Consumer theory
Tastes and circumstances affect our consumption behaviour
Budget constraints
● Income (M) and prices affect consumer demand
○ Income can be exogenous or endogenous
● The feasible set - the quantity of goods that can be bought
given prices and income
M
● The maximum amount that can be bought of x1 is
P1
● The price ratio = the slope of the budget constraint
○ The slope measures the opportunity cost of consuming good 1
Δ x2 −p1
○ =
Δ x1 p2
● Bundles below the budget constraint is affordable
○ A bundle on the budget constraint is just affordable
● The budget constraint shifts inwards if income falls or prices rise
Preferences
● Preferences are described by utility functions
● Completeness - the consumer can compare bundles and make a decision
● Transitivity - if X>Y and Y>Z, then X>Z
○ Allows relationships to be drawn between different goods
● Completeness and transitivity give us rational behaviour
● Continuity - if X>Y and Z is in a small radius of Y, then X>Z
● Monotonicity / non-satiation - more is better (goods we like)
○ Bad goods - IC would be upward sloping
● Convexity - averages are better than extremes
○ Weak convexity - averages are not worse than extremes
○ Strong convexity - averages are better than extremes
Indifference curves
● Bundles on IC3 are preferred to those on IC1
○ Consumers aim for the highest possible indifference curve
● Indifference curves are continuous and cannot cross
○ Crossing curves would violate transitivity
● Most indifference curves are convex to the origin
○ Averages > extremes
● Downward sloping - to remain on the same level of utility, you have to give up
some of good B if good A increases
Perfect substitutes
, ● The sum total of the two goods affects utility
● Linear indifference curves
● U(C, P) = aC + bP
Perfect complements
● The minimum quantity in the bundle of goods affects utility
● L-shaped indifference curves
● U(R, L) = min(aR, L)
Cobb-Douglas
● Used when thinking about varying substitutability within bundles
● The lower the level of substitutability, the more curved the IC
● U ( x 1 , x 2 )=x a1 x b2
● Convex and downward sloping
Utility and monotonic transformations
● Any bundle on an IC gives the same amount of utility - the further from the
origin, the higher the utility
○ Interested in ordinal, not cardinal utility
● Monotonic transformations create a new utility function with the same
preferences
○ Cannot work backwards from optimal demand for an exact utility
function due to transformations
● Can transform a utility function and yield the same IC
Behaviour and preferences
● Revealed preferences allow us to observe consumer choice
● If P1 X 1+ P 2 X 2 ≥ P 1 Y 1❑+ P2 Y 2 then (X1, X2) is directly preferred to (Y1, Y2)
● WARP refers to directly revealed preferences
○ WARP is satisfied if a household’s preferences are asymmetric
○ Shows if a household is rational and is attempting to maximise utility
○ If there is symmetry, irrational behaviour exists as the axiom is violated
○ If X>Y at one set of prices, but Y is chosen at another set, it must be
that X is no longer affordable
● SARP refers to indirectly and directly revealed preferences
○ If preferences are not transitive, SARP is violated
The marginal rate of substitution
● Utility is constant at all points on an indifference curve
● Marginal utility is the rate at which total utility changes
Δ x2 M U 1
● MRS = the slope of an IC at a particular point = =
Δ x1 M U 2
○ MRS = partial differential wrt x1 / partial differential wrt x2
Tastes and circumstances affect our consumption behaviour
Budget constraints
● Income (M) and prices affect consumer demand
○ Income can be exogenous or endogenous
● The feasible set - the quantity of goods that can be bought
given prices and income
M
● The maximum amount that can be bought of x1 is
P1
● The price ratio = the slope of the budget constraint
○ The slope measures the opportunity cost of consuming good 1
Δ x2 −p1
○ =
Δ x1 p2
● Bundles below the budget constraint is affordable
○ A bundle on the budget constraint is just affordable
● The budget constraint shifts inwards if income falls or prices rise
Preferences
● Preferences are described by utility functions
● Completeness - the consumer can compare bundles and make a decision
● Transitivity - if X>Y and Y>Z, then X>Z
○ Allows relationships to be drawn between different goods
● Completeness and transitivity give us rational behaviour
● Continuity - if X>Y and Z is in a small radius of Y, then X>Z
● Monotonicity / non-satiation - more is better (goods we like)
○ Bad goods - IC would be upward sloping
● Convexity - averages are better than extremes
○ Weak convexity - averages are not worse than extremes
○ Strong convexity - averages are better than extremes
Indifference curves
● Bundles on IC3 are preferred to those on IC1
○ Consumers aim for the highest possible indifference curve
● Indifference curves are continuous and cannot cross
○ Crossing curves would violate transitivity
● Most indifference curves are convex to the origin
○ Averages > extremes
● Downward sloping - to remain on the same level of utility, you have to give up
some of good B if good A increases
Perfect substitutes
, ● The sum total of the two goods affects utility
● Linear indifference curves
● U(C, P) = aC + bP
Perfect complements
● The minimum quantity in the bundle of goods affects utility
● L-shaped indifference curves
● U(R, L) = min(aR, L)
Cobb-Douglas
● Used when thinking about varying substitutability within bundles
● The lower the level of substitutability, the more curved the IC
● U ( x 1 , x 2 )=x a1 x b2
● Convex and downward sloping
Utility and monotonic transformations
● Any bundle on an IC gives the same amount of utility - the further from the
origin, the higher the utility
○ Interested in ordinal, not cardinal utility
● Monotonic transformations create a new utility function with the same
preferences
○ Cannot work backwards from optimal demand for an exact utility
function due to transformations
● Can transform a utility function and yield the same IC
Behaviour and preferences
● Revealed preferences allow us to observe consumer choice
● If P1 X 1+ P 2 X 2 ≥ P 1 Y 1❑+ P2 Y 2 then (X1, X2) is directly preferred to (Y1, Y2)
● WARP refers to directly revealed preferences
○ WARP is satisfied if a household’s preferences are asymmetric
○ Shows if a household is rational and is attempting to maximise utility
○ If there is symmetry, irrational behaviour exists as the axiom is violated
○ If X>Y at one set of prices, but Y is chosen at another set, it must be
that X is no longer affordable
● SARP refers to indirectly and directly revealed preferences
○ If preferences are not transitive, SARP is violated
The marginal rate of substitution
● Utility is constant at all points on an indifference curve
● Marginal utility is the rate at which total utility changes
Δ x2 M U 1
● MRS = the slope of an IC at a particular point = =
Δ x1 M U 2
○ MRS = partial differential wrt x1 / partial differential wrt x2
