Chapter 9 - Perfectly Competitive Markets

Instructor: Patrick Turner

March 20, 2017

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Outline

Introduction

Assumptions for Perfect Competition

Firm Supply Decision

Short-Run Equilibrium

Short-Run Market Supply Curve

Long-Run Equilibrium

Industry Costs

Producer Surplus

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Market for Roses

Nevado Roses

I 1.5 billion roses bought annually in the United States and 400million come from Ecuador

I Nevado Roses is one of the largest rose producers in Ecuadorwith 750 workers, but there are about 400 other rose sellers inEcuador and many more in countries like Colombia

I Because its proportion of the market is small, its productiondecision has virtually no impact on the market price of roses.

I The key decision for Nevado is not how much to charge forroses (price), but how many to grow (quantity)

I This is an example of a firm operating in a perfectlycompetitive market

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Introduction

Perfectly Competitive markets consists of firms that:

I Produce identical products that sell at the same price

I Have a small share of the total volume of output so that nosingle firm has an impact on the market price

Examples:

I Agriculture Products, Minerals, ...

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Introduction

This chapter:

1. Will see how market supply is determined

2. Will see how market price is determiend

3. Learn the dynamics of firm entry and exit

4. Learn key concepts of how markets work

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Assumptions of Perfect Competition

1. Fragmentation

2. Undi↵erentiated Products

3. Perfect Information About Products

4. Equal Access to Resources

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(1) Fragmentation

I Industry is fragmented which means it consists of manybuyers and sellers

I Each buyer’s purchases are so small that they do not a↵ectthe market price

I Each seller’s output is so small in comparison to marketdemand that they do not a↵ect market price

I Each seller’s input purchases (labor) are so small that they donot a↵ect the price of inputs (wages)

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(2) Undi↵erentiated Products

I Consumer perceives the product to be identical no matter whoproduces them

I A rose is a rose no matter who produced it

I This probably doesn’t hold for many of the products youpurchase (brand power)

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(3) Perfect Information About Prices

I Consumer knows the prices of all the sellers in the marketI Florist will know the wholesale price of roses from all

distributors (or can easily use the phone/internet to find out)

I What goods do you know the prices for?

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(4) Equal Access to Resources

I All firms in the industry and all potentially new entrants havethe same access to inputs and technologies

I Firms can hire inputs (labor, capital, materials) as they needthem and release them as they no longer need them

I This assumption also referred to as “free entry and exit”.I Firms in the airline industry violate this assumption.

Companies like Southwest need access to gates at airportswhich are not easily available to new entrants.

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Implications of Assumptions

Assumption (1) =) sellers and buyers act as price takers

I When making output decision, the firm:I Takes the prices of inputs as givenI Takes the price of output as given

I When making a purchasing decision, consumers:I Take the market price of the product as given

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Implications of Assumptions

Assumption (1) =) sellers and buyers act as price takersI When making output decision, the firm:

I Takes the prices of inputs as givenI Takes the price of output as given

I When making a purchasing decision, consumers:I Take the market price of the product as given

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Implications of Assumptions

Assumption (1) =) sellers and buyers act as price takersI When making output decision, the firm:

I Takes the prices of inputs as givenI Takes the price of output as given

I When making a purchasing decision, consumers:I Take the market price of the product as given

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Implications of Assumptions

Assumptions (2) & (3) =) Law of One Price

I Transactions between buyers and sellers occur at a singlemarket price because all products are identical

I The buyer knows the price at all firms and will purchase atthe lowest price. So, all firms must o↵er the lowest price orthey won’t sell anything.

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Implications of Assumptions

Assumptions (2) & (3) =) Law of One PriceI Transactions between buyers and sellers occur at a single

market price because all products are identical

I The buyer knows the price at all firms and will purchase atthe lowest price. So, all firms must o↵er the lowest price orthey won’t sell anything.

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Implications of Assumptions

Assumptions (2) & (3) =) Law of One PriceI Transactions between buyers and sellers occur at a single

market price because all products are identical

I The buyer knows the price at all firms and will purchase atthe lowest price. So, all firms must o↵er the lowest price orthey won’t sell anything.

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Implications of Assumptions

Assumption (4) =) Free Entry into IndustryI If it is profitable for a new firm to enter into the industry, they

will do so.

I It will cost them some set-up costs but they have access to allthe same technology and inputs

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Profit Maximization by a Price Taking Firm (Perfect

Competition)

In Chapter 7, we solved the following problem

minL,K

TC = wL+ rK Total Economic Costs

s.t. Q = f (L,K ) Production Function where Q̄ was given

I We found the optimal amounts of L⇤ and K ⇤ to make Q̄

In Chapter 8, we used L⇤ and K ⇤ to derive the total cost function

TC (Q) = wL⇤(Q) + rK ⇤(Q)

In Chapter 9

I Firm selects the profit maximizing amount of Q

I Q is no longer taken as given

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Profit Maximization by a Price Taking Firm (Perfect

Competition)

In Chapter 7, we solved the following problem

minL,K

TC = wL+ rK Total Economic Costs

s.t. Q = f (L,K ) Production Function where Q̄ was given

I We found the optimal amounts of L⇤ and K ⇤ to make Q̄

In Chapter 8, we used L⇤ and K ⇤ to derive the total cost function

TC (Q) = wL⇤(Q) + rK ⇤(Q)

In Chapter 9

I Firm selects the profit maximizing amount of Q

I Q is no longer taken as given

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Profit Maximization by a Price Taking Firm (Perfect

Competition)

In Chapter 7, we solved the following problem

minL,K

TC = wL+ rK Total Economic Costs

s.t. Q = f (L,K ) Production Function where Q̄ was given

I We found the optimal amounts of L⇤ and K ⇤ to make Q̄

In Chapter 8, we used L⇤ and K ⇤ to derive the total cost function

TC (Q) = wL⇤(Q) + rK ⇤(Q)

In Chapter 9

I Firm selects the profit maximizing amount of Q

I Q is no longer taken as given

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Firm Profits

Profits: ⇡ = TR(Q)� TC (Q)| {z }Derived in Ch. 8

If the firm is a price taker, we can re-write the profit equation as

⇡ = PQ � TC (Q)

where

I P is the price an output good can sell for

I Q is the quantity produced

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Marginal Revenue

Marginal Revenue: The rate at which total revenue changes withoutput

MR =@TR

@Q

When the firm is a price taker, total revenue is

TR = PQ

So,

MR =@TR

@Q= P

For a price taking firm: MR = P

I Suppose the price of a rose if $1

I If I sell one more rose, my total revenue will go up by $1

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Marginal Revenue

Marginal Revenue: The rate at which total revenue changes withoutput

MR =@TR

@Q

When the firm is a price taker, total revenue is

TR = PQ

So,

MR =@TR

@Q= P

For a price taking firm: MR = P

I Suppose the price of a rose if $1

I If I sell one more rose, my total revenue will go up by $1

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Marginal Revenue

Marginal Revenue: The rate at which total revenue changes withoutput

MR =@TR

@Q

When the firm is a price taker, total revenue is

TR = PQ

So,

MR =@TR

@Q= P

For a price taking firm: MR = P

I Suppose the price of a rose if $1

I If I sell one more rose, my total revenue will go up by $1

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Marginal Revenue

Marginal Revenue: The rate at which total revenue changes withoutput

MR =@TR

@Q

When the firm is a price taker, total revenue is

TR = PQ

So,

MR =@TR

@Q= P

For a price taking firm: MR = P

I Suppose the price of a rose if $1

I If I sell one more rose, my total revenue will go up by $1

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Marginal Revenue

Marginal Revenue: The rate at which total revenue changes withoutput

MR =@TR

@Q

When the firm is a price taker, total revenue is

TR = PQ

So,

MR =@TR

@Q= P

For a price taking firm: MR = P

I Suppose the price of a rose if $1

I If I sell one more rose, my total revenue will go up by $1

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Firm’s Profit Maximization Problem: find the Q that maximizes ⇡

maxQ

⇡ = TR(Q)� TC (Q)

First-Order Condition:

@⇡

@Q=

@TR

@Q� @TC

@Q= 0

@TR

@Q=

@TC

@Q

MR = MC

All firms maximize profit where MR = MC

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Profit Maximization

Second-Order Condition:

@2⇡

@Q2

����Q=Q⇤

< 0

Marginal Profit must be decreasing at the optimal output level ofQ⇤

I Q < Q⇤ profit is increasing

I Q > Q⇤ profit is decreasing

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Profit Maximization

If a firm is a price taker, we can re-do this

maxQ

⇡ = PQ � TC (Q)

First-Order Condition:

@⇡

@Q= P � @TC

@Q= 0

P = MC

Price taking firms maximize profit where P = MC

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Profit Maximization

If a firm is a price taker, we can re-do this

maxQ

⇡ = PQ � TC (Q)

First-Order Condition:

@⇡

@Q= P � @TC

@Q= 0

P = MC

Price taking firms maximize profit where P = MC

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Profit Maximization

If a firm is a price taker, we can re-do this

maxQ

⇡ = PQ � TC (Q)

First-Order Condition:

@⇡

@Q= P � @TC

@Q= 0

P = MC

Price taking firms maximize profit where P = MC

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Profit Maximization

If a firm is a price taker, we can re-do this

maxQ

⇡ = PQ � TC (Q)

First-Order Condition:

@⇡

@Q= P � @TC

@Q= 0

P = MC

Price taking firms maximize profit where P = MC

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Profit Maximization

If a firm is a price taker, we can re-do this

maxQ

⇡ = PQ � TC (Q)

First-Order Condition:

@⇡

@Q= P � @TC

@Q= 0

P = MC

Price taking firms maximize profit where P = MC

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Thinking About Optimal Quantity

Recall,

MC =@TC

@Q

Tells us rate at which costs change with output orif the firm produces 1 more rose how much morewill it cost

So if,

MR > MC if the firm produces one more rose, they will getmore revenue from selling the last rose than it costthem to make (Profit increases)

MR < MC if the firm produces one more rose, they will get lessrevenue from selling the last rose than it cost themto make (Profit decreases)

The firm wants to keep increasing output Q just to whereMR = MC (P = MC for price takers)

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Thinking About Optimal Quantity

Recall,

MC =@TC

@Q

Tells us rate at which costs change with output orif the firm produces 1 more rose how much morewill it cost

So if,

MR > MC if the firm produces one more rose, they will getmore revenue from selling the last rose than it costthem to make (Profit increases)

MR < MC if the firm produces one more rose, they will get lessrevenue from selling the last rose than it cost themto make (Profit decreases)

The firm wants to keep increasing output Q just to whereMR = MC (P = MC for price takers)

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Thinking About Optimal Quantity

Recall,

MC =@TC

@Q

Tells us rate at which costs change with output orif the firm produces 1 more rose how much morewill it cost

So if,

MR > MC if the firm produces one more rose, they will getmore revenue from selling the last rose than it costthem to make (Profit increases)

MR < MC if the firm produces one more rose, they will get lessrevenue from selling the last rose than it cost themto make (Profit decreases)

The firm wants to keep increasing output Q just to whereMR = MC (P = MC for price takers)

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Thinking About Optimal Quantity

Recall,

MC =@TC

@Q

Tells us rate at which costs change with output orif the firm produces 1 more rose how much morewill it cost

So if,

MR > MC if the firm produces one more rose, they will getmore revenue from selling the last rose than it costthem to make (Profit increases)

MR < MC if the firm produces one more rose, they will get lessrevenue from selling the last rose than it cost themto make (Profit decreases)

The firm wants to keep increasing output Q just to whereMR = MC (P = MC for price takers)

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Profit Maximization

Notice: There are two quantities at which MR = MC

1. Profit minimum: Q = 60

2. Profit maximum: Q = 300

This is why there are two conditions for profit maximization in aperfectly competitive arket

1. P = MC

2. MC must be increasing

If these conditions do not hold, the firm is not profit maximizing

Where to now?

I Construct an individual firm’s short-run supply curve.

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Profit Maximization

Notice: There are two quantities at which MR = MC

1. Profit minimum: Q = 60

2. Profit maximum: Q = 300

This is why there are two conditions for profit maximization in aperfectly competitive arket

1. P = MC

2. MC must be increasing

If these conditions do not hold, the firm is not profit maximizing

Where to now?

I Construct an individual firm’s short-run supply curve.

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What is the short-run?

1. The number of firms in the industry is held fixed

2. At least one input of each firm is held fixed

I New firm’s can’t enter the market even if there is a profitbecause at least one of their inputs is fixed at zero or can’taccess production technology

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Short-run Total Cost of Producing Q

I We discussed short-run costs of: STC (Q) = TFC + TVC (Q)

I Now, we will consider two types of fixed costs

1. Sunk Fixed Costs (SFC ): a fixed cost a firm cannot avoid if ittemporarily suspends operation and produces zero output.

I Example: lease on land that stipulates the firm can’t rent outland to anyone else

2. Nonsunk Fixed Costs (NSFC ): a fixed cost (doesn’t vary withoutput) that can be avoided if output is reduced to zero units

I Example: Electricity costs for lighting

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Short-run Total Cost of Producing Q

I We discussed short-run costs of: STC (Q) = TFC + TVC (Q)

I Now, we will consider two types of fixed costs

1. Sunk Fixed Costs (SFC ): a fixed cost a firm cannot avoid if ittemporarily suspends operation and produces zero output.

I Example: lease on land that stipulates the firm can’t rent outland to anyone else

2. Nonsunk Fixed Costs (NSFC ): a fixed cost (doesn’t vary withoutput) that can be avoided if output is reduced to zero units

I Example: Electricity costs for lighting

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Short-run Total Cost of Producing Q

I We discussed short-run costs of: STC (Q) = TFC + TVC (Q)

I Now, we will consider two types of fixed costs

1. Sunk Fixed Costs (SFC ): a fixed cost a firm cannot avoid if ittemporarily suspends operation and produces zero output.

I Example: lease on land that stipulates the firm can’t rent outland to anyone else

2. Nonsunk Fixed Costs (NSFC ): a fixed cost (doesn’t vary withoutput) that can be avoided if output is reduced to zero units

I Example: Electricity costs for lighting

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Short-run Cost Structure of Price-Taking Firm

Short-run Total Costs (STC )

STC (Q) =

(SFC + NSFC + TVC (Q) when Q > 0

SFC when Q = 0

I If the firm produces positive output (Q > 0) then the firmincurs their sunk fixed costs, nonsunk fixed costs, and variablecosts

I If the firm produces zero output (Q = 0) then the firm onlyincurs their sunk fixed costs

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Short-run Firm Supply

With the firm’s short-run total cost function STC (Q), we can nowthink about the firm’s supply function

I Remember, if the firm produces, the firm will choose Q sothat P = MC .

I This is the firm’s profit maximizing quantity

We will think about 3 cases

1. All fixed costs are sunk fixed costs (NSFC = 0)

2. Some (but not all) fixed costs are nonsunk (NSFC 6= 0)3. All fixed costs are nonsunk (SFC = 0)

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Case 1: NSFC = 0

I No nonsunk fixed costs

I The firm will not take sunk costs into the production decision(why?)

I Let’s look at a graph.

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Case 1: NSFC = 0

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Case 1: NSFC = 0

Let’s look at the firm’s decision for a few di↵erent prices

I P = 0.25

I P = 0.30

I P = 0.05

I P = 0.18

Shut Down Rule: P < minimum AVC

So now we can draw the short-run supply curve

S(P) =

(0 P < minimum AVC

MC P � minimum AVC

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Case 1: NSFC = 0

Let’s look at the firm’s decision for a few di↵erent prices

I P = 0.25

I P = 0.30

I P = 0.05

I P = 0.18

Shut Down Rule: P < minimum AVC

So now we can draw the short-run supply curve

S(P) =

(0 P < minimum AVC

MC P � minimum AVC

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Case 1: NSFC = 0

Let’s look at the firm’s decision for a few di↵erent prices

I P = 0.25

I P = 0.30

I P = 0.05

I P = 0.18

Shut Down Rule: P < minimum AVC

So now we can draw the short-run supply curve

S(P) =

(0 P < minimum AVC

MC P � minimum AVC

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Example: NSFC = 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Find the short-runsupply curve.

We need a couple of things to solve this problem:

1. Average variable cost curve

2. Marginal cost curve

3. The minimum average variable cost to find the shut-downprice

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Example: NSFC = 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Find the short-runsupply curve.

We need a couple of things to solve this problem:

1. Average variable cost curve

2. Marginal cost curve

3. The minimum average variable cost to find the shut-downprice

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q

=20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q

= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q

= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0

STC = 100 + 20Q + Q2

Step 1: What is the equation for Average Variable Costs (AVC )?

AVC (Q) =TVC

Q=

20Q + Q2

Q= 20 + Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

Step 3: What is the minimum AVC? (occurs at SMC = AVC )

AVC = SMC

20 + Q = 20 + 2Q

Q = 0 =) minimum AVC = 20

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Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

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Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

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Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q

solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Example: NSFC = 0Step 4: What is the supply function?

I When P < 20 the firm produces nothing (below shut-downprice)

I When P � 20 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 201

2P � 10 P � 20

32/66

Case 2: NSFC 6= 0

In this case, some of the fixed costs are nonsunk

TFC = SFC + NSFC

In this scenario, our shut-down rule will change

I Firm not only concerned with covering their AVC , also needto consider average nonsunk fixed costs ANSFC

I These are called average nonsunk costs (ANSC )

ANSC = AVC +NSFC

Q

I Let’s look at the graph

33/66

Case 2: NSFC 6= 0

34/66

Case 2: NSFC 6= 0

I Consider P = 0.15

I Profit-maximizing quantity is Q = 35

I At this price, firm covers AVC , but does not cover all ANSC .

I Firm should shutdown at this price because then they wouldnot incur their nonsunk fixed costs

This gives us our new shut-down rule

Shut Down Rule: P < minimum ANSC

That is, shut down when the price is below the level of averagenonsunk costs at the output where P = MC .

35/66

Case 2: NSFC 6= 0

I Consider P = 0.15

I Profit-maximizing quantity is Q = 35

I At this price, firm covers AVC , but does not cover all ANSC .

I Firm should shutdown at this price because then they wouldnot incur their nonsunk fixed costs

This gives us our new shut-down rule

Shut Down Rule: P < minimum ANSC

That is, shut down when the price is below the level of averagenonsunk costs at the output where P = MC .

35/66

Case 2: NSFC 6= 0

I Consider P = 0.15

I Profit-maximizing quantity is Q = 35

I At this price, firm covers AVC , but does not cover all ANSC .

I Firm should shutdown at this price because then they wouldnot incur their nonsunk fixed costs

This gives us our new shut-down rule

Shut Down Rule: P < minimum ANSC

That is, shut down when the price is below the level of averagenonsunk costs at the output where P = MC .

35/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q

=20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q

= 20 + Q +64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q

= 20 + 2Q

36/66

Example: NSFC 6= 0

Suppose a firm has a short-run total cost curve given by

STC = 100 + 20Q + Q2

where TFC = 100 and TVC = 20Q + Q2. Total fixed costs aredivided into SFC = 36 and NSFC = 64. Find the short-run supplycurve.Step 1: What is the equation for Average Nonsunk Costs (ANSC )?

ANSC (Q) =TVC

Q+

NSFC

Q=

20Q + Q2

Q+

64

Q= 20 + Q +

64

Q

Step 2: What is the equation for Marginal Cost (MC )

SMC (Q) =@STC

@Q= 20 + 2Q

36/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0

STC = 100 + 20Q + Q2

Step 3: What is the minimum ANSC? (occurs at SMC = ANSC )

ANSC = SMC

20 + Q +64

Q= 20 + 2Q

64

Q= Q

Q2 = 64

Q = 8

So, minimum average nonsunk cost is

ANSC (8) = 20 + 8 +64

8= 36

37/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q

solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Example: NSFC 6= 0Step 4: What is the supply function?

I When P < 36 the firm produces nothing (below shut-downprice)

I When P � 36 the firm produces at the quantity whereP = MC

P = MC

P = 20 + 2Q solve for Q since P is given

2Q = P � 20

Q =1

2P � 10

Step 5: Write the supply function

Q = S(P) =

8<

:0 P < 361

2P � 10 P � 36

38/66

Case 3: SFC = 0

All fixed costs are nonsunk

I We will have a new shut down rule

I Since all fixed costs are nonsunk, they can be avoided if thefirm does not produce any output

I In this case, the firm will never operate when there is negativeprofit

I This intuition gives us our shutdown rule

Shut Down Rule: P < minimum SAC

39/66

Short-Run Market Supply Curve

How do we go from the firm’s supply curve to the market supplycurve?

Market Supply Curve: tells us the quantity supplied in theaggregate by all firms in the market

I Tells us the marginal cost of the last unit supplied in themarket

How do we graph this? Need to add up how much each firm in theindustry would supply at each price (horizontal sum of supplycurves)

40/66

Short-Run Market Supply Curve

How do we go from the firm’s supply curve to the market supplycurve?

Market Supply Curve: tells us the quantity supplied in theaggregate by all firms in the market

I Tells us the marginal cost of the last unit supplied in themarket

How do we graph this? Need to add up how much each firm in theindustry would supply at each price (horizontal sum of supplycurves)

40/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

Two Types of firms (100 of each)Low Cost and High Cost

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

Two Types of firms (100 of each)Low Cost and High Cost

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

Two Types of firms (100 of each)Low Cost and High Cost

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

What is market supply?

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Market Supply Curve

Q (Thousands)

0.10

0.20

0.30

0.40

0.50

10 20 30

P

ss1

ss2

Q (Millions)

P

0.10

0.20

0.30

0.40

0.50

1 2 3 4

SS

41/66

Short-Run Competitive Equilibrium

1. Occurs where supply equals demand

QD(P) = QS(P) Gets you Q⇤ and P⇤

Q

P

SS

D

Q⇤

P⇤

42/66

Comparative Statics in the Short-Run Equilibrium

1. What happens to equilibrium values of Q⇤ and P⇤ if there isan increase in the number of firms?

43/66

Comparative Statics in the Short-Run Equilibrium

1. What happens to equilibrium values of Q⇤ and P⇤ if demandincreases?

44/66

Comparative Statics in the Short-Run Equilibrium

1. What happens to equilibrium values of Q⇤ and P⇤ if demandincreases?

44/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profits

Long-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profits

Long-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profitsLong-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profitsLong-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profitsLong-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profitsLong-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

Long-Run Output and Plant-Size Adjustments by

Established Firms

Short-Run

1. Firm’s operate within a given plant size (capital fixed)

2. Number of firms in industry does not change

=) Firms might earn positive or negative economic profitsLong-Run

1. Firms can adjust plant size

2. Firms can leave the industry and new firms can enter

=) In long run, firms enter or exit market until economic profitsare driven to zero

I If firms make positive economic profits, new firms will beattracted to industry and increase market supply causingprices to fall (decrease profit)

I What about if firms make negative profits?

45/66

The Firm’s Long-Run Supply Curve

I Firms should decide how much output to produce (Q) and ifit should stay in the industry using the long-run cost functions

I Still maximize profits where MR = MC where MR = P sincethe firm takes the price as given

Shut-Down Rule in the Long-Run?

I In the long-run, all costs can be avoided so no sunk costs

I Firm loses economic profit when P < ACmin, so will notproduce when the price is lower than ACmin

I Draw graph with MC and AC curves

S(P) =

(0 P < ACminP = MC P � ACmin

46/66

The Firm’s Long-Run Supply Curve

I Firms should decide how much output to produce (Q) and ifit should stay in the industry using the long-run cost functions

I Still maximize profits where MR = MC where MR = P sincethe firm takes the price as given

Shut-Down Rule in the Long-Run?

I In the long-run, all costs can be avoided so no sunk costs

I Firm loses economic profit when P < ACmin, so will notproduce when the price is lower than ACmin

I Draw graph with MC and AC curves

S(P) =

(0 P < ACminP = MC P � ACmin

46/66

The Firm’s Long-Run Supply Curve

I Firms should decide how much output to produce (Q) and ifit should stay in the industry using the long-run cost functions

I Still maximize profits where MR = MC where MR = P sincethe firm takes the price as given

Shut-Down Rule in the Long-Run?

I In the long-run, all costs can be avoided so no sunk costs

I Firm loses economic profit when P < ACmin, so will notproduce when the price is lower than ACmin

I Draw graph with MC and AC curves

S(P) =

(0 P < ACminP = MC P � ACmin

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The Firm’s Long-Run Supply Curve

I Firms should decide how much output to produce (Q) and ifit should stay in the industry using the long-run cost functions

I Still maximize profits where MR = MC where MR = P sincethe firm takes the price as given

Shut-Down Rule in the Long-Run?

I In the long-run, all costs can be avoided so no sunk costs

I Firm loses economic profit when P < ACmin, so will notproduce when the price is lower than ACmin

I Draw graph with MC and AC curves

S(P) =

(0 P < ACminP = MC P � ACmin

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Long-Run Perfectly Competitive Equilibrium

Free Entry:

I In the short-run, the number of firms were fixed. In thelong-run, firms will enter industry if, given the market price, itcan earn an economic profit.

Recall: What characterized a short-run competitive equilibrium?

I Occurred when short-run market supply equaled marketdemand

I Equilibrium was the market price P⇤ and quantity of outputQ⇤

What do you think we will need to characterize a long-runcompetitive equilibrium?

I Market price P⇤, quantity of output Q⇤, and # of identicalfirms n⇤

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Long-Run Perfectly Competitive Equilibrium

Free Entry:

I In the short-run, the number of firms were fixed. In thelong-run, firms will enter industry if, given the market price, itcan earn an economic profit.

Recall: What characterized a short-run competitive equilibrium?

I Occurred when short-run market supply equaled marketdemand

I Equilibrium was the market price P⇤ and quantity of outputQ⇤

What do you think we will need to characterize a long-runcompetitive equilibrium?

I Market price P⇤, quantity of output Q⇤, and # of identicalfirms n⇤

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Long-Run Perfectly Competitive Equilibrium

Free Entry:

I In the short-run, the number of firms were fixed. In thelong-run, firms will enter industry if, given the market price, itcan earn an economic profit.

Recall: What characterized a short-run competitive equilibrium?

I Occurred when short-run market supply equaled marketdemand

I Equilibrium was the market price P⇤ and quantity of outputQ⇤

What do you think we will need to characterize a long-runcompetitive equilibrium?

I Market price P⇤, quantity of output Q⇤, and # of identicalfirms n⇤

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Long-Run Perfectly Competitive Equilibrium

Free Entry:

I In the short-run, the number of firms were fixed. In thelong-run, firms will enter industry if, given the market price, itcan earn an economic profit.

Recall: What characterized a short-run competitive equilibrium?

I Occurred when short-run market supply equaled marketdemand

I Equilibrium was the market price P⇤ and quantity of outputQ⇤

What do you think we will need to characterize a long-runcompetitive equilibrium?

I Market price P⇤, quantity of output Q⇤, and # of identicalfirms n⇤

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Long-Run Perfectly Competitive Equilibrium

Long-Run Perfectly Competitive Equilibrium Occurs when:

1. Long-Run profit max w.r.t. output

P⇤ = MC (Q⇤)

2. Zero Economic Profit

P⇤ = AC (Q⇤)

Note: this give you that P = ACmin because firms entermarket until there are zero profits

3. Market Demand = Market Supply

Qd(P⇤) = D(P⇤) = n⇤Q⇤ or n⇤ =D(P⇤)

Q⇤

where n⇤ is the optimal number of (identical) firms and Q⇤ iseach firm’s optimal supply decision

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

P⇤ = $15

Q⇤ = 50 D(P⇤) = 10

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Equilibrium Example

Q (1000s)

P

Q (Millions)

PLR Cost-Min ! TC curve

MC

AC

D(P)

P⇤ = $15

Q⇤ = 50 D(P⇤) = 10

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

D(P) from Util. Max Problem

P⇤ = $15

Q⇤ = 50 D(P⇤) = 10

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

P⇤ = $15

LR Price is ACmin

Q⇤ = 50 D(P⇤) = 10

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

P⇤ = $15

Q⇤ = 50

Firm operates at

Minimum E�cient Scale

D(P⇤) = 10

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

P⇤ = $15

Q⇤ = 50 D(P⇤) = 10

Price determines market size

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Equilibrium Example

Q (1000s)

P

Q (Millions)

P

MC

AC

D(P)

P⇤ = $15

Q⇤ = 50 D(P⇤) = 10

n⇤ =D(P⇤)

Q⇤=

10, 000, 000

50, 000

n⇤ = 200

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Calculating LR Equilibrium

Recall: The solution for a long-run equilibrium needs 3 things:(P⇤,Q⇤, n⇤)

Problem In this market, all firms and potential entrants areidentical. The long-run total cost curve isTC (Q) = 40Q � Q2 + 0.01Q3, where Q is thousands of units peryear. The market demand curve is D(P) = 25, 000� 1, 000P ,where D(P) is measured in thousands of units. Find the long-runequilibrium quantity per firm, price, and number of firms.

Three steps to solve:

1. Find quantity per firm.I Equilibrium at MES: AC (Q) = MC (Q).

2. Find price.I Plug quantity into MC or AC .

3. Find the number of firms.I Market demand at P⇤ divided by quantity per firm Q⇤

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Calculating LR Equilibrium

Recall: The solution for a long-run equilibrium needs 3 things:(P⇤,Q⇤, n⇤)

Problem In this market, all firms and potential entrants areidentical. The long-run total cost curve isTC (Q) = 40Q � Q2 + 0.01Q3, where Q is thousands of units peryear. The market demand curve is D(P) = 25, 000� 1, 000P ,where D(P) is measured in thousands of units. Find the long-runequilibrium quantity per firm, price, and number of firms.Three steps to solve:

1. Find quantity per firm.

I Equilibrium at MES: AC (Q) = MC (Q).

2. Find price.

I Plug quantity into MC or AC .

3. Find the number of firms.

I Market demand at P⇤ divided by quantity per firm Q⇤

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Calculating LR Equilibrium

Recall: The solution for a long-run equilibrium needs 3 things:(P⇤,Q⇤, n⇤)

Problem In this market, all firms and potential entrants areidentical. The long-run total cost curve isTC (Q) = 40Q � Q2 + 0.01Q3, where Q is thousands of units peryear. The market demand curve is D(P) = 25, 000� 1, 000P ,where D(P) is measured in thousands of units. Find the long-runequilibrium quantity per firm, price, and number of firms.Three steps to solve:

1. Find quantity per firm.I Equilibrium at MES: AC (Q) = MC (Q).

2. Find price.

I Plug quantity into MC or AC .

3. Find the number of firms.

I Market demand at P⇤ divided by quantity per firm Q⇤

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Calculating LR Equilibrium

Recall: The solution for a long-run equilibrium needs 3 things:(P⇤,Q⇤, n⇤)

Problem In this market, all firms and potential entrants areidentical. The long-run total cost curve isTC (Q) = 40Q � Q2 + 0.01Q3, where Q is thousands of units peryear. The market demand curve is D(P) = 25, 000� 1, 000P ,where D(P) is measured in thousands of units. Find the long-runequilibrium quantity per firm, price, and number of firms.Three steps to solve:

1. Find quantity per firm.I Equilibrium at MES: AC (Q) = MC (Q).

2. Find price.I Plug quantity into MC or AC .

3. Find the number of firms.

I Market demand at P⇤ divided by quantity per firm Q⇤

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Calculating LR Equilibrium

Recall: The solution for a long-run equilibrium needs 3 things:(P⇤,Q⇤, n⇤)

Problem In this market, all firms and potential entrants areidentical. The long-run total cost curve isTC (Q) = 40Q � Q2 + 0.01Q3, where Q is thousands of units peryear. The market demand curve is D(P) = 25, 000� 1, 000P ,where D(P) is measured in thousands of units. Find the long-runequilibrium quantity per firm, price, and number of firms.Three steps to solve:

1. Find quantity per firm.I Equilibrium at MES: AC (Q) = MC (Q).

2. Find price.I Plug quantity into MC or AC .

3. Find the number of firms.I Market demand at P⇤ divided by quantity per firm Q⇤

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Long-Run Market Supply Curve

Long-Run Market Supply Curve: A curve that shows the totalquantity of output that will be supplied in the market at variousprices, assuming that all long-run adjustments (plant size, newentry) take place

I So far, we have just derived a point on the long-run marketsupply curve

I Since new firms can enter into the market in the long-run, wecannot obtain LR market supply curve by horizontallysumming firm’s supply curve because there is no fixed amountof firms

Let’s use arguments about changes in short-run to derive thelong-run market supply curve.

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Long-Run Market Supply Curve

Long-Run Market Supply Curve: A curve that shows the totalquantity of output that will be supplied in the market at variousprices, assuming that all long-run adjustments (plant size, newentry) take place

I So far, we have just derived a point on the long-run marketsupply curve

I Since new firms can enter into the market in the long-run, wecannot obtain LR market supply curve by horizontallysumming firm’s supply curve because there is no fixed amountof firms

Let’s use arguments about changes in short-run to derive thelong-run market supply curve.

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

Initial equilibrium in SR and LR

D1

$23

10.4

$23

52

SS1

18

LS

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

What happens when demand "

D1

$23

10.4

$23

52

SS1

18

LS

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

D1

$23

10.4

$23

52

In SR - Price ", Quantity "

SS1

18

LS

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

D1

$23

10.4

$23

52

In SR - Firms make positive profits

SS1

18

LS

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

D1

$23

10.4

$23

52

SS1

18

So more firms enter until ⇡ = 0

LS

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Long-Run Market Supply Curve

Q (1000s)

P

Q (Millions)

P

SMC

ACSAC

$15

50

SS0

D0

$15

10

D1

$23

10.4

$23

52

SS1

18

LS

LS is flat at ACmin or MES

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Long-Run Market Supply

I So in a perfectly competitive market that is initially inlong-run equilibrium, additional market demand is fullysatisfied by new entrants into the market

I In the short-run, increases in demand may increases the price,but in the long-run the price remains unchanged at the levelof the minimum of the average cost curve.

But there is more to the story!

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Long-Run Market Supply

I So in a perfectly competitive market that is initially inlong-run equilibrium, additional market demand is fullysatisfied by new entrants into the market

I In the short-run, increases in demand may increases the price,but in the long-run the price remains unchanged at the levelof the minimum of the average cost curve.

But there is more to the story!

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Constant Cost, Increasing Cost, and Decreasing Cost

Industries

I Thus far, we have been assuming that when firms enter orexit the industry, prices of inputs remain unchanged

I This assumption makes sense when demand for an input inone industry is just a small portion of the demand for theinput by all other industries

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Some Definitions

Constant-Cost Industry: An industry in which the increase ordecrease of industry output does not a↵ect the prices of inputs

I This is the case we just analyzed

Increasing-Cost Industry: An industry in which increases ofindustry output increases the prices of inputs

I This occurs if there are industry specific inputs and the inputsare relatively scarce (e.g., master grower)

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Increasing-Cost Industry

When new firms enter, the price of inputs rises so AC0 " AC1, andACmin " $20. So, LS is now upward sloping

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Some More Definitions

Decreasing-Cost Industry: An industry in which increases inindustry output decreases the prices of some or all inputs

I If there is more demand for inputs, this may allow producersof the inputs to produce at a greater volume and reduce thecost of the input (e.g., computer chip industry)

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Decreasing-Cost Industry

When new firms enter, the price of inputs decreases so AC0 # AC1,and ACmin # $12. So, LS is now downward sloping

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Summary of Perfect Competition

I Free entry will eventually drive economic profit to zero.

I When profit opportunities are freely available to all firms,economic profits will not last.

I Remember though: The assumptions that we placed on thesemarkets - free entry, price taking, perfect information,undi↵erentiated products, etc. - are highly restrictive. Thesewill likely not exist in many markets.

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Producer Surplus

I Supplier’s gain from producing in the market is measured byproducer surplus

I Producer surplus is the di↵erence between the amount forwhich a good sells and the minimum amount the seller wouldbe willing to sell the good for (the firm’s avoidable productioncosts)

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Producer Surplus Example

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Producer Surplus More Generally

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Does Producer Surplus = Economic Profit?

It depends...

I Economic Profit = TR � TC (includes sunk costs)I Producer Surplus = TR � TNSC (doesn’t include sunk costs)

In the short-run

I If the firm has sunk costs, the two are not equal

In the long-run

I There are no sunk costs, so the two are equal

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Producer Surplus in the Short-Run

Market Producer Surplus

I You could figure this out from the market supply curve

OR

I Calculate individual firm’s producer surplus. Then, sumproducer surplus over all of the firms

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Producer Surplus in the Long-Run

In the long-run

Producer Surplus = Economic Profit

but, Economic Profit = 0 in the long-run. Therefore, ProducerSurplus = 0

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Calculating Producer Surplus

Suppose that the market supply curve for milk is given byQ = 60P , where Q is the quantity of milk sold per monty(measured in thousands of gallons) when the price is P dollars pergallon.

(a) What is the producer surplus in this market when the price ofmilk is $2.50 per gallon?

(b) By how much does producer surplus increase when the price ofmilk increases from $2.50 to $4.00 per gallon?

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