micro

Question 1

normal etc good

Answer 1

derivative wealth <0 inferiorio 0-1 normal 1+ luxury

Question 2

giffen good

Answer 2

own price derivative positive

Question 3

elasticity

Answer 3

dx/dw*w/x

Question 4

hicksian comp

Answer 4

e(p’, u0) - w

Question 5

sluts comp

Answer 5

p’*x(p, w) - w

Question 6

Roy

Answer 6

x = - grad(p)/grad(w) of v(p, w)

Question 7

Shephard’s lemma

Answer 7

h= grap(p) e(p, u)

Question 8

EV

Answer 8

e(p0, u1) - w
v(p0, w+EV)=u1

Question 9

CV or wtp

Answer 9

w - e(p1, u0)
v(p1, w-CV)=u0

Question 10

CV >< EV

Answer 10

Normal EV>CV
inferior EV<CV

Question 11

Hotelling lemma

Answer 11

y(p) = grad(p) pi(p)

Question 12

Shephard’s lemma production

Answer 12

z=grad(w) c
cond factor demand corresp, cost function

Question 13

certainty equivalent

Answer 13

u(CE)=u(x) CE \sim x
int u(x) dF(x)

Question 14

Risk and shape of u

Answer 14

averse u concave (u’‘<0)
neutral linear
lover convex

Question 15

Absolute risk av

Answer 15

-u’‘(x)/u’(x)

Question 16

Cara

Answer 16

1-exp(-Rx) / R

Question 17

crra

Answer 17

x^(1-r)/1-r

Question 18

proof WL assumptions and steps

Answer 18

LNS p»0
LNS = spend entire wealth
market good 1 clears
sum across individuals = 0
P>0 so sum X2 - w2 = 0

Question 19

Utility poss convex

Answer 19

Assume convex prod and cons + concave ut
need feasible and ui<u(x) for all i
take (x,y) (x’,y’) feasible. (x’‘,y’’) lincomb feasible
u(x’’)>=lincomb(u(x) u(x’)) by concavity for all i. done

Question 20

WE z<0

Answer 20

WE p>=0 (with strong monotonicity =, also z=0) iff
-y<0, py=0
-xi=xi(p, pw) for all i
-sum xi - sum wi= yi*
=> follow from i, iii
<= take xi=xi(p, pw), y=sum(xi-wi)
py=sum(px-pw)=0 bc by LNS pw=px

Question 21

Existance

Answer 21

P»0. By H0, can price unit simplex. sum p = 1

zl+(p) = Max (zl(p), 0)
alpha(p)= sum(pl+zl+(p))
f(p)= 1/alpha(p) * (p + zl+(p))

Brower fixed point E p=f(p)

WL pz(p)=0

Question 22

Warp multivalued

Answer 22

(p, w) (p’, w’) x in x(p,w) x’ in x(p’, w’)
p’x<w’ x in x
px’<w x’ in x

Question 23

Probability premium

Answer 23

take middle point ex 16 4 is 10
u(10)=(1/2-p)u(4) + (1/2+p)u(16) (–, ++)

Question 24

SODS

Answer 24

F sods G if integral 0-x F-G dt <0 for all x in range

Question 25

elasticity of subs

Answer 25

1/1-p (x^p+y^p)^1/p p neg inf leont, inf subs, 1 cobb

Question 26

WA

Answer 26

p z(p) diff and pz(p’)<=0 implies p’z(p)>0

Question 27

Necessity WA

Answer 27

esistono 2, buttali in Y* come py<=0 p’y<=0 e ce l’hai xk eq prices but different z

Question 28

Sufficiency WA

Answer 28

Take 2 eq. Lincom p’‘y<0 easy
WL pz(p’’) or p’ negative <=
Suppose one. But z(p) in Y implies p’‘z(p)<=0
Can WA only if z=z. So 3 demands same prices multiples H0

Question 29

WE in crs

Answer 29

(p, x(p, pw), y(p)=z(p)
py<=0 for all y necessary in PMP
z(p) in Y feasible from market clearing
py*(p)=pz(p)=0 WL maximize profits

Question 30

PMP py

Answer 30

for all y in Y, py*>=py

Question 31

Sum of x* in F/STWE

Answer 31

sumpx=sumw=pw+sum py*
w+sum y*