1. Big Idea Assume 1. Market structure is perfectly competitive (not monopoly or duopoly) 2. No externalities (my action hurts or benefits others, but I don’t take into account. Like pollution.) Then the unregulated market (laissez-faire) allocation is efficient. (maximizes the size of the social pie.)

First Welfare Theorem

Adam Smith was on to this. Wealth of Nations, 1776 “Every individual... neither intends to promote the public interest, nor knows how much he is promoting it…(but)…by directing that industry (to) …its … greatest value, he is …led by an invisible hand to promote an end which was no part of his intention.” Market maximizes the pie. (Efficiency) But what does it say about how it is divided up? (Equity). We will talk about that too.

Economics Terminology: Allocation At list specifying all the relevant decisions in a particular context: • Who gets to consume (and what they consume? • How much they pay? • Who produces? • How much producers receive? • What inputs are used? • …..

Feasible Allocation • The technology exists and sufficient resources are available so the allocation is possible.

An Efficient Allocation?

2. Pareto Efficiency Vilfredo Pareto 1848-1923

Pareto Efficient Allocation A feasible allocation that can’t be beat by a Pareto Improvement (So impossible to find another feasible allocation that makes at least one person better off without making any other person worse off.)

Start with a feasible allocation. If there is an alternative feasible allocation that makes at least one person better off and none worse off, we call it a Pareto Improvement

Example 1: Ping Pong Table •

Annoying me, taking up room even folded. Get it out! • I will pay $50 just for someone to haul it away. • Friend just bought a house, very empty…. Pareto Improvement? 1. Friend takes table 2. Friend takes table and gives me $10 3. Friend takes table and I give her $50. All are Pareto Improvements!

Example 2: Albert rooms with Bill Charles rooms with Dale Facts: Albert • hates rooming with Bill, • would like to room with Dale Bill • Doesn’t care about whom he rooms with

Charles • Doesn’t care about whom he rooms with • is having trouble with his economics class • thinks switching rooms would be a bit of a pain Dale • Would prefer rooming with Albert • Would hate moving out of his current room • is an economics major Pareto Improvement: Albert and Charles trade rooms Dale helps Charles with Econ.

3. Pareto Efficiency In Econland

All this to be demonstrated in a model economy Complete—Everything we need to know about everybody completely described.

Econland Inhabitants: D1, D2, D3,….D10 S1, S2, S3, ….,S10 Two kinds of food: widgets and dollars. Dollars: everybody likes to eat them.

Simple Widgets: only D people eat them. A D person has a reservation value for one widget. Amount of dollars he would be exactly willing to give up to get one.

Table of reservation values Name Reservation price for one widget D1 9 D2 8 D3 7 D4 6 D5 5 D6 4 D7 3 D8 2 D9 1 D10 0 D1 thinks $20 and 0 widget = $11 and 1 widget

S people • don’t eat widgets. • but know how to make them • get hungry from widget work Cost to a S person to make one widget. Amount of dollars we have to give her so she is just willing to do it.

Table of Costs Cost of one Name widget (dollars) 1 S1 2 S2 3 S3 4 S4 5 S5 6 S6 7 S7 8 S8 9 S9 10 S10 D1 thinks $20 and making 0 widgets = $19 and making 1 widget

Gather the Information Up Reservation Prices and Costs for Widgets Name Res. Cost Name Price D1 9 1 S1 D2 8 2 S2 D3 7 3 S3 D4 6 4 S4 D5 5 5 S5 D6 4 6 S6 D7 3 7 S7 D8 2 8 S8 D9 1 9 S9 D10 0 10 S10 Each has endowment of 20 dollars

Search for Pareto Efficient Allocations Possibility 1: Is $1,000,000 for all and no widgets for all Pareto Efficient? Not Feasible Possibility 2: Autarky self sufficiency. (Everybody consumes endowment like Robinson Crusoe) S1 makes widget and gives it to D1, D1 gives S1 $5. Both better off (no one worse off) (A Pareto Improv.) Autarky not Pareto Efficient.

Econland Tastes and Technology Reservation Prices and Costs for Widgets Name Res. Cost Name Price D1 9 1 S1 D2 8 2 S2 D3 7 3 S3 D4 6 4 S4 D5 5 5 S5 D6 4 6 S6 D7 3 7 S7 D8 2 8 S8 D9 1 9 S9 D10 0 10 S10 Plus: Each person endowed with $10

4 Conditions for Pareto Efficiency Condition 1: Efficient Allocation of Consumption. Widgets go the D people with the highest reservation prices. Suppose have allocation where D5 gets widget, D1 does not. This is not Pareto Efficient because we can come up with the following Pareto Improvement D5 gives widget to D1, D1 gives $7 to D5 D1 better off by $9-$7=$2 D5 better off by $7-$5=$2. Note: prices of $5,$6,$8,$9, also work

Reservation Prices and Costs for Widgets Name Res. Cost Name Price D1 9 1 S1 D2 8 2 S2 D3 7 3 S3 D4 6 4 S4 D5 5 5 S5 D6 4 6 S6 D7 3 7 S7 D8 2 8 S8 D9 1 9 S9 D10 0 10 S10

Condition 2: Efficient Allocation of Production. Widgets are produced the S people with the lowest costs. Suppose have allocation where S5 makes widget, S1 does not. This is not Pareto Efficient because we can come up with the following Pareto Improvement S1 makes widget instead of S5, S5 gives $3 to S5

S1 better off by $3-$1=$2 S5 better off by $5-$3=$2. Note: prices of $1,$2,$4,$5, also work

Efficient Quantity? Need some new words Q Marginal Consumer (last one in) Marginal Producer (last one in) Marginal Reservation Price: reservation price of marginal consumer Marginal Cost cost of marginal producer Marginal Social Surplus = MRP - MC

Marg Res. Price 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10 0

Marg Marg Cost Social Surplus 1 8 2 6 3 4 4 2 5 0 6 -2 7 -4 8 -6 9 -8 10 -10

Total Social Surplus 8 14 18 20 20 18 14 8 0 -10

Condition 3: Efficient Quantity Set output so that the marginal reservation price equals marginal cost. and D1, D2 eat, S1,S2 make. Suppose Q = 2. This is not Pareto Efficient because we can come up with the following Pareto Improvement S3 makes widget and gives it to D3. D3 gives $5 to S3.

Summing Up: Pareto Efficiency: Four Conditions 1. Efficient allocation of consumption 2. Efficient allocation of production 3. Set Q to that marginal reservation price equals marginal cost 4. No obvious waste

Condition 4: No obvious waste. Don’t throw dollars or widgets in trash.

In Econland, this means:

• •

Q=5 S1, S2, S3, S4, S5 make a widget • D1, D2, D3, D4, D5 eat a widget • $10 per person endowment distributed in some way (no dollars end up in trash) • Social Pie = $20 in Social Surplus from the widget market plus total endowment from dollars

Graphs Marg Res. Price 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10 0

Marg Marg Cost Social Surplus 1 8 2 6 3 4 4 2 5 0 6 -2 7 -4 8 -6 9 -8 10 -10

Total Social Surplus 8 14 18 20 20 18 14 8 0 -10

10 9 8 Marginal Cost

7 6 Dollars

Q

5 4

Marginal Reservation Price

3 2 1 0 0

1

2

3

4

5 Quantity

6

7

8

9

10

Marg Res. Price 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10 0

Marg Marg Cost Social Surplus 1 8 2 6 3 4 4 2 5 0 6 -2 7 -4 8 -6 9 -8 10 -10

Total Social Surplus 8 14 18 20 20 18 14 8 0 -10

10 9 8 Marginal Cost

7 6 Dollars

Q

5 4

Marginal reservation price

3 2 1 0 0

1

2

3

4

5

6

7

8

Quantity

Social Surplus at Q = 1

9

10

Marg Res. Price 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10 0

Marg Marg Cost Social Surplus 1 8 2 6 3 4 4 2 5 0 6 -2 7 -4 8 -6 9 -8 10 -10

Total Social Surplus 8 14 18 20 20 18 14 8 0 -10

10 9 8 Marginal Cost

7 6 Dollars

Q

5 4

Marginal reservation price

3 2 1 0 0

1

2

3

4

5

6

7

8

Quantity

Social Surplus at Q = 2

9

10

Marg Res. Price 1 9 2 8 3 7 4 6 5 5 6 4 7 3 8 2 9 1 10 0

Marg Marg Cost Social Surplus 1 8 2 6 3 4 4 2 5 0 6 -2 7 -4 8 -6 9 -8 10 -10

Total Social Surplus 8 14 18 20 20 18 14 8 0 -10

10 9 8 Marginal Cost

7 6 Dollars

Q

5 4

Marginal reservation price

3 2 1 0 0

1

2

3

4

5

6

7

8

Quantity

Social Surplus at Q = 5

9

10

What happens when Econland is a Market Economy?

•Q = 5 •P = 5 • S1, S2, S3, S4, S5 produce • D1, D2, D3, D4, D5 consume • No dollars thrown in trash Competitive allocation is Pareto efficient First Welfare Theorem also known as Adam Smith’s Invisible Hand Theorem

Marginal Reservation Price = demand curve Marginal Cost = supply curve 10 9 8 Marginal Cost

7 Dollars

6 5 4

Marginal Reservation Price

3

So what is equilibrium?

2

P = MC = MRP

1 0 0

1

2

3

4

5 Quantity

6

7

8

9

10

How is Social Surplus Divided? Consumer surplus of particular buyer = reservation price – price paid Producer surplus of seller = price received – cost

Q Res. price CS Price paid 5 4 1 9 2 8 5 3 3 7 5 2 5 1 4 6 5 5 5 0 6 4 0 7 3 0 8 2 0 9 1 0 10 0 0 Total 10 TS = CS + PS 20 = 10 + 10

Price Cost PS rec. 5 1 4 5 2 3 5 3 2 5 4 1 5 5 0 6 0 7 0 8 0 9 0 10 0 10

See in graph Consumer Surplus and Producer Surplus in Competitive Equilibrium

Consumer Surplus Area between demand curve and price line

10

Producer Surplus Area between price line and supply curve

9 8 Marginal Cost

7 Dollars

6 5 4

Marginal reservation price

3

In Econland, demand and supply curves look like steps

2 1 0 0

1

2

3

4

5 Quantity

6

7

8

9

10

In economy with lots of people, we won’t notice the steps, things will smooth out.

Consumer Surplus and Producer Surplus in Competitive Equilibrium 10

10

9

9

8

8 Marginal Cost

7 6

6 Dollars

Dollars

S

7

5 4

Marginal reservation price

3

5 4

D

3

2

2

1

1

0

0 0

1

2

3

4

5 Quantity

6

7

8

9

10

0

1

2

3

4

5

6

Quantity

CS = Area of Triangle = ½×5 ×5 = 12.5 PS = ½×5 ×5 = 12.5 TS = CS + PS = 25

7

8

9

10

We will put this information in a table

Q P CS PS TS

Some Equilibrium Government in Unregulated Policy… Market Economy 5 5 12.5 12.5 25

Leave Econland for moment and let’s look at another market. (Smigets?) 10 9 8 7 6 5 4 3 2 1 0

Equilibrium in Unregulated Market Economy Q P CS PS TS

0 1 2 3 4 5 6 7 8 9 10

Tax is a wedge…

Taxes Big Picture: • We will see how taxes distort decision making in Econland •

With taxes we won’t be getting socially efficient quantity (But remember, no externalities here)

•

But government gets revenue and it might do something useful with it….

between price consumer pays and price producer receives PD = tax + PS To find equilibrium under tax, find quantity where distance between demand and supply equals the tax.

Econland

P S D Q

10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10 Q8 Q4 Equilibrium with tax of 0, 4, and 8

4. Who bears the burden of tax? Above example, when tax = $4 “change in PD” = ΔPD = $2 “change in PS” = ΔPS = -$2 So burden is split half each. Only happens when supply and demand are mirror images of each other.

Econland 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10 Q4 Q0

Econland with no taxes

Consumer Surplus at PD = 5

Econland with $4 Widget Tax

Consumer Surplus at PD = 7 10 9 8 7 6 5 4 3 2 1 0

10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

ΔCS and ΔPS (PD from 5 to 7) (PS from 5 to 3 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Effect of $4 Tax in Econland Surplus Calculations

Q PS PD

No Tax 5 5 5

CS 12.5 PS 12.5 Gov’t 0 Surplus TS 25

$4 Tax Change 3 3 7

-2 -2 2

4.5 4.5 12

-8 -8 12

21

-4

Transfer from D1,D2, D3 to Gov't Transfer from S1, S2, S3 to

Change in Government Surplus ΔGS = Q × tax = 3 × 4 = 12 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10 Deadweight loss. Allocation with tax not Pareto Efficient.

Call in Economics Doctor Diagnosis the Source of Inefficiency. Problem: Breakdown of Condition 3, Efficient Quantity where Marginal Reservation Price (MRP) equal to Marginal Cost (MC). Q = 3 is too small (Tax puts wedge between MRP and MC)

Other three conditions still satisfied We still get: (1) Efficient Consumption (D1, D2, D3 consume). (2) Efficient Production (S1, S2, S3 produce) (4) No Obvious Waste (as long as tax revenue $12 given to someone to eat and not thrown in the ocean. Or build “Bridge to Nowhere.”)

Suppose gov’t needs money. D10 did something special, Government revenue needed to give him a prize of him $12. Alternative 1 Head Tax $0.60 a person. Tax 20 people raises $12. No deadweight loss from widget tax. Tax widgets, number changes Tax heads, number won’t change No distortions of behavior

Example: In 1377 in England, everyone over the age of 14 and not exempt had to pay a groat to the Crown (to fight war with France)

Head tax is a regressive tax (low income taxes that are a higher proportion of their income than high income people

Alternative 2: Tax of $2 for people with last names <=3. (So S1,S2,S3, D1,D2,D3 all pay $2) Pareto improvement compared to $4 widget tax. Principle Taxes that distort decision making reduce the size of the social pie compared to taxes that don’t distort decisions.

Taxes in Actual Economy Where are the big distortions? • Gasoline? o High tax, but maybe not high enough! Biggies: 1 2 To raise money to pay for government spending, in the U.S. we go after ____ and _____. But in the process: 1. _____ _____ reduced 2. Deadweight loss

Marginal tax rate of my wife If she earns one more dollar as self-employed worker, how much more consumption can she get? AMT=

Income Taxes Alternative Minimum Tax .32 AMT .15 Social Security .08 State .55 Total Left to spend .45 = 1 - .55 But with $0.45, how much consumption? Buy lunch at Plymouth Chipotle, pay tax of .065. So earning one more dollar gets .45 So marginal tax $.423 = ────. rate = 1 - .423 1.065 = .577

Ed Prescott, 2004 Nobel Laureate

• Taxes and Labor Supply • Area of great debate among economists. • Prescott’s analysis compares Europe and the US

Period Country

Labor Supply 1993- Germany 19.3 1996 France 17.5 25.9 United States 1970- Germany 1974 France United States

Tax Rate .59 .59 .40

24.6

.52

24.4 23.5

.49 .40

Labor supply is hours worked per person age 15-64 per week.

Effects of Taxes Depend on Elasticity of D and S Econland: Widget Tax 50/50 split consumers and producers (burden of tax is split equally) PD goes from $5 to $7 PS goes from $5 to $3 Burden is Different if Elastiticies of D & S are different.

Special Case: Perfectly Inelastic Supply 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

$2 Tax

Q PS PD

Effects of Tax No $2 Tax Tax 5 5 5

CS 12.5 PS Gov’t 0 Surplus TS Henry George Theorem: Tax land and get no distortions Does that mean there are no distortions with Property tax?

Special Case: Perfectly Elastic Supply 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

$2 Tax

Q PS PD

Effects of Tax No $2 Tax Tax 5 5 5

CS 12.5 PS Gov’t 0 Surplus TS Think about this in terms of bargaining power. Suppose demand perfectly inelastic. Who bears burden?

Price Controls Price floor: rule that P≥Pmin Examples:

Price ceiling: rule that P≤Pmax. Examples

Banning Price Gouging

Qceiling is minimum of QD and QS Excess demand = QD – QS. In market allocation, don’t have to deal with this. All willing to pay at the market price get the good. With ceiling, have to determine: How allocate? How ration?

Market: P↑ implies QD↓ and QS↑ Price ceiling: ΔP = 0, ΔQS=0, nothing to choke off increase in demand

Answer has a big impact for efficiency.

$3 Price Ceiling in Econland Effects? (compared to free market) 10 9 8 7 6 5 4 3 2 1 0

Easy part: effect on producers. 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Effects of Price Ceiling

Q P PS

Hard Part: Effect on Consumers It depends: Four Cases

Price Change Free Market Ceiling 5 3 -2 5 3 -2 12.5

4.5

-8

1. Efficient Rationing: Highest value consumers get widgets. 2. Inefficient Rationing: Lowest value consumers (who want them) get widgets 3. Consumer Resales: Ceiling applies only to S people. D people allowed resales. 4. Waiting lines

1. Subsidy: pS = pD + subsidy So top of subsidy touches supply, bottom touches demand. If $3 subsidy, then 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

2. Consumer Surplus when Consumers are Treated Differently Remember competitive equilibrium in Econland? 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Can show just the surplus to D1, D3, and D5)when each pays $5

Things can get even trickier if consumers pay different prices. Suppose D1 pays $3, D3 pays $7 and D5 pays $3 and no one else buys

10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

This is what overall consumer surplus would be if D2 and D4 are excluded from market at P = 5.

10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

$3 Price Ceiling in Econland Effects? (compared to free market) 10 9 8 7 6 5 4 3 2 1 0

Easy part: effect on producers. 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Effects of Price Ceiling

Q P PS

Free Price Change Market Ceiling 5 3 -2 5 3 -2 12.5

4.5

-8

Hard Part: Effect on Consumers It depends: Four Cases (Four-handed economist?) 1. Efficient Rationing: Highest value consumers get widgets. 2. Inefficient Rationing: Lowest value consumers (who want them) get widgets 3. Consumer Resales: Ceiling applies only to S people. D people allowed resales. 4. Waiting lines

Case 1: Efficient Rationing 3 units supplied. Assume go to the consumers with the highest reservation price (D1, D2, D3) CS free market 10 9 8 7 6 5 4 3 2 1 0

CS under ceiling: efficient rationing 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

Effects of Price Ceiling Efficient Rationing 10 9 8 7 6 5 4 3 2 1 0

CS

PS

0 1 2 3 4 5 6 7 8 9 10

Dead weight loss

Transfer Firms to consumers

Effects of Price Ceiling Efficient Rationing 10 9 8 7 6 5 4 3 2 1 0

What does this look just like? Like a tax.

Except…. Goes to CS instead of Gov't

0 1 2 3 4 5 6 7 8 9 10 Note: Many of you now might think that the pink triangle is obvious waste. It is obvious now that you have learned some economics! I want to save this for things that are obvious to people not taking Econ 1101. Time spent waiting in line will be an example of obvious waste. That will be like throwing $ in the trash.

Which efficiency conditions are satisfied? 1. Efficient Consumption (highest value consume) 2. Efficient Production (lowest cost produe 4. No obvious waste (no $ in trash) Which is not? 3: Efficient Quantity (that is 5, not 3)

Case 2: lowest reservation price (that want it) get widgets (Inefficient Rationing) Give it to D5, D6, D7 at P = $3.

At P=$, D1, D2, D3, D4, D5, D6, D7 all want to buy. What happens when D5, D5, D7 get it?

CS: inefficient rationing 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Effects of Price Ceiling Free Price Change Market Ceiling PS

12.5

4.5

Case 1: Efficient Rationing CS 12.5 16.5 TS 25 21

-8

Efficiency condition violations? With a price ceiling and inefficient rationing, we get violations of: Condition 1. Efficient Allocation of consumption.

4 -4

Case 2: Inefficient Rationing CS 12.5 4.5 -8 TS 25 9 -16

Above table sums up we have learned so far. Note: PS is the same for each case, so don't have a different entry for each case.

Condition 3: Efficient Quantity (should be 5, is 3).

Pareto Improvements are possible. D7 can sell his widget to D1 for $6 and both are better off. But this would be against the law (since there is a ceiling of $3).

Case 3 Resales Price ceilings that only apply to S people Resales by D people allowed (scalping allowed) : Supply Curve with Resales and Price Ceiling at $3 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Why does supply look like this? P < 3 on supply curve of S people (the widget makers) P > 3 only the D people can be sellers. If a D person initially gets a widget and keeps it, best to think of him as buying it from himself at the resale price. Get word “opportunity cost” in. (Make up for lost time) Equilibrium in scalping market is pD = 7. At this opportunity cost, 3

What do D people get? Two parts Part 1:CS at PD = 7 (the opportunity cost) = ? Part 2: Scalping profit = 7 – 3 = $4 per unit. (× 3 units)=12 Free Price Change Market Ceiling PS

12.5

Case 3: Resales CS 12.5 TS

25

4.5

-8

4.5+12 = 16.5 21

4 -4

$3 Price Ceilings with Consumer Resales Permitted Surplus 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Diagnosis? Condition 3 Violation (output too small)

Case 4: Waiting Lines Market opens 8 a.m. Value of time 50 cents an hour. Equilibrium with waiting time?

Otherwise, patient looks fine as far as efficiency is concerned. (What about equity?) What does this look like? Looks most like Case 1: Efficient Rationing. In fact, if D1,D2,D3 get the widgets initially, Case 3 and Case 1 are the same. But another possibility is D8, D9, D10 get the scalping profit instead.

Full price = P + value of waiting time

How figure out equilibrium? Step 1: Q pinned down by price ceiling and supply curve. Here QS = 3 at PCeiling = $3 Step 2: Full price will be bid up to clear market on demand side. Here Full Price=$7 Look at demand, at what price is QD=3? Step 3. Value of waiting time (per unit)= full price – purchase price Here value of waiting = $7-$3 = $4

10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Step 4: Total Value of waiting = value per unit × number of hours Here $4 = $.50×8

Effects of Price Ceiling Free Price Change Market Ceiling PS

12.5

4.5

-8

Case 4: Waiting lines CS 12.5 4.5 TS 25 9

8 -16

Surplus with Waiting Lines 10 9 8 7 6 5 4 3 2 1 0

0 1 2 3 4 5 6 7 8 9 10

Need to calculate CS at full price

Diagnosis: Loss from too small Q (Condition 3 violation) Obvious waste of waiting lines (Condition 4 violation)