Jr Chapter 1

Front 1

four building blocks of consumer choice

Back 1

consumption set, feasible set, preference relation, behavioral assumption

Front 2

the set of all alternatives that consumer can imagine

Back 2

consumption set

Front 3

x=(x1, . . . , xn) a vector containing different quantities of n commodities

Back 3

consumption bundle

Front 4

1. X ⊆ Rn+.
2. X is closed.
3. X is convex.
4. 0 vector ∈ X.

Back 4

consumption set properties

Front 5

consumption set properties

Back 5

1. X ⊆ Rn+.
2. X is closed.
3. X is convex.
4. 0 vector ∈ X.

Front 6

For all x1 and x2 in X, either x1 is at least as good as x2 or x2 is at least as good as x1.

Back 6

completeness

Front 7

completeness

Back 7

For all x1 and x2 in X, either x1 is at least as good as x2 or x2 is at least as good as x1.

Front 8

transitivity

Back 8

For any three elements x1, x2, and x3 in X, if x1 is at least as good as x2 and x2 is at least as good as x3,
then x1 is at least as good as x3.

Front 9

x1 is at least as good as x2 and x2 is at least as good as x1.

Back 9

x1 ~ x2

Front 10

For all x ∈ Rn+, the ‘at least as good as’ set, >~(x), and the ‘no better than’ set, <~(x), are closed in Rn+.

Back 10

continuity

Front 11

continuity axiom 3 PF

Back 11

For all x ∈ Rn+, the ‘at least as good as’ set, >~(x), and the ‘no better than’ set, <~(x), are closed in Rn+.

Front 12

If each element yn of a sequence of bundles is at least as good as x and yn converges to y, then y is at least as good as x

Back 12

equivalent continuity using convergence

Front 13

For all x0 ∈ Rn+, and for all ε > 0, there exists some x ∈Bε(x0) ∩ Rn+ such that x is preferred to x0

Back 13

local non-satiation axiom 4prime -- no zones of indifference

Front 14

axiom that no zones of indifference will exist in preference relation without implying that giving the consumer more of everything MUST make him better off

Back 14

For all x0 ∈ Rn+, and for all ε > 0, there exists some x ∈Bε(x0) ∩ Rn+ such that x is preferred to x0 ----- local non-satiation

Front 15

For all x0, x1 ∈ Rn+, if x0 ≥ x1 then x0 is at least as good as x1, while if x0 >> x1, then x0 is preferred to x1

Back 15

strict monotonicity

Front 16

strict monotonicity

Back 16

For all x0, x1 ∈ Rn+, if x0 ≥ x1 then x0 is no worse than (at least as good as) x1, while if x0 >> x1, then x0 is preferred to x1

Front 17

a consumption bundle is strictly better
if it contains strictly more of every good

Back 17

strict monotonicity

Front 18

If x1 is at least as good as x0, then tx1 + (1 − t)x0 is preferred to x0 for all t ∈ [0, 1].

Back 18

convexity

Front 19

If x1=/=x0 and x1 is at least as good as x0, then tx1 + (1 − t)x0 is preferred to x0 for all t ∈ (0, 1)

Back 19

strict convexity

Front 20

convexity of preference relation

Back 20

If x1 is at least as good as x0, then tx1 + (1 − t)x0 is preferred to x0 for all t ∈ [0, 1].

Front 21

strict convexity

Back 21

If x1=/=x0 and x1 is at least as good as x0, then tx1 + (1 − t)x0 is preferred to x0 for all t ∈ (0, 1)

Front 22

rules out all combinations of concave to the origin indifference sets

Back 22

convexity

Front 23

no point to the northeast or the southwest may lie in the same indifference curve

Back 23

strict monotonicity

Front 24

the absolute value of the slope of an indifference curve

Back 24

marginal rate of substitution of good two for good one

Front 25

marginal rate of substitution of good two for good one

Back 25

the absolute value of the slope of an indifference curve

Front 26

the principle of diminishing marginal rate of substitution requires that, as you move NW to SE, rate of trade for x2 to x1 must be ____

Back 26

diminishing or constant

Front 27

a real-valued function u: Rn+ → R is a utility function for "at least as good as" if ___________

Back 27

for all x0, x1 ∈ Rn+, u(x0) ≥ u(x1)⇐⇒x0 is at least as good as x1

Front 28

For the existence of a utility function, the binary relation 'at least as good as' must be

Back 28

complete, transitive, continuous, and strictly monotonic

Front 29

Let "at least as good as" be a preference relation on Rn+ and suppose u(x) is a utility function that represents it. Then v(x) also represents "alaga" if and only if v(x) = f (u(x)) for every x, where f : R→R
is strictly increasing on the set of values taken on by u.

Back 29

invariance of utility function to monotonic transforms

Front 30

u: Rn+→R for "alaga:" u(x) is strictly increasing iff _________

Back 30

"alaga" is strictly monotonic

Front 31

u: Rn+→R for "alaga:" is quasiconcave iff_______

Back 31

"alaga" is convex

Front 32

u: Rn+→R for "alaga:" u(x) is strictly quasiconcave iff _________

Back 32

"alaga" is strictly convex

Front 33

MRS1,2(x1) = ____________

Back 33

∂u(x1)/∂x1 over
∂u(x1)/∂x2

Front 34

∂u(x1)/∂x1 over
∂u(x1)/∂x2

Back 34

MRS1,2(x1)

Front 35

first order partial derivative of u(x) wrt xi

Back 35

marginal utility of good i

Front 36

we assume preference relation is

Back 36

complete, transitive, continuous, strictly monotonic, and strictly convex on Rn+

Front 37

the budget set

Back 37

B = {x | x ∈ Rn+, p · x ≤ y}.