (1X + 2Y = 20). o New X-intercept (=20) (double), Y-intercept unchanged at (10). © The line pivots rightward around the Y-intercept. Thus, income changes cause parallel shifts, whereas price changes cause rotations of the budget line. « Practical Implications for Consumer Equilibrium 1. After an income increase the budget line shifts outward; the tangency point with the highest reachable indifference curve moves to a bundle with more of both goods (provided preferences are monotonic). 2. After a price fall of X the line pivots outward; the new tangency typically features a higher quantity of X and possibly a different quantity of Y, depending on the shape of the indifference curves. 3. General equilibrium condition (re-stated for clarity): Px may stay the same (income change) or change (price change). MUy _ MUy Py <= MRSxy = « When the budget line shifts or rotates, the RHS ((\frac{P_X}{P_Y})) + The consumer re-optimizes by moving to the new point where the marginal utility per rupee is again equal across goods. iu] Summary Table of Budget-Line Transformations Trigger Income * Income v (P_X) v (P_X) t (P_Y) + Budget-line response Parallel rightward shift Parallel leftward shift Pivot rightward around Y-intercept Pivot leftward around Y-intercept Pivot upward around X-intercept Slope change? No (price ratio unchanged) No Flatter (less negative) Steeper (more negative) Flatter (less negative) Intercepts change? Both (X)- and (Y)-intercepts increase Both intercepts decrease x-intercept increases, Y-intercept same X-intercept decreases, Y-intercept same Y-intercept increases, X-intercept same Typical consumer response Purchase more of both goods Purchase fewer of both goods Buy more X, adjust Y Buy less X, possibly more Y Buy more Y, adjust X 
