MIDTERM CHEAT SHEET — Supply, Demand, Equilibrium, Surplus, Shortage, Taxes

1. Demand & Supply Basics

Law of Demand

Price ↑ → Quantity demanded ↓
Price ↓ → Quantity demanded ↑
Graph: downward-sloping line.

Demand Function:

Q_d = a - bP

a = intercept (max quantity demanded when price = 0)
b = slope (how much Qd changes when P changes by 1)

Law of Supply

Price ↑ → Quantity supplied ↑
Price ↓ → Quantity supplied ↓
Graph: upward-sloping line.

Supply Function:

Q_s = c + dP

c = intercept (supply when price = 0)
d = slope (positive)

2. Market Equilibrium (VERY IMPORTANT)

Equilibrium is when:

Q_d = Q_s

This gives:

Equilibrium price (P)*
Equilibrium quantity (Q)*

How to solve equilibrium:

Example from your notes:

Q_d = 10 - 2P

Q_s = 2 + 2P

Set them equal:

10 - 2P = 2 + 2P

10 - 2 = 4P

8 = 4P

P = 2

Now plug back:

Q_d = 10 - 2(2) = 6

Q_s = 2 + 2(2) = 6

Equilibrium: P\ = 2_,_ Q\ = 6**

3. Shortage & Surplus — HOW TO KNOW

Shortage

(Excess Demand)

Happens when:

Q_d > Q_s

Example from your graph:

At price = 5

Qd = 12

Qs = 5

Since 12 > 5 → Shortage

Means price is too low → consumers want more than suppliers produce.

Surplus

(Excess Supply)

Happens when:

Q_s > Q_d

Example from your graph:

At price = 12

Qs = 12

Qd = 8

Since 12 > 8 → Surplus

Price is too high → suppliers produce more than consumers buy.

4. Graph Interpretation (Your messy drawings → fixed)

What matters on the graph:

Intersection = equilibrium
Above equilibrium price → surplus
Below equilibrium price → shortage

Demand curve = downward

Supply curve = upward

5. Consumer Surplus & Producer Surplus

Consumer Surplus (CS)

Area above price, below demand curve, up to quantity sold.

Triangle formula:

CS = \frac{1}{2} \times \text{base} \times \text{height}

Example (yours):

Base = Q = 100
Height = max willingness to pay (400) – price (200) = 200

CS = \frac{1}{2} \cdot 100 \cdot 200 = 10,000

Producer Surplus (PS)

Area below price, above supply curve, up to quantity sold.

Example:

Base = 100
Height = price (200) – minimum acceptable price (0)

PS = \frac{1}{2} \cdot 100 \cdot 200 = 10,000

Total Surplus (TS):

TS = CS + PS

Your example:

TS = 10{,}000 + 10{,}000 = 20{,}000

6. Taxes — The Clean Version

A tax wedges a gap between:

what consumers pay
what producers receive

Tax = difference between the two prices.

Example:

$100 tax

→ consumers pay +50 more

→ producers receive -50 less

Graph changes:

Quantity falls
CS becomes smaller
PS becomes smaller
Government earns tax revenue
A deadweight loss triangle appears

Summary Table

Concept	Condition	Meaning
Equilibrium	Qd = Qs	Market clears
Shortage	Qd > Qs	Price too low
Surplus	Qs > Qd	Price too high
CS	Area above price, below demand	Buyer benefit
PS	Area below price, above supply	Seller benefit
TS	CS + PS	Total welfare
Tax effect	Creates wedge	Reduces quantity + creates DWL

Elasticity!!

1. PRICE ELASTICITY OF DEMAND (PED)

Measures how sensitive Qd is to a change in price.

Formula (Midpoint Method)

— ALWAYS use this in exams:

\text{%ΔQd} = \frac{Q_2 - Q_1}{\frac{Q_1 + Q_2}{2}} \times 100

\text{%ΔP} = \frac{P_2 - P_1}{\frac{P_1 + P_2}{2}} \times 100

E_{d} = \frac{%Δ Q d}{%Δ P}

Interpreting PED

||Condition|Meaning|
|Elastic|Ed > 1|Quantity reacts strongly to price|
|Inelastic|Ed < 1|Quantity reacts weakly|
|Unit elastic|Ed = 1|Proportional reaction|

PED & Total Revenue (TR)

If price ↑	Demand type	TR effect
Price ↑	Elastic	TR ↓
Price ↑	Inelastic	TR ↑
Price ↑	Unit elastic	TR unchanged

✅

Example

P changes: 70 → 90

Qd changes: 5000 → 3000

%Δ Q d = \frac{5000 - 3000}{4000} \times 100 = 50%

%Δ P = \frac{90 - 70}{80} \times 100 = 25%

E_{d} = \frac{50}{25} = 2

✅ Demand is elastic.

If price ↑ → TR will fall.

2. INCOME ELASTICITY OF DEMAND (YED)

Measures how quantity demanded changes when income changes.

Y E D = \frac{%Δ Q d}{%Δ Income}

Interpreting YED

Value	Meaning
Positive (+)	Normal good (demand ↑ when income ↑)
Negative (–)	Inferior good (demand ↓ when income ↑)

Example (Starbucks problem)

YED = 2.6

Income expected ↑ 6%

%Δ Q d = 2.6 \times 6% = 15.6%

Starbucks coffee is a normal good (positive elasticity).

Demand will ↑ 15.6%.

3. CROSS-PRICE ELASTICITY OF DEMAND (XED)

Measures how Qd of Good A reacts when price of Good B changes.

X E D = \frac{%Δ Q d _{A}}{%Δ P _{B}}

Interpreting XED

Value	Interpretation	Meaning
Positive (+)	Substitutes	When price of B ↑ → demand for A ↑
Negative (–)	Complements	When price of B ↑ → demand for A ↓
Zero / near zero	Unrelated goods	No relationship

Question 3 (Cross-Price = −8.7)**

Sign = negative
Therefore goods are complements, NOT substitutes

Correct explanation:

The statement “A and B are substitutes” is incorrect.

Since cross-price elasticity is −8.7, it means the goods are strong complements.

When price of one increases, demand for the other falls.

Elasticity Summary Map (clean version)

Elasticity Types → What sign means → What to conclude

1. PED (Price Elasticity of Demand)

No sign analysis — always negative, so use absolute value
Value > 1 → Elastic
Value < 1 → Inelastic

2. YED (Income Elasticity)

Positive (+) → Normal good
Negative (–) → Inferior good

3. XED (Cross-Price Elasticity)

Positive (+) → Substitutes
Negative (–) → Complements
Zero → Unrelated

PROFIT MAXIMIZATION — CLEAN NOTES

1. Profit Maximization Rule

A firm maximizes profit at the quantity where:

MR = MC

MR (Marginal Revenue) = change in total revenue when quantity increases by 1 unit

MR = \frac{ΔTR}{ΔQ}
MC (Marginal Cost) = change in total cost when quantity increases by 1 unit

MC = \frac{ΔTC}{ΔQ}

Before Q* (profit-max quantity):

MR > MC → producing more increases profit

After Q*:

MC > MR → producing more decreases profit

2. Given Table (from your notes)

Q	Price	TC
0	10	5
1	10	9
2	10	15
3	10	23
4	10	33
5	10	45

3. Step 1: Compute Total Revenue (TR)

TR = P \times Q

Q	TR
0	0
1	10
2	20
3	30
4	40
5	50

4. Step 2: Compute Profit

\pi = TR - TC

Q	TR	TC	Profit
0	0	5	-5
1	10	9	1
2	20	15	5
3	30	23	7
4	40	33	7
5	50	45	5

Profit is highest at Q = 3 and Q = 4, but we must use MR = MC to choose the correct Q.

5. Step 3: Compute Marginal Revenue (MR)

MR = ΔTR

From Q→Q+1	MR
0→1	10
1→2	10
2→3	10
3→4	10
4→5	10

Since price is constant at 10, MR is constant at 10.

6. Step 4: Compute Marginal Cost (MC)

MC = ΔTC

From Q→Q+1	MC
0→1	4
1→2	6
2→3	8
3→4	10
4→5	12

7. Step 5: Locate MR = MC

Compare MR and MC:

Q	MR	MC
1	10	4
2	10	6
3	10	8
4	10	10
5	10	12

The equality occurs at:

MR = MC = 10 \quad \text{at} \quad Q = 4

That is the profit-maximizing quantity.

Final Answer

The profit-maximizing quantity is Q = 4, because this is where MR = MC.

1. TAXES: Consumer Surplus, Producer Surplus, Tax Revenue, Deadweight Loss

When a per-unit tax is imposed:

Demand curve stays the same.
Supply curve shifts upward by the amount of the tax.
Consumers pay a higher price (Pc).
Producers receive a lower price (Pp).
The difference Pc − Pp = tax per unit.
Quantity exchanged decreases.

After-Tax Prices (example in your notes)

Tax = 100

Consumers pay 50 more

Producers lose 50

So if original equilibrium price = 200, then:

Pc = 250

Pp = 150

Consumers Surplus (CS)

Area between demand curve and Pc, up to new quantity.

Producers Surplus (PS)

Area between supply curve and Pp, up to new quantity.

Tax Revenue

\text{Tax Revenue} = (\text{tax per unit}) \times Q_{\text{after tax}}

In your example:

Tax = 250 − 150 = 100

Quantity = 75

\text{Tax Revenue} = 100 \times 75 = 7500

Deadweight Loss (DWL)

Triangle between demand and supply between Q_without_tax and Q_with_tax.

2. BUDGET LINE

A budget line represents all combinations of two goods a consumer can afford.

General budget equation:

P_1Q_1 + P_2Q_2 = M

Key Points

Any point on the line = affordable using entire budget.
Points inside the line = affordable but not using full budget.
Points outside the line = unaffordable.

Slope of the Budget Line

\text{Slope} = -\frac{P_1}{P_2}

Interpretation:

The slope tells you how many units of good 1 must be sacrificed to gain 1 unit of good 2.

Example from your screenshot

Good1 changes from 0 to 20

Good2 changes from 10 to 0

\text{Slope} = \frac{+20}{-10} = -2

Interpretation:

Increasing good 2 by 1 requires giving up 2 units of good 1.

3. OPPORTUNITY COST ON THE BUDGET LINE

Opportunity cost of good 2 (in terms of good 1):

OC_{G2} = \frac{P_2}{P_1}

Opportunity cost of good 1 (in terms of good 2):

OC_{G1} = \frac{P_1}{P_2}

From your example:

Slope = -2 means opportunity cost of 1 unit of good 2 = 2 units of good 1.

4. UTILITY AND MARGINAL UTILITY

Total Utility (TU)

Total satisfaction from consuming Q units.

Marginal Utility (MU)

Additional satisfaction from consuming one more unit.

MU = \frac{ΔTU}{ΔQ}

Example (from your notes)

Trips to London:

TU = [10, 18, 23, 26, 27, 27]

MU values:

10, 8, 5, 3, 1, 0

Law of Diminishing Marginal Utility

As consumption increases, marginal utility decreases.

Graphically:

Quantity consumed ↑ → MU ↓

5. PROFIT MAXIMIZATION: MR = MC

A firm maximizes profit at the quantity where:

MR = MC

Definitions

Total Revenue:

TR = P \times Q

Marginal Revenue:

MR = \frac{ΔTR}{ΔQ}

Marginal Cost:

MC = \frac{ΔTC}{ΔQ}

Profit:

\pi = TR - TC

Your table

Q	P	TC
0	10	5
1	10	9
2	10	15
3	10	23
4	10	33
5	10	45

Compute TR:

Q	TR
0	0
1	10
2	20
3	30
4	40
5	50

Compute MR (ΔTR):

MR = [10, 10, 10, 10, 10]

Compute MC (ΔTC):

MC = [4, 6, 8, 10, 12]

Decision

Find where MR = MC:

At Q = 4:

MR = 10

MC = 10

Thus Q* = 4 maximizes profit.

6. COSTS: MC, AFC, AVC, ATC

From the “Marginal Cost and Average Costs” slide:

Average Fixed Cost (AFC)

AFC = \frac{FC}{Q}

Average Variable Cost (AVC)

AVC = \frac{VC}{Q}

Average Total Cost (ATC)

ATC = \frac{TC}{Q} = AFC + AVC

Marginal Cost (MC)

MC = \frac{ΔTC}{ΔQ}

Example from notes:

Going from Q=10 to Q=30:

TC goes from 150 to 250

ΔTC = 100

ΔQ = 20

MC = \frac{100}{20} = 5

Grandeur

Explorer

Untitled 2

MIDTERM CHEAT SHEET — Supply, Demand, Equilibrium, Surplus, Shortage, Taxes

1. Demand & Supply Basics

Law of Demand

Demand Function:

Law of Supply

Supply Function:

2. Market Equilibrium (VERY IMPORTANT)

How to solve equilibrium:

3. Shortage & Surplus — HOW TO KNOW

Shortage

(Excess Demand)

Surplus

(Excess Supply)

4. Graph Interpretation (Your messy drawings → fixed)

What matters on the graph:

5. Consumer Surplus & Producer Surplus

Consumer Surplus (CS)

Producer Surplus (PS)

Total Surplus (TS):

6. Taxes — The Clean Version

Example:

Summary Table

Elasticity!!

1. PRICE ELASTICITY OF DEMAND (PED)

Formula (Midpoint Method)

— ALWAYS use this in exams:

Interpreting PED

PED & Total Revenue (TR)

✅

Example

2. INCOME ELASTICITY OF DEMAND (YED)

Interpreting YED

Example (Starbucks problem)

3. CROSS-PRICE ELASTICITY OF DEMAND (XED)

Interpreting XED

Question 3 (Cross-Price = −8.7)**

Correct explanation:

Elasticity Summary Map (clean version)

1. PED (Price Elasticity of Demand)

2. YED (Income Elasticity)

3. XED (Cross-Price Elasticity)

PROFIT MAXIMIZATION — CLEAN NOTES

1.

Profit Maximization Rule

2.

Given Table (from your notes)

3.

Step 1: Compute Total Revenue (TR)

4.

Step 2: Compute Profit

5.

Step 3: Compute Marginal Revenue (MR)

6.

Step 4: Compute Marginal Cost (MC)

7.

Step 5: Locate MR = MC

Final Answer

1. TAXES: Consumer Surplus, Producer Surplus, Tax Revenue, Deadweight Loss

After-Tax Prices (example in your notes)

Consumers Surplus (CS)

Producers Surplus (PS)

Tax Revenue

Deadweight Loss (DWL)

2. BUDGET LINE

Key Points

Slope of the Budget Line

Example from your screenshot

3. OPPORTUNITY COST ON THE BUDGET LINE

4. UTILITY AND MARGINAL UTILITY

Total Utility (TU)

Marginal Utility (MU)

Example (from your notes)

Law of Diminishing Marginal Utility

5. PROFIT MAXIMIZATION: MR = MC

Definitions

Your table

Decision