Car owners: There are 100 car ownersj = 1, ., 100and the true value of
car owner js used car is $ (j 100). An owner would sell her car as long as
she is paid no less than the true value of her car and would not sell her car
if she were paid less than the
Intermediate Microeconomics
Spring 2017
Musatti
Recitation Outline 2
o
Optimal Bundle
More on preferences and interior solutions
Corner solutions
When prices or the initial endowment change: Demand
o
1) Using Algebra to find the optimal bundle
Intermediate Microeconomics
Spring 2017
Musatti
Recitation Outline Week 5
Topics: Consumers Welfare (Ch. 14)
1.
Equivalent and Compensating Variation
2.
Deadweight Loss
3.
Consumer Surplus
The equivalent variation of a price change or of a poli
Intermediate Microeconomics
Spring 2017
Musatti
Recitation Outline Week 4
Income and Substitution effect Slutsky
Income and Substitutions effect - Hicks
When the price of item X increases, people change their quantity demanded for two reasons. On t
250
PROFIT MAXIMIZATION
(Ch. 19)
19.1 (0) The short-run production function of a competitive firm is
given by f (L) = 6L2/3 , where L is the amount of labor it uses. (For
those who do not know calculusif total output is aLb , where a and b
are constants,
266
COST MINIMIZATION
(Ch. 20)
kinks in the indierence curves. Then you found that the consumers
choice might occur at a boundary or at a kink. Usually a careful look
at the diagram would tell you what is going on. The story with kinks
and boundary soluti
238
TECHNOLOGY
(Ch. 18)
Example: Let the production function be f (x1 , x2 ) = mincfw_x1 , x2 . Then
f (tx1 , tx2 ) = mincfw_tx1 , tx2 = min tcfw_x1 , x2 = t mincfw_x1 , x2 = tf (x1 , x2 ).
Therefore when all inputs are multiplied by t, output is also
1. Money in the Keynesian Model
1. Explain how monetary policy can affect the interest rate in the Keynesian model.
When the government prints money, the supply of money increases. Because price is sticky in
the short run, real and nominal interest rate a
P ROFESSOR X P RESENTS .PROBLEM SET 7
This problem set is due on Sunday, December 4th .
You should submit your solutions on CourseWorks by 10:00 PM on the due date. Late problem sets will NOT be accepted.
You can either type your solutions and submit the
Lecture 9:
Repeated Games
Key Terms in Lecture
Stage game
Trigger strategies
Finitely repeated game
Innitely repeated game
Repeated Games
In many real-world se?ngs, players play the same game over and
over again
the simple consCtuent game that i
Lecture 7:
Game Theory
1
Key Terms in Lecture
Mixed strategies
Continuum of actions
Tragedy of the commons
2
Mixed Strategies
When a players strategy calls for doing one
thing or another with certainty, she is following a
pure strategy
In practice, p
Lecture 8:
Game Theory
1
Key Terms in Lecture
Sequential game
Subgame and proper subgame
Subgame perfect Nash Equilibrium (SPNE)
Backward induction
2
Sequential Games
In some games, the order of moves
matters
a player who can move later in the game can
W3211
Professor Vogel
Recitation solutions for the week of January 30
1. The objective function is
f ( x, y) = ln x + ln y,
and the constraint is
px + qy = I,
where , , p, q > 0 are positive constants.
1a. Find the canditate solution to the problem: maxx,
W3211
Professor Vogel
Recitation Solutions - Sequential move games
Question 1. Recall the Prisoners Dilemma payoff matrix:
Tell
Slient
Tell
Silent
1,1
0,3
3,0
2,2
Suppose that this is a sequential game in which Player 1 moves first and Player 2 follows,
a
W3211 Fall 2014
Professor Vogel
Recitation Solutions - Risk and uncertainty
Bobs utility as a function of his wealth, w, is U (w) = w1/2 . Bobs wealth is $16. He is
given the option to either keep his $16 or to invest his $16 in a new firm called Spri. If
W3211
Professor Vogel
Recitation - Put option
Suppose that $1 today and one year from today are equivalent. Suppose that there is an
option that costs x. Whoever owns the option has the right to sell y shares of Google stock
(to whomever sold the option)
W3211
Professor Vogel
Recitation - Sequential move games
Question 1. Recall the Prisoners Dilemma payoff matrix:
Tell
Slient
Tell
Silent
1,1
0,3
3,0
2,2
Suppose that this is a sequential game in which Player 1 moves first and Player 2 follows,
after seein
Car owners: There are 100 car ownersj = 1, ., 100and the true value of
car owner js used car is $ (j 100). An owner would sell her car as long as
she is paid no less than the true value of her car and would not sell her car
if she were paid less than the
W3211 Fall 2014
Professor Vogel
Recitation - Risk and uncertainty
Bobs utility as a function of his wealth, w, is U (w) = w1/2 . Bobs wealth is $16. He is
given the option to either keep his $16 or to invest his $16 in a new firm called Spri. If he
invest
W3211
Professor Vogel
Recitation - Put option
Suppose that $1 today and one year from today are equivalent. Suppose that there is an
option that costs x. Whoever owns the option has the right to sell y shares of Google stock
(to whomever sold the option)
1
Key Terms in Lecture
Game
players
actions
strategies
payoffs
Nash Equilibrium
Dominant Strategy
weak
strict
2
Game Theory
In economics we consider an agent choosing actions to
maximize its objective function (subject to constraints)
eg: choos
Intermediate Microeconomics - Spring 2016
Mark Dean
Maths Refresher Questions
Due For Practice Only
Question 1 Take the rst and second derivatives of the following functions
1. f (x) = a + bx + cx2
1
2. f (x) = ln(x) + x 2
3. f (x) = 2x (hint: use the fac
Intermediate Microeconomics - Spring 2016
Mark Dean
Homework 2
Due Wednesday 10th February
Question 1 (Indierence Curves) For each of the following set of preferences sketch the indierence curves. Also explain whether the preferences satisfy weak monotoni
Intermediate Microeconomics - Spring 2016
Mark Dean
Homework 1
Due Wednesday 3rd February
Question 1 (Budget Sets 1) This question concerns a consumer who is choosing how many of
two goods to buy: Footballs (the round ones, that you kick with your foot) a
Intermediate Microeconomics
Mark Dean
Homework 7
Due Wednesday, 6th April
1
Question 1 Consider a rm with a production function f (x1 ) = x12 , who faces wages equal to 1
and price for their good equal to 5. Now look at the gure below
This gure has three
S`Q#H2K a2i N aQHmiBQMb
T`BH ky- kyRe
Zm2biBQM R UZmMiBiv ht2bV
RX i 2[mBHB#`BmK- bmTTHv 2[mHb /2KM/, D(p) = S(p)
a bp = c + dp
p=
ac
b+d -
q=
bc+ad
b+d
BMp2`b2 /2KM/ 7mM+iBQM, p =
D(p)
a
b b
BMp2`b2 bmTTHv 7mM+iBQM, p = dc + S(p)
d (BMi2`b2+ib rBi?
bc+a
Intermediate Microeconomics - Spring 2016: Homework 8
Solutions
Prof. Mark Dean
April 14, 2016
Question 1.
part 1.
The inverse supply curve is
p(x) =
8
<M C(x)
:undef ined
if x
x1
otherwise
i.e. the inverse supply curve is the M C curve where marginal cos
Intermediate Microeconomics - Spring 2016
Mark Dean
Homework 5
Due Wednesday 2nd March
Question 1 (Pareto E ciency) Consider the economy and endowments described in Question
1 of Homework 4
1. Show that the equilibrium of the economy is Pareto e cient (sh