Microeconomic theory
preferences properties
1) completeness
2) transitivity
3) continuity
4) nonsatiation
5) convexity
completeness
an individual can always rank
transitivity
the individuals choices are internally consistent
continuity
if a is preferred to b then situations "close to" a must be preferred to b
no-satiation
more is always better in terms of economic goods
convexity
a consumers indifference curves are bowed inwards (concave to the origin)
MRS(21)
MRS(21)=-dx2/dx1
what does Cobb-douglas, CES and linear preferences have in common?
all are homothetic functions
optimization principle
to max utility, given fixed income to spend, an individual will buy goods/services that exhaust his total income for which the MRS is equal to the rate at which goods can be traded for one another in the marketplace.
slope of budget constraint
=-p1/p2
the feasible set
all combinations of goods that the consumer can afford
slope of indifference curves
=-MRS=dx2/dx1
utility maximization
utility is maximized where indifference churve js tangent to the budget line. at optimum: u1/u2=p1/p2
what is a corner solution?
a corner solution is when the individuals preference js to only consume one good
homothetic functions
a function is homothetic if it can be written as a monotonic transformation of a homogeneous function, i.e. scaling all inputs by a constant factor leads to proportional changes in the function's value, after applying monotonic transformation.
net demand
the difference between a consumer's gross demand and initial endowment. i.e the amound the consumer want to buy/sell in the marker after accounting for what they already have. net demand = gross demand - initial endowment. positive net demand = consumer wants to buy more (net buyer
slutsky equation (own price effect)
what happens with demand of x1 when price of x1 changes?
dxi/dpi=dx̄i/dpi - dxi/dI*xi
slutsky equation (cross price effect)
what happens with demand of x1 when price of x2 changes?
dxi/dpj=dx̄i/dpj - dxi/dI*xj
gross substitutes
marshallian demand and slutsky equation:
if dDi(p,M)/dpj > 0 i and j are gross complements
gross complements
marshallian demand and slutsky equation:
if dDi(p,M)/dpj < 0 i and j are fross complements
net substitutes
hicksian demand and slutsky equation
if dHi(p,M)/dpi >0 i and j are net substitutes
net complements
hicksian demand and slutsky equation
if dHi(p,M)/dpj < 0 i and j are net complements