econ-115 lecture 02 - kids in prison program · “thinking on the margin.” (econ 1/ econ 100)...

ECON 115

Industrial Organization


1. Tonight is a calculus review.

2. And a review of basic

microeconomics.

3. We will do a couple of

problems in class.


First hour: Calculus

• “Thinking on the margin.”

• Introducing basic

differential calculus and

its relationship to

economics

– Finding “the margin”

– Finding the maximum

• Two quick problems

Second Hour: Micro

• Simple Demand Curve

• Perfect Competition

• P = MR = MC

• Monopoly

– Marginal Revenue Curve

– Profit maximization (MR =

MC)

• Efficiency

• Deadweight loss & monopoly

• One quick problem


• We are going to do a BRIEF calculus

review.

• This is NOT a math class; it’s not a

particularly math-oriented class.

• However, in presenting the concepts in this

course, it is often less cumbersome and more

instructive to be able to use calculus.


• Economic relationships are often expressed

in terms of “functions” that relate one

economic value to another.

• Examples include Cost Functions, Demand

Functions and Production Functions.


• Economists also talk about the concept of

“thinking on the margin.” (ECON 1/ ECON 100)

• “Rational people often make decisions by

comparing marginal benefits to marginal costs.”

• The “margin” refers to incremental change.

“Marginal revenue,” for example, refers to the

incremental change in total revenue; “marginal

cost” refers to the change in total costs.


• Economic decisions are made on the margin

because everything we do of necessity creates

change. Some change makes you better off (a

benefit), while other change makes you worse

off (a cost).

Industrial OrganizationThings we might

do:

Added (marginal)

benefits:

Added (marginal)

costs

Eat cookies

Go to work

Start a business

Study for I/O

Watch TV

Industrial OrganizationThings we might

do

Added (marginal)

benefits

Added (marginal)

costs

Eat cookies Tastes great!! Fattening

Go to work Increase income Wake up early

Start a home

business

Set my own hours Give up my day

job

Watch TV Mindless fun Study time

Study for I/O Real fun ????


We do things

because of

the changes

these actions

induce . . .

. . . especially

if the added

benefits >

than the

added costs.

That’s what

it means to

“think on the

margin.”


• If decisions are made on the margin, how

can economists identify marginal values?

• The most prominent method is calculus.

• Calculus was invented by two men –

Newton and Leibniz – in the 17th century,

independently of one another.


• To understand how calculus works,

remember there are two expressions similar

to the concept of “the margin”:

• “rate of change”

• “slope of the tangent line” of a function


P EXAMPLE:

Downward sloping

Curve

Q

• The slope of the tangent

line tells us the rate of

change at that particular

point on the line

rise

run


• “Slope of the tangent line,” “rate of

change” and “margin” are (almost) the

same.

• One type of calculus – differential calculus –

allows us to determine the slope of the

tangent line for certain functions.

• This method is called differentiation, and the

result that is obtained is called the derivative.


• Notations for the Derivative:

• Given y = f(x), then

f’(x) y’ dydx

all represent the derivative of f at x


• Interpretations of the Derivative:

Slope of the tangent line

Instantaneous rate of change

• Question: given a function, how do

you calculate the derivative?

General Formulas

1 Constant Rule

2 Factor Rule

3 Factor Rule

4 Sum Rule

5 Product Rule

6 Product Rule

7

Quotient Rule

8 Chain Rule

9 Power Rule

10 Power Rule

11

Selected Differentiation Rules


Differentiate: y = 3x2 + 2x

• Solution:

Step #1 – Sum Rule

(3x2)’ + (2x)’

Step #2 – Power Rule

2*3*x2-1 + 1*2x1-1

= 6x + 2

Differentiate f(x) = (3x + 1)4

• Solution

Step #1 – Gen’l Power Rule

u = 3x + 1; n = 4

nun-1 = = 4(3x + 1)3

du/dx = (3x + 1)’ = 3

Therefore: nun-1*du/dx =

4(3x + 1)3 * 3

= 12(3x + 1)3


• For multivariable functions, we take derivatives

for each variable individually, holding the other

variable(s) constant. These are partial

derivatives, represented by rather than d.

• If U is a function of (y, x) the partial derivatives

are represented by U/y and U/x.

• All the differentiation rules presented for single

variable equations apply. Remember, when

taking the partial derivative of one variable, the

other variable is treated like a constant.


• EXAMPLE: U is a function of (y, x)

U = y3 + 3yx2 + 4x

• The partial derivatives are:

U/y = 3y2 + 3x2

U/x = 6yx + 4


• In economics, we use derivatives to find

marginal values.

– The Marginal Cost Function approximates the change in the

actual cost of producing an additional unit.

• Given a cost function C(x), MC = C’(x)

– The Marginal Revenue Function measures the rate of change

of the revenue function. It approximates the revenue from the

sale of an additional unit.

• Given the revenue function, R(x), MR = R’(x)


Find the marginal cost function.

Step 1 – Sum Rule

(575)’ + (25x)’ + (-.25x2)’

Step 2 – Constant & Power Rules

(0) + (25) + 2*-.25x2-1

MC Function = 25 - .5x

• Total Costs = C(x) = 575+ 25x - .25x2


• Why do we say “approximate” for MC and MR?

• The formal definition of the derivative is:

• f’(x) = Lim f (x + h) – f (x)h 0 h

• Marginal revenue/cost is the incremental change

from adding ONE unit. If C(x) is a cost function,

then Marginal Cost = C (x + 1) – C (x).

Instantaneous Incremental

Lim f (x + h) – f (x) C (x + 1) – C (x)

h 0 h 1


P

e

x x+1 Q

Difference between f’(x) & MC

MC Curve


• Now comes the most important piece of this

puzzle.

MAXIMIZATION

• Much of economics involves

maximizing some function:

– Maximize utility

– Maximize profits


• At the maximum point of

a function, the slope of

the tangent line = 0.

• Therefore, if you find the

slope of the tangent line

= derivative, and set it to

0, you can find the

maximum!

P

Slope of the tangent line = 0

Max Point

Xmax Q


• Example: Find the maximum revenue

Demand equation p = 10 - .001q

Revenue (R) = p*q

= q*(10 - .001q)

= 10q - .001q2

R’ (derivative) = 10 - .002q

Set = to 0 0 = 10 - .002q

Therefore MAX R is reached at q = 5000


• There are tests to determine if an answer is

the absolute maximum.

• What is important here is the concept of

maximizing a function by (1) taking the

derivative and (2) equalizing it to 0.

• This is a very critical technique used by

almost all economists.


• Basic Microeconomics

• Contrast between two polar opposite cases:

– Perfect competition

– Monopoly

• What is efficiency? (Pareto Optimality)

– No reallocation of the available resources makes one economic agent better off without making some other economic agent worse off.


• We will begin with examining the profit

maximizing behavior of firms.

• Assume a standard linear inverse demand

curve, P = A – BQ

• P = price

• Q = quantity

• A = intercept

• B = slope


Equation:

P = A - BQ

linear

demand

Maximum willingness

to pay$/unit

Quantity

A

A/B

Demand

P1

Q1

Constant

slope

At price P1 a consumer

will buy quantity Q1


• We start with Perfect Competition.

• Firms and consumers are price-takers.

• A firm can sell as much as it likes at the prevailing market price.

– Firms believe that their actions will not affect the market price.

• Therefore, marginal revenue equals price.

• What about profits?


• All firms maximize profits.

p = profit; R = revenues; C = costs

• Profit = p(q) = R(q) - C(q)

• Profit maximization: dp/dq = 0

• This implies dR(q)/dq - dC(q)/dq = 0

• dR(q)/dq = marginal revenue (MR)

• dC(q)/dq = marginal cost (MC)

• So profit maximization implies MR = MC.


• Therefore, for perfectly competitive, profit-

maximizing firms, p = MR = MC.

• The next question: how does a perfectly

competitive market work?


$/unit

Quantity

$/unit

Quantity

D1S1

QC

AC

MC

PCPC

(b) The Industry(a) The Firm

qc

D2

Q1

P1P1

q1

S2

Q´C

$/unit

Quantity

$/unit

Quantity

D1

S1

QC

AC

MC

PCPC

1. With market demand D1

and market supply S1

equilibrium price is PC

and quantity is QC

1a. With market price PC

the firm maximizes

profit by setting

MR (= PC) = MC and

producing quantity qc

qc

D2

2. Now assume

Demand

increases to D2

Q1

P1P1

4.With market demand D2

and market supply S1

equilibrium price is P1

and quantity is Q1

q1

3a. Firms maximize

profits by increasing

output to q1

3. Excess profits

induce firms to

enter the market

•5. Firms enter. The supply curve moves right•6. Price falls; entry continues while profits exist

• 7. Long-run equilibrium is restored at price PC & supply curve S2

S2

Q´C


• Definition of normal profit

– not the same as zero profit

– implies that a firm is making the market

return on the assets employed in the

business

– those returns = opportunity cost of capital


• Now we come to the other pole: monopoly.

• A monopoly is the only firm in the market

– market demand is the firm’s demand

– output decisions affect market clearing

price


$/unit

Quantity

Demand

P1

Q1

P2

Q2

Loss of revenue from the

reduction in price of units

currently being sold (L)

Gain in revenue from the sale

of additional units (G)

Marginal revenue from a

change in price is the

net addition to revenue

generated by the price

change = G - L

At price P1

consumers

buy quantity

Q1

At price P2

consumers

buy quantity

Q2

L

G

41


• Derivation of the monopolist’s marginal revenue

Demand: P = A - BQ

Total Revenue: TR = PQ = AQ - BQ2

Marginal Revenue: MR = dTR/dQ

Therefore: MR = A - 2BQ

With a linear demand the

marginal revenue curve is also

linear with the same price

intercept but twice the slope of the

demand curve.

$/unit

Quantity

Demand

MR

A

Industrial Organization• The monopolist maximizes profit by equating

marginal revenue with marginal cost

• This is a two-stage process

$/unit

Quantity

Demand

MR

AC

MC

Stage 1: Choose output where MR = MC

This gives output QM

QM

Stage 2: Identify the market clearing price

This gives price PM

PMMR is less than price;

Price is greater than MC: loss of

efficiency

Price is greater than average costACM

Positive economic profit

Long-run equilibrium: no entryQC

Output by the

monopolist is less

than the perfectly

competitive

output QC

Profit


• Having presented two distinct market models –

perfectly competitive and monopolistic – we

need to add the method by which economists

evaluate these outcomes.

• Why is one highly regarded and the other

highly regulated?

• The answer is efficiency.

Industrial Organization• Economists use a concept called “Pareto

Optimality” or “Pareto Efficiency.”

• Pareto Optimal: no one can be made better off

without someone being made worse off.

• We can put this in the form of a question:

– Can we reallocate resources to make some individuals

better off without making others worse off?

• To answer the question, we need a measure of

well-being = surplus.


• There are three aspects to the concept of the

surplus in economics. First is consumer

surplus:

– consumer surplus: difference between the

maximum amount a consumer is willing to pay

for a good and the amount actually paid.

Aggregate consumer surplus is the sum over all

units consumed by all consumers.


• Then there is producer surplus:

– producer surplus: difference between the

amount a producer receives from the sale of a

unit and the amount that unit costs to produce.

The aggregate producer surplus is the sum over

all units produced by all producers

• Together they comprise total surplus = the

consumer surplus + the producer surplus.

47

Quantity

$/unit

Demand

Competitive

Supply

PC

QC

The demand curve measures the

consumers willingness to pay for

each unit

Consumer surplus is the area

between the demand curve and the

equilibrium price

Consumer

surplusThe supply curve measures the

marginal cost of each unit

Producer surplus is the area

between the supply curve and the

equilibrium price

Producer

surplus

Aggregate surplus is the sum of

consumer surplus and producer surplus

Equilibrium occurs

where supply equals

demand: price PC

quantity QC


The competitive equilibrium is

efficient

Chapter 2: Basic Microeconomic 48


Demand

Competitive

Supply

QC

PC

$/unit

MR Quantity

Assume that the industry is

monopolizedThe monopolist sets MR = MC to

give output QM

The market clearing price is PM

QM

PMConsumer surplus is given by this

areaAnd producer surplus is given by

this area

The monopolist produces less

surplus than the competitive

industry. There are mutually

beneficial trades that do not take

place: between QM and QC

This is the deadweight

loss of monopoly

Deadweight loss of Monopoly


• Example: Water Produced (2.5)

– Demand: P = 25 – ½ Q

– TC = 100 + 10Q; dTC/dQ = MC = 10

• Price at efficient allocation?

• Price to maximize profits?

• What is the deadweight loss of monopoly?

.


• Efficient allocation: P = MC; 25 – ½ Q = 10. Q =

30, P = 10

• Monopoly pricing:

– P = 25 – ½ Q

– PQ = 25Q = ½ Q2

– MR = d(PQ)/dQ = 25 – 2*1/2Q = 25 – Q

– MR = MC = 25 – Q = 10; Q = 15, P = 17.5


Deadweight loss?

= Triangle BCD

To calculate DWL:

Base: 30 – 15 = 15

Height 17.5 – 10 = 7.5

DWL = 15*7*5/2 =

56.25


• Why can’t the monopolist appropriate the

deadweight loss?

– Increasing output requires a reduction in price.

– this assumes that the same price is charged to everyone.

• The monopolist does create a surplus.

– some goes to consumers

– some appears as profit

• The monopolist bases its decisions purely in its surplus alone.

• The monopolist undersupplies relative to the competitive

outcome.


• Recall the quote from Smith:

• “The monopolists, by keeping the market

constantly understocked, by never fully

supplying the effectual demand, sell their

commodities much above the natural

price.”

Adam Smith, The Wealth of Nations (1776)


• We have covered most of Chapter 2, except Part 2.2 on discounting.

• Next week we will do discounting, and also cover Chapter 3 on Market Structure and Market Power and Chapter 4 on Technology and Cost.

• Please keep reading:

– PRN, Chapters 1 – 4

econ-115 lecture 02 - kids in prison program · “thinking on the margin.” (econ 1/ econ 100)...

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