Final exam

Question 1

weak axiom of revealed preferences

Answer 1

if x was chosen when y was also available, y was never chosen when x was also available

Question 2

convex preferences

Answer 2

abs value of MRS decreases as q1 increases, q2 decreases

Question 3

Perfect Substitutes

Answer 3

MRS is constant, consumer spends all budget on good with highest marginal U per dollar

Question 4

Perfect Complements

Answer 4

U = min(aq1, bq2)

consumer goods in ratio of a to b

Question 5

Concave preferences

Answer 5

choose u maximizing corner solution

Question 6

how to find demand

Answer 6

set MRS = -p1/p2

then plug into budget constraint

Question 7

giffen good

Answer 7

as price increases, so does demand
positive income effect
PED > 0 if large share of income

Question 8

substitution effect

Answer 8

q(old utility, new prices) - q(old prices, old income)

always negative

Question 9

income effect

Answer 9

q( new prices, new income) - q(old utility, new prices)

positive for normal goods, negative for inferior

Question 10

income elasticity

Answer 10

dD1/dy(Y/D1)

curly sigma

Question 11

price elasticity

Answer 11

dD1/dp(P/D1)

sigma

Question 12

slutsky equation

Answer 12

PED = PE comp D - exp. share of income * IED

Question 13

labor supply budget constraint

Answer 13

pq + wN

Question 14

Firm profit maximization

Answer 14

1. Find cost
MRTS = df/dL/(df/dk) = -w/r
Solve for K, plug into production function
c(q) = wL +rk
2. Maximize profit
Pi(q) = pq - c(q)
FOC
3.
If MC(q) >0:
p  MC(0): solve p=MC(q)
If MC(q) is u-shaped:
p  min ATC: solve p = MC(q)

Question 15

gross/net complements

Answer 15

dD1/p2 and dD2/p1

Question 16

gross/net substitutes

Answer 16

dD1/p2 and dD2/p1 > 0

net if compensated demand

Question 17

if abs MRS > abs MRT

Answer 17

good one is valued more, consume more good 1

Question 18

walras law

Answer 18

if the market for good one is in equilibrium, so is the market for good 2

Question 19

general equilibrium and production

Answer 19

1. Firms
Each maximizes profit: p*f(l) -wl, FOC
use to find q, plug in to find profit
2. Consumers
profit income = 1/2(Profit 1 + Profit 2)
demand for each (cob doug) = a/(a+b) (labor inc +profit inc)/p

Question 20

Pareto efficiency

Answer 20

no other allocation gives at least as high utility to every consumer or strictly higher utility to some consumer

Question 21

finding contract curve

Answer 21

A’s MRS = B’s MRS
q1 B = total endow 1 - q1 A
plug in, solve for q2 A

Question 22

welfare theorems

Answer 22

1. equilibria are Pareto efficient (price taking, no externalities, complete markets)
2. If preferences are convex, lump sum transfers of initial endowments can make any point on the contract cuve an equilibrium

Question 23

arrow’s axioms

Answer 23

1. Pareto Efficiency: if everybody prefers x to y, so does society
2. No Dictatorship
3. Independence of Irrelevant Alternatives: society’s rankings of x and y depend only only individual rankings of x and y, not alternatives

Question 24

CV

Answer 24

how much change in income insures that your utility stays the same despite price increases
old utility with new prices (delta income)

Question 25

EV

Answer 25

which loss of income would reduce your utility by as mcuh as the price increase does
new utility with old prices (delta income)

Question 26

risk based on SOC of U

Answer 26

> 0 : risk prefering

0: risk neutral

Question 27

arrow-prat measure of risk

Answer 27

-U”(x)/U(x)

Question 28

risk averse decision makers:

Answer 28

buy full insurance when offered at fair odds, buy at least a small amount of any investment with expected positive return

Question 29

Lerner index

Answer 29

(p-MC)/p = -1/PED

Question 30

Bertrand Model

Answer 30

duopoly with identical products
identical and constant MC: c(q) = cq
NE: p1 = p2 = C
(if 3, maybe not)

Question 31

Cournot Model

Answer 31

N firms with identical profits
NE:
-maximize profits for each firm, solve for q1, q2 and p
-Pi( q1, q2) = p(Q)qi -Ci(qi)

Question 32

positive externatlites

Answer 32

solutions:

subsidies for consumers, enforce consumption of more of the good with the externaltity, allow consumers to selll

Question 33

negative externalities

Answer 33

solutions:

tax, ration, turn into private property, force firms to use less

Question 34

adverse selection

Answer 34

information is known to one side of the market but not the other (exogenous)
(lemons v new cars)

Question 35

moral hazard

Answer 35

observed by one side of market but not the other (endogenous)
guaranteed/contract, expend less effort