INTRODUCTION
REVIEW
AND
ECON 8500 – Summer 2022
Iryna Dudnyk
Organization of the Course
Teacher: Iryna [ir`ina] Iryna_Dudnyk@bcit.ca
Textbook: Perloff 5th ed with MyEconLab
Grading:
• Online and paper homework 20%
• Midterm 35%
(mix of written `theory`
questions and analytical problems)
• Final 45%
Plan For Class:
Lecture for 1.5 – 2 hrs
Lab time – self study in class
Lab answers
TOPICS
• Consumer behavior
• Uncertainty
• Production and Costs in Short-Run
•
Competitive Firms and Markets
• Monopoly
• Price Discrimination
• Game Theory
• Oligopoly
WHAT IS ECONOMICS
Standard Definition: about efficient allocation of
scarce resources.
Social Science: just another way to look at
behavior and what drives choices.
Each science is defined by its assumptions.
Basic assumption:
Everyone is selfish and acts in order to advance their
own well-being – the principle of MAXIMIZATION.
CONSUMER’S CHOICE:
Suppose you go shopping to Metrotown
• Will you only buy things you need?
• Will you buy things you like the most?
• Will you buy something because it is the
cheapest?
CONSUMER’S CHOICE
So, when you go shopping you are facing a
constrained optimization problem:
The OBJECTIVE is to maximize utility (value)
The CONSTRAINT is budget
When shopping, consumers take income and
prices as given and choose how much and what to
buy.
Result: demand curves and optimal bundles.
DEMAND
Suppose I go shopping for peaches. The amount
of peaches I will buy QUANTITY DEMANDED
depends on:
•
•
•
•
LAW of DEMAND
DEMAND CURVE tells us the amount of good
consumers wish to buy at different P’s ceteris
paribus.
IMPORTANT: when price
changes, quantity
demanded changes.
There is NO change in
demand.
CHANGE in DEMAND
Iryna’s demand for sushi
2002 Income = 12,000
2007 Income = 30,000
CHANGE in DEMAND
How does demand for peaches respond to
change in price of nectarines?
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃
𝑃𝑃𝑁𝑁0 = $2.99
𝑃𝑃𝑁𝑁′ = $4.99
Review: Profit Maximization
Firm’s maximization problem:
𝑀𝑀𝑀𝑀𝑀𝑀 𝜋𝜋 = 𝑅𝑅 − 𝐶𝐶
How does a firm know whether to produce more,
less, or it is already maximizing?
Each additional unit will change both revenue
(MR) and cost (MC), need to balance
Result – depends on the market structure:
Competitive firm: S curve is 𝑃𝑃 = 𝑀𝑀𝑀𝑀
Firms with market power (monopoly, oligopoly)
do not have a supply curve.
Review: Equilibrium
EQUILIBRIUM: a situation when nobody wants to
change their behavior.
In equilibrium everybody is doing their best
(maximizing
well-being)
given
the
circumstances.
In market equilibrium:
-Consumers max consumer surplus (utility)
-Firm(s) max profits
-Market clears: Q demanded = Q produced
Review: Competitive Equilibrium
ELASTICITY - IMPORTANT !!!!
Is about how one variable responds to change in
another variable
It is a number.
A number can be
• Positive or negative
• Large
• Small
• Zero
• Infinite
• Elasticity of demand is always negative, most
of the time we will use absolute value 𝜀𝜀
ELASTICITY
Elaticity of demand measures how quantity
demanded responds to change in price.
𝜀𝜀 = by how many % the Q will change if price
changes by 1%.
Notice:
curve.
∆𝑄𝑄
∆𝑃𝑃
∆%𝑄𝑄 ∆𝑄𝑄 𝑃𝑃
𝜀𝜀 =
=
�
∆%𝑃𝑃 ∆𝑃𝑃 𝑄𝑄
is the inverse of the slope of the D
ELASTICITY and REVENUE
Suppose that elasticity is -2. What does this
mean?
∆%𝑄𝑄 > ∆%𝑃𝑃
Demand is ELASTIC when 𝜀𝜀 > 1
Suppose a firm raises the price by 10%, what
will happen to the quantity of the good sold?
∆%𝑄𝑄 =
What will happen to the firm’s revenue?
𝑅𝑅 =
𝑃𝑃 � 𝑄𝑄
E and R
Suppose that elasticity is -0.5. What does this
mean?
Suppose a firm raises the price by 10%, what
will happen to the quantity of the good sold?
∆%𝑄𝑄 =
Demand is INELASTIC when 𝜀𝜀 < 1
What will happen to the firm’s revenue?
𝑅𝑅 =
𝑃𝑃 � 𝑄𝑄
E and R
Suppose that elasticity is -1. What does this
mean?
Suppose a firm raises the price by 10%, what
will happen to the quantity of the good sold?
∆%𝑄𝑄 =
Demand is UNIT ELASTIC when 𝜀𝜀 = 1
What will happen to the firm’s revenue?
𝑅𝑅 =
𝑃𝑃 � 𝑄𝑄
LINEAR DEMAND 𝜺𝜺 =
∆%𝑸𝑸
∆%𝑷𝑷
CALCULUS IS ABOUT DERIVATIVES
• Any time you see the word ‘marginal’ it will
be a derivative of something
• What does the value of derivative tell us?
• On a diagram the value of the derivative
measures the slope of a curve in a point
• As such the number tells us what will happen
to the dependent variable (Y) if independent
variable increases
• Idea is similar to elasticity: the number tells
us how one thing responds to a small change
in another thing.
CONSTANT RULE
If 𝑓𝑓 𝑥𝑥 = 𝐾𝐾 then f ′ 𝑥𝑥 = 0
Where 𝐾𝐾 is some constant, for example, 𝐾𝐾 = 100
𝑓𝑓 𝑥𝑥 = 100
POWER RULE
If 𝑓𝑓 𝑥𝑥 = 𝑎𝑎𝑥𝑥 𝑛𝑛 the derivative is 𝑓𝑓 ′ 𝑥𝑥 = 𝑎𝑎𝑎𝑎𝑥𝑥 𝑛𝑛−1
• If 𝑦𝑦 = 2𝑥𝑥
then 𝑎𝑎 = 2, 𝑛𝑛 = 1 𝑦𝑦 ′ =
• If 𝑦𝑦 = 2𝑥𝑥 0.5 then 𝑎𝑎 = 2, 𝑛𝑛 = 0.5 𝑦𝑦 ′ =
• 𝑦𝑦 = 𝑥𝑥 2 , 𝑦𝑦 ′ =
At max or min the value
of derivative = 0
TWO VARIABLES
Suppose 𝑦𝑦 = 𝑓𝑓(𝑥𝑥, 𝑧𝑧)
𝑦𝑦 responds to both changes in 𝑥𝑥 and 𝑧𝑧. Partial
derivatives allow us to measure the response to each
variable. The trick is to change one thing at a time
Partial derivative with respect to 𝑥𝑥, 𝑦𝑦𝑋𝑋 tells us how y
will respond if x increases by 1 while 𝑧𝑧 stays
constant.
Partial derivative with respect to 𝑧𝑧, 𝑦𝑦𝑧𝑧 tells us how y
will respond if 𝑧𝑧 increases by 1 while 𝑥𝑥 stays
constant.
2-variable calculus example
Suppose the function is 𝑓𝑓 𝑥𝑥, 𝑧𝑧 = 2𝑥𝑥 0.5 � 𝑧𝑧 0.6
Partial w.r.t 𝑥𝑥:
𝑎𝑎 =
, 𝑛𝑛 =
,
𝑓𝑓𝑥𝑥 =
𝑎𝑎 =
, 𝑛𝑛 =
,
𝑓𝑓𝑧𝑧 =
Partial w.r.t 𝑧𝑧:
Algebra
1
3
2
3
𝑥𝑥 𝑎𝑎 𝑥𝑥 𝑏𝑏 = 𝑥𝑥 𝑎𝑎+𝑏𝑏
For example, 𝑥𝑥 𝑥𝑥 =
(𝑥𝑥 𝑎𝑎 )𝑏𝑏 = 𝑥𝑥 𝑎𝑎𝑎𝑎
For example, (𝑥𝑥 2 )3 =
For example, 𝑥𝑥 −.5 =
𝑥𝑥
−𝑎𝑎
1
= 𝑎𝑎
𝑥𝑥
CONSTRAINED MAXIMIZATION
Suppose you want to maximize
𝑈𝑈 = 𝑥𝑥𝑦𝑦 2 (Objective)
Subject to a constraint
2𝑥𝑥 + 𝑦𝑦 = 300 (Constraint)
To do that we use Lagrange method
Lagrange
1. Construct the Lagrange:
2. Take the derivatives, set equal to zero:
Lagrange
3. From (1) and (2): carry lambda to the RHS
and divide:
Lagrange
4. Isolate x or y and substitute into constraint:
Lab Question
Use Lagrange to
1
3
Maximize 𝑈𝑈 = 𝑥𝑥 𝑦𝑦
2
3
Subject to 6𝑥𝑥 + 3𝑦𝑦 = 120