This Class
Objective
! Measuring inflation
! How can we measure the cost to the
consumer of inflation?
! How can we determine the deadweight loss
of taxes?
! Introduce Expenditure Minimization Problem
! Price indices
! Hicksean demand
! Deadweight Loss of
H 2: E500
Fall, 2012
The homework is due on Wednesday, September 19. Each questions is worth 0.8points.
No partial credits.
For the computer exercises, you need to attach a printout of each Excel worksheet. In
addition, you need to type on an extra sheet
H 4: E500
Fall 2012
The homework is due on Wednesday, October 3 Each questions is worth 0.8 points. No
partial credits.
For the graphic arguments, use the graphing paper that is attached. For the computer
exercises, you need to attach a printout of each E
H 3: E500
Fall, 2012
The homework is due on Wednesday, September 26. Each questions is worth 0.8 points.
No partial credits.
For the graphic arguments, use the graphing paper that is attached.
Question 1 Suppose an oil company has supplies of ve crude pro
H 5: E 500
Fall, 2012
The homework is due on Wednesday, October 17 at 4pm.
0.5 points
x0.6
1
x0.3 .
2
Prices are p1 = 3,
+
Question 1 A utility function is given by u(x1 , x2 ) =
p2 = 3. Determine the equation of the income oer curve. Plot this curve usin
H 6: E500
Fall, 2012
The homework is due on Wednesday, October 24 at 4pm. No partial credits.
Question 1 A persons utility function is given by u(L, c) = L2 c, where L is leisure and c
is consumption. The persons income is derived from work. I.e., if is t
H 9: E500
Fall, 2012
As usual the homework is due on Wednesday, November 14 at 4pm. Each questions is
worth 0.8 points each.
Question 1 The quality of car can be described by a variable q [0, 1]. Suppose that
the value to a buyer is 1, 000 + 30, 000q. The
Homework 1, Econ 500
Each questions is worth 0.8 points. The homework is due on Wednesday, September 12
Question 1: Consider a competitive market for which the quantities demanded and supplied per
year at various prices are
Price (Dollars)
Demand (Million
H 3: E500
Fall, 2012
The homework is due on Wednesday, September 26. Each questions is worth 0.8 points.
No partial credits.
For the graphic arguments, use the graphing paper that is attached.
Question 1 Suppose an oil company has supplies of ve crude pro
H 7: E500
Fall, 2012
The homework is due on Wednesday, October 31 at 4pm. No partial credits.
0.8point
Question 1 A persons Bernoulli utility function is given by u(x) = ln(x). The person
has wealth w and invests fraction into a risky asset and 1 into a r
H 9: E500
Fall, 2011
The homework is due on Wednesday, Deember 5. Each question is worth 0.8 points.
Question 1 There are 400 rms in an industry. Half of the rms use newer technology
resulting in a cost function c(Q) = 50 + Q2 , while the the remaining rm
This Class
! Perfect Competition
! Profit Maximization
! Economies of scale, diseconomies of scale,
constant returns to scale
! Efficiency
Perfect Competition
! Many firms competing to produce and sell the
same product.
! Each firm has only a small market
This Class
Choice Under Uncertainty
! Choice under uncertainty
! Examples: Risky assets, insurance
! Risk aversion
Daniel Bernoulli:
Jan. 29, 1700-March 17, 1782
The St. Petersburg Game
Toss a coin: The game ends when tails appears for
the first time.
Nic
Topics of this Class
Explanation of the Algorithm
! Explanation of Algorithm for Optimization
Linear
Non-Linear (more will be discussed later)
! Preferences
Feasible set
Indifference Curves
Willingness to Pay/MRS
Utility
Explanation of the Algorithm
The Budget Set
This Class
Consumption Set:
! Effects on the Budget Set when
Consumption Bundle:
2 goods
! Prices change
! Wealth Changes
n goods
! Optimal Choice
Equation of
the budget
line
p1 x1 + p2 x2 = I
p1 x1 + p2 x2 + !+ pn xn = I
Budget
constraint
The Capital Asset Pricing Model
This Class
Ri = R f + !i ( Rm ! R f )
! Estimating the CAPM
! Asymmetric Information
Return
Ri
! Used car market
! Quality in production
! Insurance
Theoretically, any arbitrary asset
Slope: (R be f)
must also m-Ron the mar
This Class
Adverse Selection in Insurance
! Informational Problem:
! Adverse Selection
! Insurance
! Loan Market
Adverse Selection in Insurance
! Informational Problem:
! Consumers are better informed than insurance
providers.
! If an insurance company of
This Class
! Welfare Effects of Price Changes:
! Equivalent Variation
! Compensating Variation
! Income and substitution effect
! Slutzky Equation
Shepards Lemma
!e( p,u)
= h j ( p,u)
!p j
Let x*=h(p*,u), where p* is fixed.
Define g(p)=x*p-e(p,u).
Then g(
This Class
! Income and Substitution Effect
! Substitution Matrix
! Slutzky Equation
Example
Let u(x1,x2)=x1x2. We have shown that
x1 ( p1 , p2 , I ) =
I
I
, x2 ( p1 , p2 , I ) =
2 p1
2 p2
Suppose I=12, p1=1, p2=1 and the price of good 2
increase to p2=2.
This Class
!
!
!
!
Cost minimization
Marginal costs and average costs
Short run costs
Perfect competition
Cost Minimization
Cost Minimization
Production function: f(K,L).
Suppose the cost of a unit of capital is r (rent), and
the cost of a unit of labor i
This Class: Asymmetric
Information
! Adverse Selection
! Moral Hazard
! Agency Problems
Solving Adverse Selection
Problems
! Used car market:
! Reputation of a used car dealer
! Warranties
! Firms choice of production quality:
! Reputation
! Loan markets:
This Class: Asymmetric
Information
! Adverse Selection
! Moral Hazard
! Agency Problems
Solving Adverse Selection
Problems
! Used car market:
! Reputation of a used car dealer
! Warranties
! Firms choice of production quality:
! Reputation
! Loan markets:
This Class
! Risk aversion
! The capital asset pricing model (CAPM)
Concave Functions
Bernoulli
utility
wealth
x
x
u(x) (I.e., the blue curve) is concave if the red
line is always below the blue curve, for all
points x, x.
Concave Functions
A Characteriza
ECON500 General Microeconomic Theory
Fall 2015 - M2
A
1 variables:
2 x
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Starting x
1
3
4
B
C
4.328454 objective:
D
y*
E
F
G
H
I
J
-0.36508 =B2^6-18.8*B2^5+144.35*B2
ECON500 General Microeconomic Theory
Fall 2015 - M2
b) Qd' = 31 - (p+6)
Qd' = 25 - p
c) Qs' = 4 + 2(p-6)
Qs' = -8 + 2p
Homework 1 - Question 4
d) In both cases total tax revenue is q * 6.
As q*' = q*' = 18, tax revenue is 108.
Gustavo Santinoni Vera
Rafae
H 10, E500
Fall, 2014
The homework is due on Tuesday, December 10 at 4pm. Each questions is worth 0.8
points.
Question 1 A monopolist sells a product in two dierent markets. Demand in the rst
market is Q = 120 2P. Demand in the second market is Q = 120 8P
H 9: E500
Fall, 2014
The homework is due on Tuesday, December 2. Each question is worth 0.8 points.
Question 1 There are 200 rms in an industry. Half of the rms use newer technology
resulting in a cost function c(Q) = 200 + Q2 , while the the remaining rm