Answer all of the following questions:
1. Consider the following utility function:
U (x; y) = x + y ; 0 <
<1
(a) Find the income and substitution eects.
(b) Does the substitution eect increase or decrease when
plain.
increases? Ex-
2. Consider the followi
(e) There are 3 NEs:
(1) Player 1 playing V, player 2 playing DV/V, DV/DV
(2) Player 1 playing DV, player 2 playing V/V, V/DV
(3) Player 1 playing DV, player 2 playing DV/V, V/DV
(f) There are 3 subgames:
(1) The entire subgame
(2) The game played by Teen
Suggested Answers
Question 1
The utility function is given as: x + y
1
We can multiple it by for a monotonic transformation to:
x
Max
+
y
x
+
y
.
subject to [I Px x Py y] = 0
x
+ y + [I Px x Py y]
L=Max
FOCs yield:
x1 Px = 0 x1 = Px
y 1 Py = 0 y 1 = Py
Unit 4
Now, we focus on how goods are produced from inputs. The two concepts
related to production are cost and production functions. We discuss various
production functions in some details and take a look at the dierence between
long and short-run cost f
Unit 4
Our aim is to know:
what is an isoquant
different production functions
returns to scale
how to derive a cost function
how to derive a contingent input demand
the difference between LR and SR cost functions
Production Function
The production functio
Unit 5
We continue with the theory of the rm and now we look at how rms
allocate their resources to produce goods. A rm in neoclassical model is prot
maximizing. We discuss this optimization process in the context of competitive
and non-competitive market
UNIT 5
We are going to learn about:
price elasticity of demand
how to maximize profit
the SR supply function
the input demand functions
producer surplus
Elasticity
Elasticity is defined as the percentage (%) change in a
dependent variable y divided by the
SU GGEST ED SOLU T ION S to HW 1
2.1U (x, y) = 4x2 + 3y 2
a. U = 8x, U = 6y,
x
y
b. U = 8, U = 12,
x
y
c.dU = 8xdx + 6ydy
dy
d. dx = U x = 8x
Uy
6y
e. x = 1, y = 2 U = 4(1)2 + 3(2)2 = 16
dy
f. dx = 8x
12
g. 4x2 + 3y 2 = 16
2.2 = Pr of it = R C = 70q q 2 q
HW 3
11.1 T C = :1q 2 + 10q + 50
a. = 20q :1q 2 10q 50
@
:2q = 0 ! q = 50
@q = 10
2
b. Plugging in q = 50; = 20 (50) :1 (50)
10 (50) 50 = 200
c. M C = :2q + 10
AV C = :1q + 10
Atq = 0; M C = AV C and f or q > 0; M C > AV C
So as long as P 0;the rm will su
5.1
a. U = 3 x + y
8
I
b. x = Px if Px < 3 Py
8
I
x = [0; Px ] if Px = 3 Py
8
x = 0 if Px > 3 Py
8
c. Will be drawn in the class.
d. Income will shift up the demand curve. If Py changes, the demand
3
curve will not change unless it reverses the inequality
Unit 3
Our goal is to know:
how to derive and draw Marshallian demand curves
how to derive and draw compensated demand curves
how to derive income and substitution effects
mathematically and graphically
how to measure the change in welfare
Marshallian Dem
Unit 3
The discussion on utility functions continues. We illustrate graphically and
mathematically the dierence between income and substitution eects. We also
dene complementarity and substitutability among goods. Our goal is to know:
how to derive and d
UNIT 2
In this unit, we are going to learn:
what is a utility function
what is an indifference curve and what is the
marginal rate of substitution
what are the necessary and sufficient conditions
for utility maximization
the definitions of Concavity, Quas
Unit 7
In partial equilibrium models, only one market clears. Reality consists of
many such markets that are interrelated. How such multitude of exchange
clears is the topic of this lecture. It is called general equilibrium denoting the
how all the market
Unit 7
Production Possibilities Frontier
how factor markets clear
how equilibrium prices are determined
what is production efficiency and Pareto efficiency
Walras's law
welfare theorems
In the last class, we developed a model where supply and demand are
e
Unit 8
Unlike the ctitious market model described above, the real world is plagued
by risk and uncertainty. At this point, we discuss how a rational consumer
handles risk and uncertainty. While doing so, we dene a risk averse person and
introduce the econ
Unit 8
what is risk-aversion?
how to measure the degree of risk-aversion?
the difference between expected utility and expected value
risk-premium
the portfolio problem
What is risk-aversion?
Option 1: Flip a coin. If you get H, you win $1. You lose $1 if
Unit 9
Over the years, Game Theory has evolved as a separate discipline and has
introduced us to a whole new set of tools and a novel way of thinking to understand the surrounding world. In this brief introduction, we discuss Nash
Equilibrium, sequential
Unit 9
Simultaneous games
Sequential games
Repeated games
In game theory,
Players are basically decision makers.
Strategy is basically the choice set of actions each player can choose.
Payoffs are the final returns of the players.
Simultaneous Game
A game
Unit 10
The equilibrium conditions of imperfect market markedly dier from the
previously discussed perfect competition. In these two chapters we discuss the
origins of monopoly, and the reason behind price discrimination among consumers. We also address t
Unit 10
Our goal is to know:
how a monopoly maximizes its profit
what is price-discrimination
what is Bertrand equilibrium
what is Cournot equilibrium
what is Stackelberg equilibrium
Monopoly
For a price-searching firm like a monopoly, price itself is a v
Unit 1
We basically discuss how microeconomics has evolved over the years to the
present state. Next we move on to a brief review of math. The math review
covers, calculus, optimization with one or more than one variables, the necessary
and su cient condi
UNIT 1
At the end of this unit, you should be able to know :
basic differentiation rules
how to optimize
the necessary and sufficient conditions for optimization
the implicit function rule
integration
History of Economic Thought
Neoclassical school was de
Unit 2
First, we dene utility functions. Afterwards, we move to utility maximization and the necessary and su cient conditions of it. We also dene and show
how to calculate indirect utility and expenditure functions. This lecture will
exemplify how mathem
Unit 6
At this point, we combine the two threads of our discussions - consumers and
producers to see how markets really work together. In other words, we see how
supply (producers response) and demand (the need of the consumer) respond
to each other. We c