RL1
Review
Review
A
decisionmaker chooses its most
preferred alternative from the
affordable ones.
 Budget set
 Preferences (Utility)
 Choice (Demand)
Budget set

a)
b)
c)
d)
e)
Budget set: given p1 , p 2 , m
Write down budget constraint
Illustrate it geometrically (numbers)
Interpret the slope (econ. and geom.)
Changes: Price and Income
Modifications:
e.g. Taxes, Subsidies, Gifts
Budget set
p1  1, p 2  1, m  10  p1  2, p 2  1, m  10
Graph, Slope, Price and Income Change
Taxes, Subsidies, Gifts
Preferences






Preferences: ranking of bundles
Geometric representation – indifference c.
Goods, Bads, Satiated preferences (slopes)
Four examples of preferences
– Cob-Douglass
– Perfect Complements
– Perfect Substitutes
– Quasilinear
Utility and MRS
Monotone transformations
Preferences (4 examples)
U ( x1 , x 2 )  ln x1  ln x 2
U ( x1 , x 2 )  min(2 x1 , x 2 )
MRS (find, interpret, 0.000001)
U ( x1 , x 2 )  x1  ln( x 2 )
U ( x1 , x 2 )  3 x1  x 2
Choice – well behaved preferences
 Given p1 , p 2 , m
and U ( x1 , x 2 )
 Note: p1 , p 2 , m can be parameters
 Find optimal choice on the graph
 Secrets of happiness
– Geometric interpretation
– Economic Interpretation
 Analytical solution
 Magic formulas
Choice
U ( x1 , x2 )  x1  5 ln x2
p 1  1, p 2  1, m  10
MU 2
p2
MU 1
p1
$
$
$
$
$
$
$
$
$
$
Choice
U ( x1 , x 2 )  x1  20 ln x 2
p 1  1, p 2  1, m  10
MU 2
p2
MU 1
p1
$
$
$
$
$
$
$
$
$
$
Choice
p1  1, p 2  1, m  10
U ( x1 , x 2 )  ln x1  ln x 2
U ( x1 , x 2 )  x1  ln( x 2 )
Graph, optimality conditions, twist interiority!
Extreme preferences
p1  1, p 2  1, m  10
U ( x1 , x 2 )  min(2 x1 , x 2 )
U ( x1 , x 2 )  3 x1  x 2
Graph, optimality conditions, twist interiority, !
Magic formulas
Behavior of the demand
x1 ( p1 , p 2 , m )
x 2 ( p1 , p 2 , m )
– price change: Ordinary or Giffen
 Income change: Normal or Inferior
 Demand and Engel Curve
Plot and find them analytically
(four examples of preferences)
 Own
 Other
good price change:
Gross Substitutes or Complements
Own-price change
p1  1, p 2  1, m  10  p1  2, p 2  1, m  10
 TCH=SE+IE
 Interpretation
 Decomposition:
Auxiliary budget line
 Relation: Giffen - Inferior goods
Buying and selling
 Nominal
Income – endowment of goods
 Budget
set: buying selling
 Changing prices
 Price offer curve
 Find
net demands for extreme
preferences!
Labor supply
 Labor
leisure choice
 Budget
set
 Labor leisure Choice
 Why
labor supply is inelastic
Intertemporal choice
 Abstract
model = Two period model
 Budget set (borrowing, saving)
 Preferences (Discount factor and rate)
 Choice: Consumption and Savings
 Many
periods
 Annuity and Perpetuity formula
 Aplications