Neary

Question 1

Rationality conditions

Answer 1

1. Completeness

2. Transitivity

Question 2

WARP

Answer 2

If x chosen from any B containing x and y, then y never chosen from any B containing both x and y
p.x(p’,w’)=w’

Question 3

Revealed preference relation

Answer 3

x is at least once chosen when y is available
need not be complete or transitive
rational preferences imply WARP will be observed but not viseversa

Question 4

Which implies which:

utility function exists, rationality, WARP

Answer 4

U(.) exists means preferences must be rational which means WARP will be satisfies
But WARP is necessary but insufficient for rationality which itself almost always (but not always) implies the utility fn exists

Question 5

Engel curve

Answer 5

For fixed prices, the bundle demanded as a function of wealth
Gradient=∂x(p, w)/∂w

Question 6

Walras’ law in budget shares

Answer 6

budget share of product l: bl(p,w)=pl*xl(p,w)/w

W.L.: sum of bl=1

Question 7

Normal vs inferior products

Answer 7

income effect positive vs negative

income elasticity positive vs negative

Question 8

Luxury good vs necessity

Answer 8

budget share increases with wealth (so will also be normal) vs decreases with wealth (all inferior are necessities)
income elasticity > 1 vs < 1

Question 9

Giffen good

Answer 9

negative own price effect

Question 10

f is homogeneous of degree k if

Answer 10

x · ∇ f(x) = k f(x)

Question 11

Engel Aggregation

Answer 11

sum of budget shares times income elasticities for all goods is 1

Question 12

Cournot Aggregation

Answer 12

budget share of k plus sum of budget shares of all times cross-price elasticities of all with k = 0

Question 13

Compensated price changes

Slutsky wealth compensation

Answer 13

to identify the substitution effect
change the agent’s wealth so that the original bundle is still just affordable
change in w=(p’-p).x(p,w)

Question 14

What does Law of Demand say about Giffen goods

Answer 14

Impossible when price rises are compensated (assuming rationality ie exhausted budget set)

Question 15

SARP

Answer 15

if x1 is revealed preferred to xn via a chain of pair-wise comparisons, then xn cannot be revealed preferred to x1 in a pair-wise comparison
Essential WARP with transitivity of weak preference relation

Question 16

If u(.) is quasi-concave

Answer 16

Then preferences are convex (think indifference curves)

Question 17

Homothetic preferences

Answer 17

if indifferent between x and y then also indifferent between kx and ky
utility function is h.o.d. 1

Question 18

Quasi-linear preferences

Answer 18

take 2 indifferent bundles. If you add x units of good 1 to both bundles, then still indifferent
Utility functions: U=x1+u(x2…xL)
x1 often used as money

Question 19

Quasi-concavity implies

Answer 19

The solution to the consumer’s problem is unique

through convexity of preferences

Question 20

Indirect utility

Answer 20

The maximum utility obtainable with prices p and wealth w

Question 21

Convex shape of price indifference curves for indirect utility means

Answer 21

Prefer extreme prices to average prices

Question 22

expenditure function

Answer 22

minimum p.x s.t. u(x)>=u

Question 23

h(p,u)

Answer 23

Compensated demand function. Demand for each good given prices and utility to achieve.
Compensated means own price effect must be negative (no income effect here)

Question 24

e(p,u) is convex or concave in p?

Answer 24

Concave

Question 25

Shephard’s Lemma

Answer 25

partial of e(p,u) wrt pl=hl(p,u)

Question 26

Hicksian Substitutes vs Complements

Answer 26

Partial of hl wrt pk>0 vs <0
An increase in the price of good k increases vs decreases demand for good l
Each product always has at least one substitute
Since own price effect is negative and sum of price effects =0 as h is hod0

Question 27

Gross subs

Answer 27

partial of xl wrt pk>0

Question 28

Edgeworth Subs

Answer 28

second partial of u wrt xk, xl <0

Question 29

Roy’s identity

Answer 29

xl(p,w)=-partial of v wrt pl/partial of v wrt w

Proof starts by differentiation u=v(p,e(p,u))

Question 30

The Slutsky Equation

Answer 30

partial of xl wrt pk= substitution effect and wealth effect

=partial of hl wrt pk - partial of xl wrt w * xk(p,w)

Question 31

If a good is normal and gross substitutes with k then

Answer 31

the two products must also be Hicksian substitutes

Question 32

With homothetic preferences:
e(p,u)=
v(p,w)=
x(p,w)=

Answer 32

u(.) is hod1 in x:
e=e(p)u
v=v(p)w
x=x(p)*w

Question 33

With quasi-linear preferences, Hicksian and Walrasian demand functions for x

Answer 33

Coincide as there is no wealth effect

Question 34

Slutsky wealth compensation after a price change

Answer 34

Gives the consumer enough wealth that they can buy the old bundle
change in wealth=(p’-p)*x(p,w)
But can usually do better with this wealth with the new prices and will choose a different bundle and be happier than they were

Question 35

Hicksian wealth compensation

Answer 35

Gives the consumer enough wealth so their utility is unchanged.
w’=e(p’,v(p,w))

Question 36

If yl is positive vs negative

Answer 36

it is an output vs input

Question 37

Hotelling’s Lemma

Answer 37

the partial of the profit function wrt pl = yl(p)

Question 38

1st step of Hotelling’s Lemma proof

Answer 38

let G(p)=p.y(p*)-profit function of p

Question 39

Law of supply

Answer 39

Prices and quantities move in the same direction

Question 40

Firms version of Shephard’s Lemma

Answer 40

partial of the cost function c(w,q) wrt wl=zl(w,q) which is the conditional factor demand function (w is input prices)

Question 41

Production is efficient if

Answer 41

Can’t produce more output with same inputs or same output with fewer inputs

Question 42

The long run cost curve

Answer 42

The lower envelope of the short-run cost curves (the locus of minimum points)

Question 43

Certainty equivalent of a lottery

Answer 43

C satisfies u(C)=E(u(x))

Question 44

Risk premium

Answer 44

P satisfies u(E(x)-P)=E(u(x))

p=E(x)-C

Question 45

Coefficient of ARA

Answer 45

Ra=-u’‘(x)/u’(x)>0

Question 46

CARA

Answer 46

constant absolute risk aversion

No income effect in the demand for insurance

Question 47

DARA

Answer 47

decreasing absolute risk aversion

Insurance is an inferior good, pay less to eliminate a small risk

Question 48

If the utility function is quadratic, expected utility only depends on

Answer 48

Mean and variance of the distribution of the shock

Question 49

Coefficient of relative risk aversion

Answer 49

Rr(x)=-xu’‘(x)/u’(x)

Question 50

First step of proof that maximised profit function is convex

Answer 50

let p’‘=ap+(1-a)p’