Kapitel 3 Flashcards
Hicksian Demand
- compensated demand function
- quantity of each good that allows utility u at minimum costs when prices are given
Hicksian demands are the demands for x1 and x2 that minimize total expenditure s. t. the constraint of reaching a fixed utility level u at prices p1, p2 - Hi(p,u)
Hicksian Demand Computation
Hicksian Demand Graphically
X-P Graph
- mark p0 and x0 on graph
- mark p1 and x1 on the graph
- p1 and x1 exist after moving the income curve back to the Marshallian demand curve
- The Hicksian demand shows the substitution effect, holding utility constant
- Income is increased / decreased to hold utility constant (see top diagram).
The expenditure function
- gives the minimum level of expenditure necessary to attain utility u at prices p, which can be interpreted as the minimum level of expenditure necessary to attain a specific “standard of living” at prices p
- The expenditure function is concave in prices.
- M=m(p,u)
- expenditure function and indirect utility function are inverse to each other
The expenditure function calculation
The expenditure function graphically
The expenditure function is concave in prices.
- p-m(p,u) diagramm
Shephard’s lemma
Homogeneous functions
Marginal cost of utility
µ* as marginal cost of utility
- minimum additional expenditure necessary to increase consumers utility by one at the given prices is equal to µ*
- ableitung expenditure function nach u
Indirect utility function
- The indirect utility function tells that utility depends indirectly on the price and income situation the consumer faces.
- expenditure function and indirect utility function are inverse to each other
- u=v(p,M)
Roys Identity
Roy’s identity tells us how the maximal utility the consumer can attain changes, if the price of one good i changes.
Slutsky Equation
Slutsky Equation for j=I
Substitution effect
Slutsky Equation for j=I
Income effect
Slutsky Equation
Substitutes and complements
Compensating variation (CV)
CV<0
- Integral only for change in one price
CV Diagram
- Hicksian Demand
Equivalent variation (EV)
EV<0
- Integral only for change in one price
EV Diagram
Consumers Surplus
In most applications welfare changes are measured using the concept of consumer’s surplus (CS), which is defined as the integral below Marshallian demand
