Kapitel 3

Question 1

Hicksian Demand

Answer 1

• 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)

Question 2

Hicksian Demand Computation

Answer 2

Question 3

Hicksian Demand Graphically

Answer 3

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).

Question 4

The expenditure function

Answer 4

• 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

Question 5

The expenditure function calculation

Answer 5

Question 6

The expenditure function graphically

Answer 6

The expenditure function is concave in prices.
- p-m(p,u) diagramm

Question 7

Shephard’s lemma

Answer 7

Question 8

Homogeneous functions

Answer 8

Question 9

Marginal cost of utility

Answer 9

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

Question 10

Indirect utility function

Answer 10

• 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)

Question 11

Roys Identity

Answer 11

Roy’s identity tells us how the maximal utility the consumer can attain changes, if the price of one good i changes.

Question 12

Slutsky Equation

Answer 12

Question 13

Slutsky Equation for j=I
Substitution effect

Answer 13

Question 14

Slutsky Equation for j=I
Income effect

Answer 14

Question 15

Slutsky Equation
Substitutes and complements

Answer 15

Question 16

Compensating variation (CV)

Answer 16

CV<0
- Integral only for change in one price

Question 17

CV Diagram

Answer 17

• Hicksian Demand

Question 18

Equivalent variation (EV)

Answer 18

EV<0
- Integral only for change in one price

Question 19

EV Diagram

Answer 19

Question 20

Consumers Surplus

Answer 20

In most applications welfare changes are measured using the concept of consumer’s surplus (CS), which is defined as the integral below Marshallian demand