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πŸ“˜ Chapter 3: Demand and Supply

πŸ—‚οΈ In This Chapter:
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πŸ“– Glossary of Key Terms

| Term | Definition | |------|-----------| | **Demand** | The relationship between price and the quantity demanded of a good or service | | **Demand Curve** | Graphical representation of the relationship between price and quantity demanded | | **Demand Schedule** | A table showing a range of prices and the quantity demanded at each price | | **Quantity Demanded** | The total number of units consumers are willing to purchase at a given price | | **Supply** | The relationship between price and the quantity supplied of a good or service | | **Supply Curve** | A line showing the relationship between price and quantity supplied on a graph | | **Supply Schedule** | A table showing a range of prices and the quantity supplied at each price | | **Quantity Supplied** | The total number of units producers are willing to sell at a given price | | **Law of Demand** | A higher price leads to a lower quantity demanded (and vice versa), ceteris paribus | | **Law of Supply** | A higher price leads to a higher quantity supplied (and vice versa), ceteris paribus | | **Equilibrium** | The situation where quantity demanded equals quantity supplied | | **Equilibrium Price** | The price where quantity demanded equals quantity supplied | | **Equilibrium Quantity** | The quantity at which quantity demanded and quantity supplied are equal | | **Excess Demand (Shortage)** | At the existing price, quantity demanded exceeds quantity supplied | | **Excess Supply (Surplus)** | At the existing price, quantity supplied exceeds quantity demanded | | **Ceteris Paribus** | "Other things being equal" β€” all other variables are held constant | | **Normal Good** | A good whose demand rises when income rises, and falls when income falls | | **Inferior Good** | A good whose demand falls when income rises, and rises when income falls | | **Substitute** | A good that can replace another; higher price of a substitute increases demand for the other | | **Complement** | Goods often used together; higher price of one decreases demand for the other | | **Inputs (Factors of Production)** | Resources such as labor, materials, and machinery used to produce goods | | **Shift in Demand** | A change in a non-price factor causes a different quantity demanded at every price | | **Shift in Supply** | A change in a non-price factor causes a different quantity supplied at every price | | **Price Ceiling** | A legal maximum price | | **Price Floor** | A legal minimum price | | **Price Controls** | Government laws to regulate prices instead of letting market forces determine them | | **Consumer Surplus** | The extra benefit consumers receive: willingness to pay minus the actual price paid | | **Producer Surplus** | The extra benefit producers receive: actual price received minus willingness to accept | | **Social (Total) Surplus** | Sum of consumer surplus and producer surplus | | **Deadweight Loss** | Loss in total surplus when the economy produces at an inefficient quantity | ---

3.1 Demand, Supply, and Equilibrium in Markets for Goods and Services

### Demand for Goods and Services
Demand: The amount of a good or service that consumers are willing and able to purchase at each price. Demand is based on needs, wants, and ability to pay. Without ability to pay, there is no effective demand.
**Key Vocabulary:** - **Price:** What a buyer pays for one unit of a good or service - **Quantity Demanded:** The total number of units consumers would purchase at a specific price ### The Law of Demand
Law of Demand: As the price of a good increases, the quantity demanded decreases β€” and vice versa β€” assuming all other factors are held constant (ceteris paribus).
Example β€” Gasoline Market:
| Price (per gallon) | Quantity Demanded (millions of gallons) | |:---:|:---:| | $1.00 | 800 | | $1.20 | 700 | | $1.40 | 600 | | $1.60 | 550 | | $1.80 | 500 | | $2.00 | 460 | | $2.20 | 420 | As price rises from $1.00 to $2.20, quantity demanded falls from 800 million to 420 million gallons.
**The Demand Curve:**
Gasoline Demand Curve Quantity (millions of gallons) Price ($/gallon) $1.00 $1.20 $1.40 $1.60 $1.80 $2.00 $2.20 420 500 600 700 800 D
- Slopes **downward** from left to right (inverse relationship) - Every demand curve shares this fundamental shape
⚠️ Important Distinction:
Demand β‰  Quantity Demanded
- Demand = the entire relationship (the whole curve)
- Quantity demanded = a specific point on the curve at a specific price
--- ### Supply of Goods and Services
Supply: The amount of a good or service that a producer is willing to supply at each price. A rise in price leads to an increase in quantity supplied.
### The Law of Supply
Law of Supply: As the price of a good increases, the quantity supplied increases β€” and vice versa β€” assuming all other factors are held constant (ceteris paribus).
Example β€” Gasoline Supply:
| Price (per gallon) | Quantity Supplied (millions of gallons) | |:---:|:---:| | $1.00 | 500 | | $1.20 | 550 | | $1.40 | 600 | | $1.60 | 640 | | $1.80 | 680 | | $2.00 | 700 | | $2.20 | 720 | As price rises, firms expand production because higher prices mean higher profits.
**The Supply Curve:**
Gasoline Supply Curve Quantity (millions of gallons) Price ($/gallon) $1.00 $1.20 $1.40 $1.60 $1.80 $2.00 $2.20 S
- Slopes **upward** from left to right (positive relationship)
⚠️ Important Distinction:
Supply β‰  Quantity Supplied
- Supply = the entire relationship (the whole curve)
- Quantity supplied = a specific point on the curve at a specific price
--- ### Equilibrium: Where Demand and Supply Intersect
Equilibrium: The point where the demand curve and supply curve intersect β€” where the quantity that consumers want to buy equals the quantity that producers want to sell. There is no economic pressure to change price or quantity.
Market Equilibrium β€” Gasoline Quantity (millions of gallons) Price ($/gallon) Surplus zone Shortage zone S D E $1.40 600
Gasoline Market Equilibrium:
At $1.40/gallon: Qd = 600 million, Qs = 600 million β†’ Equilibrium!

Above equilibrium ($1.80): Qd = 500, Qs = 680 β†’ Surplus of 180 million gallons. Sellers cut prices to sell inventory, pushing price back down.

Below equilibrium ($1.20): Qd = 700, Qs = 550 β†’ Shortage of 150 million gallons. Eager buyers push price up as sellers recognize they can charge more.
πŸ’‘ Key Insight: The market has a self-correcting mechanism:
  • Surplus β†’ price falls β†’ quantity demanded rises, quantity supplied falls β†’ back to equilibrium
  • Shortage β†’ price rises β†’ quantity demanded falls, quantity supplied rises β†’ back to equilibrium
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3.2 Shifts in Demand and Supply for Goods and Services

### The Ceteris Paribus Assumption
Ceteris Paribus (Latin: "other things being equal"): The assumption that no other relevant economic factors change while we analyze the effect of one variable. This lets us isolate cause and effect.
When multiple factors change at once, analyze each **one at a time** (holding others constant), then combine the results. --- ### Factors That Shift the Demand Curve A change in **price** moves you along the demand curve. A change in **any other factor** shifts the entire curve. | Factor | Demand Shifts Right (↑) | Demand Shifts Left (↓) | |--------|------------------------|----------------------| | **Income** (normal goods) | Income rises | Income falls | | **Income** (inferior goods) | Income falls | Income rises | | **Tastes & Preferences** | Good becomes more popular | Good becomes less popular | | **Population / Composition** | More consumers enter market | Fewer consumers | | **Price of Substitutes** | Price of substitute rises | Price of substitute falls | | **Price of Complements** | Price of complement falls | Price of complement rises | | **Expectations** | Expect future price increase | Expect future price decrease |
Normal Goods vs. Inferior Goods:
- Normal good: Demand rises with income (new cars, vacations, fine jewelry)
- Inferior good: Demand falls with income (generic groceries, used cars, renting)

When incomes rise, people buy fewer generic brands and more name brands.
Substitutes vs. Complements:
- Substitutes: Goods that can replace each other. If the price of tablets falls, demand for laptops decreases (tablets substitute for laptops).
- Complements: Goods used together. If the price of golf clubs rises, demand for golf balls decreases (they're used together).
Changing Tastes:
From 1980–2021, U.S. per-person chicken consumption rose from 47 to 97 lbs/year, while beef fell from 76 to 59 lbs/year. This was a shift in taste β€” the demand curve for chicken shifted right, and for beef shifted left.
⚠️ Critical Rule: A change in the price of the good itself does NOT shift the demand curve! It causes a movement along the demand curve. Only non-price factors shift the curve.
--- ### Factors That Shift the Supply Curve | Factor | Supply Shifts Right (↑) | Supply Shifts Left (↓) | |--------|------------------------|----------------------| | **Input prices** | Input costs fall | Input costs rise | | **Technology** | New technology reduces costs | Technology setback | | **Natural conditions** | Favorable weather | Drought, disaster | | **Government policy** | Subsidies, deregulation | Taxes, regulations | | **Number of sellers** | More firms enter market | Firms exit market |
Production Costs β€” Cars:
If the price of steel rises β†’ producing cars becomes more expensive β†’ at any given price, fewer cars supplied β†’ supply curve shifts LEFT.

If the price of steel falls β†’ cars cheaper to produce β†’ at any given price, more cars supplied β†’ supply curve shifts RIGHT.
Technology β€” Green Revolution:
In the 1960s, improved seeds for wheat and rice doubled harvests per acre. This technological improvement reduced production costs and shifted the supply curve right β€” more food supplied at every price.
Government Policy:
- Taxes (on alcohol: ~$8 billion/year) β†’ increase costs β†’ supply shifts left
- Regulations (environmental, safety) β†’ increase costs β†’ supply shifts left
- Subsidies (government pays firms directly) β†’ decrease costs β†’ supply shifts right
⚠️ Critical Rule: A change in the price of the product itself does NOT shift the supply curve! It causes a movement along the supply curve.
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3.3 Changes in Equilibrium Price and Quantity: The Four-Step Process

### The Four-Step Process for Analyzing Market Changes
πŸ’‘ The Four Steps:
  1. Draw the initial demand and supply diagram with the original equilibrium.
  2. Decide whether the event affects demand or supply.
  3. Decide the direction of the shift (right or left) and sketch the new curve.
  4. Compare the new equilibrium price and quantity to the original.
### Example 1: Good Weather for Salmon Fishing (Supply Shift)
Scenario: Excellent weather conditions for commercial salmon fishing off California.

Step 1: Original equilibrium: P = $3.25/pound, Q = 250,000 fish
Step 2: Good weather affects supply (natural conditions)
Step 3: Good weather increases supply β†’ shift right (Sβ‚€ β†’ S₁)
Step 4: New equilibrium: P falls to $2.50, Q rises to 550,000

Result: Lower price, higher quantity.
Supply Shift β€” Good Weather for Salmon Quantity (thousands of fish) Price ($/pound) D Sβ‚€ S₁ Eβ‚€ E₁ $3.25 $2.50 250 550 shift right
### Example 2: Shift from Print to Digital News (Demand Shift)
Scenario: More people get news from digital sources instead of print newspapers.

Step 1: Draw initial equilibrium (Eβ‚€)
Step 2: Change in tastes affects demand
Step 3: Demand for print news decreases β†’ shift left (Dβ‚€ β†’ D₁)
Step 4: New equilibrium: Both price and quantity fall

Result: Lower price, lower quantity.
### Summary of Single Shifts | Shift | Equilibrium Price | Equilibrium Quantity | |-------|:-:|:-:| | Demand increases (β†’) | ↑ Rises | ↑ Rises | | Demand decreases (←) | ↓ Falls | ↓ Falls | | Supply increases (β†’) | ↓ Falls | ↑ Rises | | Supply decreases (←) | ↑ Rises | ↓ Falls | ### When Both Demand and Supply Shift
U.S. Postal Service Example:
Two simultaneous events:
1. Higher worker compensation β†’ costs rise β†’ supply shifts LEFT β†’ higher price, lower quantity
2. Switch from snail mail to email β†’ demand shifts LEFT β†’ lower price, lower quantity

Combined result:
- Quantity definitely decreases (both shifts reduce quantity)
- Price direction is ambiguous (one shift raises price, the other lowers it β€” net effect depends on magnitudes)
⚠️ Key Rule: When both curves shift, you can typically determine the effect on either price or quantity, but not both β€” unless you know the relative magnitudes of the shifts.
### Common Mistake: Shifts vs. Movements Along Curves
⚠️ Do NOT Confuse:
- A shift of a curve = a non-price factor changes β†’ the entire curve moves
- A movement along a curve = the price changes β†’ you slide to a different point on the same curve

Critical: A shift in one curve causes a movement along the other curve (not a shift of the other curve!). A price change NEVER shifts either curve.
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3.4 Price Ceilings and Price Floors

### Price Ceilings (Legal Maximum Price)
Price Ceiling: A legal maximum price that can be charged for a good or service. The goal is to keep prices "affordable." A price ceiling only has an effect if it is set below the equilibrium price.
Example β€” Rent Control:
Original equilibrium: Rent = $600/month, Quantity = 17,000 apartments
Government sets price ceiling at $500/month

At $500: Quantity supplied = 15,000, Quantity demanded = 19,000
β†’ Shortage of 4,000 apartments

Unintended consequences:
  • Fewer apartments available than at market price
  • Landlords convert apartments to condos
  • Landlords reduce maintenance, heating, cooling
  • Lower quality housing
Rent Control β€” Price Ceiling & Shortage Apartments (thousands) Rent ($/month) S D E $600 Ceiling: $500 15K (Qs) 19K (Qd) Shortage: 4K
πŸ’‘ Irony: A price ceiling designed to help renters actually results in fewer apartments being rented (15,000 vs. 17,000 at market equilibrium) and lower housing quality.
--- ### Price Floors (Legal Minimum Price)
Price Floor: A legal minimum price that must be charged. The goal is to keep prices "high enough" for producers. A price floor only has an effect if set above the equilibrium price.
Example β€” Minimum Wage:
The federal minimum wage in 2022 was $7.25/hour (set in 2009).
Annual income for a single person: ~$15,080 (slightly above the federal poverty line of $11,880).

If the minimum wage is set above the equilibrium wage for low-skilled labor, quantity supplied of labor (workers wanting jobs) exceeds quantity demanded (employers wanting to hire), creating a surplus of labor = unemployment.
Example β€” Agricultural Price Supports:
The EU spends ~€58 billion/year (~36% of EU budget) on agricultural price supports.
The government buys up excess supply to keep farm prices above equilibrium.

If government sets price floor at P_f above equilibrium:
Quantity supplied (Q_s) > Quantity demanded (Q_d) β†’ Surplus
Government must buy the excess, costing taxpayers billions.
Price Floor β€” Surplus Quantity Price S D Eβ‚€ Pβ‚€ Price Floor (PαΆ ) Qd Qs Surplus
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3.5 Demand, Supply, and Efficiency

### Consumer Surplus
Consumer Surplus: The difference between what consumers are willing to pay and what they actually pay. Graphically, it is the area above the market price and below the demand curve.
### Producer Surplus
Producer Surplus: The difference between the price producers actually receive and the minimum price they would have accepted. Graphically, it is the area below the market price and above the supply curve.
### Social Surplus (Total Surplus)
Social Surplus = Consumer Surplus + Producer Surplus. Social surplus is maximized at the equilibrium price and quantity. This is the definition of market efficiency.
Consumer & Producer Surplus at Equilibrium Quantity Price CS PS S D E P* Q*
**Surplus Formulas (for linear curves):** $$\text{Consumer Surplus} = \frac{1}{2} \times Q^* \times (P_{\text{max}} - P^*)$$ $$\text{Producer Surplus} = \frac{1}{2} \times Q^* \times (P^* - P_{\text{min}})$$ $$\text{Total Surplus} = CS + PS$$ where $P_{\text{max}}$ is the demand curve's price-intercept (highest willingness to pay) and $P_{\text{min}}$ is the supply curve's price-intercept (lowest willingness to accept).
Tablet Market Example:
Equilibrium: P = $80, Q = 28 million

- Some consumers would have paid $90 but only paid $80 β†’ they gained $10 each in consumer surplus
- Some producers would have accepted $45 but received $80 β†’ they gained $35 each in producer surplus

Social surplus = Area F + Area G = maximized at equilibrium
Worked Example β€” Calculating Surplus Numerically:

Suppose the demand and supply for widgets are given by:
$$Q_d = 100 - 2P \qquad Q_s = -20 + 3P$$

Step 1: Find equilibrium.
Set $Q_d = Q_s$:
$$100 - 2P = -20 + 3P \implies 120 = 5P \implies P^* = \$24$$
$$Q^* = 100 - 2(24) = 52 \text{ units}$$

Step 2: Find intercepts.
Demand intercept (P when $Q_d = 0$): $0 = 100 - 2P \implies P_{\text{max}} = \$50$
Supply intercept (P when $Q_s = 0$): $0 = -20 + 3P \implies P_{\text{min}} = \$6.67$

Step 3: Calculate surplus.
$$CS = \tfrac{1}{2} \times 52 \times (50 - 24) = \tfrac{1}{2} \times 52 \times 26 = \$676$$
$$PS = \tfrac{1}{2} \times 52 \times (24 - 6.67) = \tfrac{1}{2} \times 52 \times 17.33 = \$450.67$$
$$\text{Total Surplus} = 676 + 450.67 = \$1{,}126.67$$
--- ### Deadweight Loss from Price Controls
Deadweight Loss: The loss in total surplus that occurs when the market does NOT operate at the efficient (equilibrium) quantity. It represents transactions that would have benefited both buyers and sellers but were blocked.
Price Ceiling Example β€” Drug Market:
Equilibrium: P = $600, Q = 20,000
Price ceiling set at $400 β†’ Q produced drops to 15,000

- Consumer surplus: Some transferred from producers (area V), but area U is lost
- Producer surplus: Loses areas V and W
- Deadweight loss = U + W (transactions that no longer occur)

The gain to consumers is less than the loss to producers.
Price Floor Example β€” Movie Theaters:
Equilibrium: P = $8, Q = 1,800
Price floor set at $12 β†’ Q demanded drops to 1,400

- Consumer surplus shrinks (area H transferred to producers)
- Deadweight loss = J + K

Some consumers stop attending movies entirely β€” their surplus is destroyed.
πŸ’‘ Key Takeaway: Both price floors and price ceilings:
  • Block mutually beneficial transactions
  • Create deadweight loss
  • Transfer surplus between consumers and producers
  • Often produce unintended consequences that hurt the very people they aim to help
--- ### Demand and Supply as a Social Adjustment Mechanism As **Alfred Marshall** (1890) wrote: asking whether supply or demand determines price is like asking "whether it is the upper or the under blade of a pair of scissors that cuts a piece of paper." **Both blades are always involved.**
Markets are self-adjusting:
- If Brazil's coffee crop suffers a frost β†’ supply shifts left β†’ price rises β†’ some consumers switch to tea β†’ no government commission needed to decide allocation
- Seasonal food prices adjust naturally: fresh corn is cheap in summer, expensive in winter β†’ restaurants change menus, people change diets

Markets are the primary social mechanism for answering the three fundamental economic questions: What to produce, How to produce, and For Whom to produce.
--- ### Organic Food Case Study
Why is organic food more expensive?
Applying demand and supply analysis:

Demand side:
  • Changing tastes β†’ awareness of harmful effects of pesticides/chemicals
  • Rising incomes β†’ people can afford pricier products
  • Population growth β†’ more buyers
  • Demand curve shifts RIGHT
Supply side:
  • More farmers converting to organic (over time) β†’ supply shifts RIGHT
  • But organic production costs remain higher (organic fertilizers, pest management)
Result: Equilibrium quantity rises significantly, but price remains high because demand has increased faster than supply. Prices will only fall when supply increase exceeds demand increase.
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🧠 Brainstorming & Review Questions

Self-Check Questions:
  1. If gasoline price is $1.60/gallon, is quantity demanded higher or lower than at equilibrium ($1.40)? What about quantity supplied? Is there a shortage or surplus, and of how much?
  2. Why do economists use the ceteris paribus assumption?
  3. For the paint market: (a) Cost-saving inventions in paint technology β€” supply or demand? Direction? (b) Paint lasts longer, less repainting needed β€” supply or demand? (c) Severe hailstorms create immediate need for repainting β€” supply or demand? (d) Hailstorms damage paint factories β€” supply or demand?
  4. Predict the effects on oil market equilibrium: (a) Cars become more fuel-efficient (b) Exceptionally cold winter (c) Major new oil discovery off Norway (d) Japan's economy slows (e) Middle East war disrupts pumping (f) Landlords install insulation (g) Solar energy price drops (h) New popular plastic made from oil
  5. Jet fuel price increases 47%. Using the four-step analysis, how does this affect air travel equilibrium?
  6. The U.S. cuts tariffs on imported flat-screen TVs. Using four-step analysis, what happens to equilibrium price and quantity?
  7. What is the effect of a price ceiling on quantity demanded? On quantity supplied? Why does a price ceiling cause a shortage?
  8. Does a price ceiling change the equilibrium price?
  9. What would be the impact of a price floor set below the equilibrium price?
  10. Does a price ceiling increase or decrease transactions in a market? What about a price floor?
  11. If a price floor benefits producers, why does it reduce social surplus?
Review Questions:
  1. What determines the level of prices in a market?
  2. What does a downward-sloping demand curve mean about buyer behavior?
  3. Will all demand curves and supply curves have the same shape? How might they differ?
  4. What is the relationship between Qd and Qs at equilibrium? During a shortage? During a surplus?
  5. How can you locate equilibrium on a demand-supply graph?
  6. When price is above equilibrium, explain the market forces that push it back. Same for below equilibrium.
  7. What is the difference between demand and quantity demanded?
  8. What is the difference between supply and quantity supplied?
  9. Name factors that shift the demand curve and the supply curve.
  10. How does one analyze a market where both demand and supply shift?
  11. What causes movement along a curve vs. a shift of the curve?
  12. What is consumer surplus? Producer surplus? Total surplus? How are they illustrated?
  13. What is deadweight loss?
Critical Thinking Questions:
  1. If the government caps gasoline at $1.30/gallon (below equilibrium of $1.40), what do you anticipate?
  2. Explain why: "In the goods market, no buyer would be willing to pay more than the equilibrium price" is FALSE.
  3. If the price of hot dogs (substitute) rises AND the price of burger buns (complement) rises, what happens to demand for hamburgers? Can you tell for sure?
  4. How will an aging "Baby Boomer" population affect demand for milk?
  5. If consumers believe prices will rise in the future, how does that affect present demand?
  6. A soda tax collected from sellers is reduced. How does this affect supply, equilibrium price, and quantity?
  7. Use the four-step process to analyze the iPod's impact on the Walkman market.
  8. Most government policies have winners and losers. Who wins and who loses from a minimum wage increase?
  9. Why can't the government simply give surplus agricultural products to people experiencing poverty?
  10. Explain why voluntary transactions improve social welfare.
Practice Problems:
  1. Gasoline at $1.00: Qd = 800, Qs = 500. Shortage or surplus? How much?
  2. Bicycle market: At P = $150, Qd = 40,000 and Qs = 40,000. What is the equilibrium price?
  3. Computer market: Many more sold at much lower prices. Which shift best explains this β€” rise in demand, fall in demand, rise in supply, or fall in supply?
  4. A low-income country sets a price ceiling on bread at $2.40. Equilibrium is at $2.80 (Qd=7,500, Qs=7,500). At $2.40: Qd=8,000, Qs=6,400. What is the shortage?
Additional Worked Numerical Problems: Q-N1. The market for organic eggs has linear demand and supply: $$Q_d = 500 - 50P \qquad Q_s = -100 + 100P$$ **(a)** Find the equilibrium price and quantity. **(b)** Calculate consumer surplus, producer surplus, and total surplus. **(c)** The government sets a price ceiling at $3/dozen. Calculate the shortage, new CS, new PS, and deadweight loss.
Answer **(a)** Set $Q_d = Q_s$: $500 - 50P = -100 + 100P \implies 600 = 150P \implies P^* = \$4$, and $Q^* = 500 - 50(4) = 200$ dozen. **(b)** Demand intercept: $P_{\max} = 500/50 = \$10$. Supply intercept: $P_{\min} = 100/100 = \$1$. $$CS = \tfrac{1}{2} \times 200 \times (10 - 4) = \$600$$ $$PS = \tfrac{1}{2} \times 200 \times (4 - 1) = \$300$$ $$\text{Total Surplus} = \$900$$ **(c)** At $P = 3$: $Q_d = 500 - 150 = 350$, $Q_s = -100 + 300 = 200$. **Shortage = 150 dozen.** Only 200 units are actually traded (quantity supplied is the binding constraint). $$CS = \tfrac{1}{2}(200)(10-3) - \text{lost triangle} = \text{rectangle} + \text{triangle above } P_c$$ More precisely: $CS_{\text{new}} = (4-3) \times 200 + \tfrac{1}{2}(200)(10-4) - \tfrac{1}{2}(0)(.) = ...$ Using the trapezoid method: The CS when Q=200 traded at $P=3$: - Willingness to pay at Q=200: $P = (500-200)/50 = \$6$ - $CS = \tfrac{1}{2}(200)(10-6) + 200 \times (6-3) = 400 + 600 = \$1{,}000$ Wait β€” this exceeds original CS? That's because some surplus transfers from producers. Let's be precise: - $CS_{\text{new}} = \int_0^{200} (P_d(Q) - 3)\,dQ = \int_0^{200}(10-Q/50 - 3)\,dQ = \int_0^{200}(7-Q/50)\,dQ$ - $= [7Q - Q^2/100]_0^{200} = 1400 - 400 = \$1{,}000$ - $PS_{\text{new}} = \int_0^{200}(3 - P_s(Q))\,dQ = \int_0^{200}(3 - (Q+100)/100)\,dQ = \int_0^{200}(2 - Q/100)\,dQ$ - $= [2Q - Q^2/200]_0^{200} = 400 - 200 = \$200$ - Total new surplus $= 1{,}000 + 200 = \$1{,}200$. Wait, that's more than $900? Let me re-derive. Actually there's an errorβ€”let me redo: Supply: $Q_s = -100 + 100P \Rightarrow P_s = (Q+100)/100 = Q/100 + 1$. Demand: $Q_d = 500 - 50P \Rightarrow P_d = (500-Q)/50 = 10 - Q/50$. At equilibrium: $P^* = 4, Q^* = 200$. CS = area of triangle above $P=4$, below demand, from 0 to 200: $CS = \frac{1}{2}(200)(10-4) = 600$. PS = area below $P=4$, above supply, from 0 to 200: $PS = \frac{1}{2}(200)(4-1) = 300$. Total = 900. βœ“ With ceiling at $P=3$: $Q_s = -100 + 300 = 200$ (same amount supplied!), $Q_d = 350$. Since $Q_s = 200 = Q^*$, the same quantity is traded. The ceiling just redistributes: producers receive $3 instead of $4. - $CS_{\text{new}} = \frac{1}{2}(200)(10-4) + 200(4-3) = 600 + 200 = \$800$ - $PS_{\text{new}} = \frac{1}{2}(200)(4-1) - 200(4-3) = 300 - 200 = \$100$ - Total = $900 (unchanged)$, **DWL = 0** because quantity traded didn't change. **Key insight:** Because the supply at $P=3$ happens to equal $Q^*$, there's a shortage in terms of unsatisfied demand, but the actual quantity traded doesn't fall. DWL = 0 in this special case. The ceiling only redistributes $200 from producers to consumers. For DWL > 0, we'd need the ceiling below $P_s(Q^*) = (200+100)/100 = 3$. With ceiling at $\$2.50$: $Q_s = -100 + 250 = 150$. At ceiling price with forced quantity of 150: - $CS = \int_0^{150}(10-Q/50)\,dQ - 150(2.50) = [10(150) - 150^2/100] - 375 = (1500-225) - 375 = \$900$ Actually let me simplify: $CS = \frac{1}{2}(150)(10-P_d(150)) + 150(P_d(150) - 2.50)$, where $P_d(150) = 10 - 3 = 7$: $CS = \frac{1}{2}(150)(10-7) + 150(7-2.50) = 225 + 675 = \$900$ $PS = \frac{1}{2}(150)(2.50-1) = \frac{1}{2}(150)(1.50) = \$112.50$ Total = $1012.50$? That can't be right either. Total surplus should be ≀ original. OK I realize I should just provide a cleaner example. Let me rewrite this answer.
Actually, let me provide a cleaner version:
Answer **(a)** Set $Q_d = Q_s$: $500 - 50P = -100 + 100P \implies P^* = \$4, Q^* = 200$ dozen. **(b)** Demand intercept ($Q=0$): $P_{\max} = \$10$. Supply intercept ($Q=0$): $P_{\min} = \$1$. - $CS = \frac{1}{2}(200)(10 - 4) = \$600$ - $PS = \frac{1}{2}(200)(4 - 1) = \$300$ - **Total Surplus = $900** **(c)** At ceiling $P_c = \$3$: $Q_s = -100 + 300 = 200$, $Q_d = 500 - 150 = 350$. **Shortage = 150 dozen.** However, the quantity actually traded = min$(Q_d, Q_s) = 200$. Since $Q_s$ equals $Q^*$, the same number of transactions occur. The ceiling transfers $\$200$ from producers to consumers (rectangle of height $\$1$ Γ— width 200) but creates no DWL because output doesn't fall. If the ceiling were lower (say $\$2$), then $Q_s = 100 < Q^*$, and there would be genuine deadweight loss.
Q-N2. In the labor market for fast-food workers, demand and supply are: $$W_d = 20 - 0.01Q \qquad W_s = 5 + 0.005Q$$ where $W$ is the hourly wage ($/hr) and $Q$ is thousands of workers. **(a)** Find the equilibrium wage and employment. **(b)** The government sets a minimum wage (price floor) at $12/hr. Calculate the surplus of labor (unemployment). **(c)** How much deadweight loss does the minimum wage create?
Answer **(a)** Set $W_d = W_s$: $20 - 0.01Q = 5 + 0.005Q \implies 15 = 0.015Q \implies Q^* = 1{,}000$ (thousand workers), $W^* = 20 - 10 = \$10/\text{hr}$. **(b)** At $W = 12$: $Q_d = (20-12)/0.01 = 800$ thousand, $Q_s = (12-5)/0.005 = 1{,}400$ thousand. **Surplus of labor = 600 thousand workers unemployed.** **(c)** Only 800K workers are hired. DWL = the triangle between the demand and supply curves from Q = 800 to Q = 1,000: $$DWL = \frac{1}{2} \times (1{,}000 - 800) \times (W_d(800) - W_s(800))$$ $W_d(800) = 20 - 8 = \$12$, $W_s(800) = 5 + 4 = \$9$ $$DWL = \frac{1}{2} \times 200 \times (12 - 9) = \$300 \text{ thousand/hr}$$
Q-N3. **Case Study β€” The 2021 Lumber Price Spike:** During the COVID-19 pandemic, lumber prices surged from ~$400/thousand board feet to over $1,700 in May 2021 before crashing back. **(a)** Using the four-step process, explain which curve(s) shifted and in which direction. **(b)** Why did prices eventually fall back? What happened to supply and/or demand? **(c)** Who gained and who lost consumer/producer surplus during the price spike?
Answer **(a)** Two simultaneous shifts: 1. **Demand shifted RIGHT:** Millions of homeowners stuck at home started renovation projects; new home construction surged as people fled cities for suburbs. 2. **Supply shifted LEFT:** Sawmills had reduced capacity during early COVID lockdowns; lumber takes months to process; transportation bottlenecks further constrained supply. Both shifts pushed price up (demand↑ raises P, supply↓ raises P). The quantity effect was ambiguous, but prices quadrupled. **(b)** Prices fell because: (1) Sawmills ramped up production (supply shifted right); (2) New sawmill capacity came online; (3) Renovation demand peaked and began normalizing (demand shifted left); (4) Housing market cooled as mortgage rates rose. **(c)** During the spike: **Producers (lumber companies, sawmill owners) gained** massive producer surplus β€” selling at $1,700 what cost ~$300 to produce. **Consumers (home builders, renovators) lost** consumer surplus β€” paying 4Γ— normal prices. Some consumers were priced out entirely (DWL). Home buyers ultimately bore the cost through higher home prices.
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