The Market Flashcards
Pareto Efficient
A situation whereby we can find no way to make anyone better off without making anyone else worse off in the process.
Deadweight Loss
A measure of economic inefficiency - when resources left unexploited or excess production occcurs
Budget Line Equation
p1x2+p2x2=M
Budget Line
All affordable bundles lie on or under this line
Slope of Budget Line
-p1/p2
AXIOM of weak ordering- Completeness
A consumer must be able to say whether they prefer or are indifferent between any 2 goods
AXIOM of weak ordering - reflexivity
Bundle A must be at least as good as itself
AXIOM of weak ordering- transitivity of preference
If A is preferred to B and B is preferred to C then A is also preferred to C
Rationality
Assumes consumer satisfies axioms of completeneness, reflexivity and transitivity -> is consistent
AXIOM of weak ordering - continuity of preference
If A is weakly preferred to B, then bundles sufficiently close to A will also be weakly preferred to B
AXIOM of weak ordering - monotonicity
‘more is preferred to less’
AXIOM of weak ordering - convexity
Average is preferred to the extremes, mixed bundle is better.
MRS
The absolute value of the slope of the indifference curve = MRS = MU1/MU2
MRS DECREASING
Convex indifference curve
MRS CONSTANT
Perfect substitutes
MRS INFINITY OR ZERO
Complements
Utility Maximisation Problem
When slope of budget line = slope of indifference curve: P1/P2=MRS=MU1/MU2
Solutions to UMP are..
Marshallian demand functions for x1 and x2
Marshallian demand function for x1 when utility function is Cobb-Douglas
x1=x1(p1,p2,M) = x1=α(M/P1)
Marshallian demand function for x2 when utility function is Cobb-Douglas
x2=x2(p1,p2,M) = x2=(1-α)(M/P2)
Marshallian demand function for x2 when utility function is Leontief (perfect complements)
x2*=aM/bp1+ap2
Marshallian demand function for x1 when utility function is Leontief (perfect complements)
x1*=bM/bp1+ap2
Optimal solution to UMP (exceptions)
Generally when p1/p1=MRS, exceptions when MRS does not exist or corner solution when MRS>P1/P2 or MRS
Euler’s elasticity rule
If a function is homogenous to degree r, the sum of all elasticities will equal to r (for the Marshallian demand for any given good will have sum of price and income elasticities equal to zero)
Own Price elasticity (e11)
dx1/dp1 x p1/x1
Cobb-douglas own PED
dlnx1*/dlnp1
Cobb-douglas income elasticity of demand
dlnx1*/dlnM
Engel Curve
Tracing path of consumption as income changes, prices held constant.
Homothetic preference
When MRS is a function of only the ratio of preferences, not the quantity of the goods individually
Satiation point
The point of maximum satisfaction, the closer to this point the better off he is in terms of his preferences.
Increasing slope Engel Curve (M, x1)
x1 necessary good
Decreasing slope engel curve (M, X1)
x1 luxury good
Constant slope engel curve
ratio of x2/x1 constant, homothetic preferences - income elasticity always 1
Income elasticities of different goods are linked
s1 (budget share of x1)
S1E1m+(1-S1)E2m = 1
Gross substitutes and law of demand
If x2 is a gross substitute of x1, the law of demand holds for x1
If dx2/dp1 > 0 then x2 is gross substitute and must be the case that dx1/dp1 < 0 (law of demand holds)
Aggregate Demand
Derive market demand by summing individual marshallian demand curves
Aggregate elasticity
e = weighted sum of individual elasticities= EaZa + EbZb where Za = xA/X and Za+Zb = 1
Hicksian (Compensated) Demand Function
Refer to expenditure minimisation rather than utility maximisation
Hicksian demand function for x1 when utility function is Cobb-Douglas
x1h=(α/1-α)^(1-α) (p2/p1)^(1-α) u0
Marshallian demand function for x2 when utility function is Cobb-Douglas
x2h=(α/1-α)^(α) (p2/p1)^(α) u0
Hicksian demand and price changes - both prices change
Hicksian demand homogenous to degree zero so demand will remain unchanged
Hicksian demand and price changes - p1 increases
x1 must fall, x2 will rie (law of demand must hold for Hicksian demand functions)
What effect happens with a price increase for Hicksian demand
Only substitution effect, no income effect.
The slope of the Hicksian demand function
… is the substitution effect
Expenditure function
the minimum cost of achieving a given level of utility –> E=p1x1h+p2x2h
