Final exam Flashcards
weak axiom of revealed preferences
if x was chosen when y was also available, y was never chosen when x was also available
convex preferences
abs value of MRS decreases as q1 increases, q2 decreases
Perfect Substitutes
MRS is constant, consumer spends all budget on good with highest marginal U per dollar
Perfect Complements
U = min(aq1, bq2)
consumer goods in ratio of a to b
Concave preferences
choose u maximizing corner solution
how to find demand
set MRS = -p1/p2
then plug into budget constraint
giffen good
as price increases, so does demand
positive income effect
PED > 0 if large share of income
substitution effect
q(old utility, new prices) - q(old prices, old income)
always negative
income effect
q( new prices, new income) - q(old utility, new prices)
positive for normal goods, negative for inferior
income elasticity
dD1/dy(Y/D1)
curly sigma
price elasticity
dD1/dp(P/D1)
sigma
slutsky equation
PED = PE comp D - exp. share of income * IED
labor supply budget constraint
pq + wN
Firm profit maximization
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)
gross/net complements
dD1/p2 and dD2/p1
gross/net substitutes
dD1/p2 and dD2/p1 > 0
net if compensated demand
if abs MRS > abs MRT
good one is valued more, consume more good 1
walras law
if the market for good one is in equilibrium, so is the market for good 2
general equilibrium and production
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
Pareto efficiency
no other allocation gives at least as high utility to every consumer or strictly higher utility to some consumer
finding contract curve
A’s MRS = B’s MRS
q1 B = total endow 1 - q1 A
plug in, solve for q2 A
welfare theorems
- equilibria are Pareto efficient (price taking, no externalities, complete markets)
- If preferences are convex, lump sum transfers of initial endowments can make any point on the contract cuve an equilibrium
arrow’s axioms
- Pareto Efficiency: if everybody prefers x to y, so does society
- No Dictatorship
- Independence of Irrelevant Alternatives: society’s rankings of x and y depend only only individual rankings of x and y, not alternatives
CV
how much change in income insures that your utility stays the same despite price increases
old utility with new prices (delta income)
EV
which loss of income would reduce your utility by as mcuh as the price increase does
new utility with old prices (delta income)
risk based on SOC of U
> 0 : risk prefering
0: risk neutral
arrow-prat measure of risk
-U”(x)/U(x)
risk averse decision makers:
buy full insurance when offered at fair odds, buy at least a small amount of any investment with expected positive return
Lerner index
(p-MC)/p = -1/PED
Bertrand Model
duopoly with identical products
identical and constant MC: c(q) = cq
NE: p1 = p2 = C
(if 3, maybe not)
Cournot Model
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)
positive externatlites
solutions:
subsidies for consumers, enforce consumption of more of the good with the externaltity, allow consumers to selll
negative externalities
solutions:
tax, ration, turn into private property, force firms to use less
adverse selection
information is known to one side of the market but not the other (exogenous)
(lemons v new cars)
moral hazard
observed by one side of market but not the other (endogenous)
guaranteed/contract, expend less effort
