The Market Supply & Demand & all that

The Big Picture DemandSupply The Market Q Q Q P P P Equilibrium Price & Quantity

Demand  Analysis based on individuals' behavior, then summing of individuals into aggregate demand at various prices  Explanations  Verbal: quantity demanded changes inversely w/price  Simple graph: downward sloping curve of P vs Q  Graphic derivation: from preferences  Mathematical specification: D = f(P)  Axiomatic derivation

Indifference Curves - I Quantity of Good 1 Demanded (Q 1 ) Quant. of Good 2 Dem. (Q 2 ) I 1 < I 2 < I 3 O P1P1 qq'q" higher levels of preference higher levels of utility NB: under usual assumptions: 1. Q 1 and Q 2 are infinitely divisible, so: infinite # of smooth curves 2. curves are open, I.e., you always prefer MORE of everything Two space defines various combinations of Q 1 & Q 2 that you might choose. Some (Q 1, Q 1 ) you prefer to others, some you prefer less, some alternatives leave you indifferent. An “indifference curve” is defined by set of combinations among which you are indifferent.

Indifference Curves - II Quantity of Good 1 Demanded (Q 1 ) Quant. of Good 2 Dem. (Q 2 ) I 1 < I 2 < I 3 O P1P1 qq'q" NB: if you drop the assumption that you always prefer MORE of everything, then at some point curves close, and MORE would mean a lower level of utility

Budget Line - I Q1Q1 Q2Q2 NB: if you spend less than M, you will be at some point under the budget line in the space defined by 0,q 1,q 2. O Available budget (money) = M with prices of Q 1 = P 1, Q 2 = P 2 so, total expenditure = M = P 1 Q 1 +P 2 Q 2 which defines the “budget line.” If you rewrite M = P 1 Q 1 +P 2 Q 2 as Q 2 = (1/ P 2 )M - (P 1 / P 2 ) Q 1 you can see that the slope of the line = P 1 / P 2 (and is negative) q1q1 q2q2 If all M spent on Q 2 then you would be at q 2. If all M spent on Q 1 then you would be at q 1.

Budget Lines - II If income (M) increases, budget line shifts right Q1Q1 O P1P1 M' =P 1 Q 1 +P 2 Q 2 M=P 1 Q 1 +P 2 Q 2 If M' > M, then line shifts right. Q2Q2

Budget Lines - III If P 1 increases, budget line intercept shifts left Q1Q1 Q2Q2 O If P1 increases, max Q 1 falls (Change in P1 would have no effect on vertical intercept if all M spent on Q 2 ) If P1<P1’, then intercept shifts left.If P 2 /P 1 changes, slope changes

Utility Maximization I3I3 O M=P 1 Q 1 +P 2 Q 2 q Q2Q2 Q1Q1 To Maximize utility you will want to be on highest possible I. Highest possible I will be that which is tangent to budget line.

Graphic Derivation of Demand Curve Demand Curve shows what happens to quantity demanded as price changes. So we raise P 1 and see what happens to Q 1 Quantity of Good 1 Demanded (Q 1 ) I 1 < I 2 < I 3 O As price rises, P 1 < P 1 '< P 1 ”, quantity demanded falls, q to q’ to q” and the combinations of P 1 and q define a demand curve for Q1. P1"P1" P1'P1' qq'q" P1"P1" P1'P1' P1P1 qq" q' P1P1

Mathematical Specification of Demand Curves D = f(P) dD/dP < 0  D/  P < 0 Linear Demand Functions D = a - bP D = P

Axiomatic Derivation  Subset of Assumptions  A > B, A B, A < B, A = B  axiom of transitivity  axiom of asymmetry  comparability  egotism, no one else's consumption matters to you  continuity (continuous curves, eg., indifference curves  insatiability (no maximium, always want more)

Utility  Indifference Curves defined by:  preference - further from origin prefered  utility - further from origin, higher utility  Utility = satisfaction derived from consumption  Utility derived from "utilitarians" - Eng. Philos.  all action taken with view to utility to be derived  measured by "utils"  cardinality  law of diminishing marginal utility (maybe!)  Utility functions: U = f(x 1, x 2,.... x n )

Problem w/utility  Cardinality  you can compare utility for different people  interpersonal comparisons  Law of Diminishing Mar. Utility  how much utility depended upon how much you have  Cardinality + Law of Diminishing Utility  total social utility would increase through redistribution of money from rich to poor  a political problem! Solution: shift to ordinality( ±)  utility theory replaced by preference theory

Supply  Analysis based on each firm's behavior, then summing of firms into aggregate supply at various prices  Explanations  Verbal: quantity supplied changes directly w/price  Simple graph: upward sloping curve of P vs Q  Graphic derivation: from costs + profit maximization  Mathematical specification: S = f(P)  Axiomatic derivation

Costs average cost Marginal cost (MC) price given = marginal revenue (MR) quantity produced Price, costs Profit Maximization occurs where MC = MR

Derivation of Supply Curve Marginal cost (MC) = S quantity produced Price, costs Profit Maximization occurs where MC = MR P2 P3 P1 q1q2q3

Mathematical Specification S = f(P) dS/dP > 0  S/  P > 0 Linear Supply Functions S = a + bP S = P

Axiomatic Derivation  Subset of axioms  Existence of Production  There exists some attainable element x that can be transformed into y  Neutrality of Transformations  any two transformations T are indifferent  their inputs are indifferent and their outputs are indifferent  Convexity  Production set Y j is convex

Change in Technology  Improvements in Technology that lower costs of production, shift MC curve down, and Supply curve to Right MC/SMC'/S' marginal cost shifts down Supply shifts to the right

Equilibrium  Shapes of S & D guarantee "equilibrium", i.e., tendency to return to price that equalizes them Demand Supply equilibrium price equilibrium quantity excess supply Q P

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