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Ch. 8 & 9 Worksheet — Answer Key
Econ 101 Discussion Section · Worksheet 7 · Chapters 8 & 9
Question 1 — Norway Sugar Tax
Demand: P = 125 − (3/8)Q | Supply: P = 5 + (1/8)Q | Excise tax = 20 NOK/kg on producers
Part (a) — Equilibrium before tax
P* = 35 NOK | Q* = 240 kg
Set D = S: 125 − (3/8)Q = 5 + (1/8)Q
120 = (3/8)Q + (1/8)Q = (4/8)Q = (1/2)Q
Q = 240
P = 5 + (1/8)(240) = 5 + 30 = 35 NOK
Check: P = 125 − (3/8)(240) = 125 − 90 = 35 ✓
Part (b) — CS and PS before tax
CS = 10,800 NOK | PS = 3,600 NOK
CS = ½(125 − 35)(240) = ½(90)(240) = 10,800
PS = ½(35 − 5)(240) = ½(30)(240) = 3,600
Total Surplus = 10,800 + 3,600 = 14,400
Part (c) — After 20 NOK excise tax
Pb = 50 NOK | Ps = 30 NOK | Q = 200 kg
Tax shifts supply up by 20: new S: P = 25 + (1/8)Q
Set new S = D: 25 + (1/8)Q = 125 − (3/8)Q
100 = (1/2)Q → Q = 200
Price buyers pay: Pb = 125 − (3/8)(200) = 125 − 75 = 50 NOK
Price sellers receive: Ps = 50 − 20 = 30 NOK
Check: Ps = 5 + (1/8)(200) = 5 + 25 = 30 ✓
Part (d) — Surplus and DWL with tax
CS = 7,500 | PS = 2,500 | Tax Rev = 4,000 | DWL = 400
CS = ½(125 − 50)(200) = ½(75)(200) = 7,500
PS = ½(30 − 5)(200) = ½(25)(200) = 2,500
Tax Revenue = 20 × 200 = 4,000
DWL = ½(tax)(ΔQ) = ½(20)(240 − 200) = ½(20)(40) = 400
Check: 7,500 + 2,500 + 4,000 + 400 = 14,400 = pre-tax total surplus ✓
| Before Tax | After Tax | Change |
|---|
| CS | 10,800 | 7,500 | −3,300 |
| PS | 3,600 | 2,500 | −1,100 |
| Tax Revenue | — | 4,000 | +4,000 |
| DWL | — | 400 | −400 |
| Total | 14,400 | 14,400 | 0 |
Question 2 — Space Fuel Trade
Demand: P = 80 − Q | Supply: P = 20 + 2Q | World price: $30 | Tariff: $20
Part (a) — Autarky equilibrium
P* = $60 | Q* = 20 million gallons
Set D = S: 80 − Q = 20 + 2Q
60 = 3Q → Q = 20
P = 80 − 20 = $60
Check: P = 20 + 2(20) = 60 ✓
Part (b) — CS and PS (autarky)
CS = $200 | PS = $400
CS = ½(80 − 60)(20) = ½(20)(20) = $200
PS = ½(60 − 20)(20) = ½(40)(20) = $400
Total = $200 + $400 = $600
Part (c) — Free trade at world price $30
Qs = 5 | Qd = 50 | Imports = 45 | CS = $1,250 | PS = $25
Since world price $30 < domestic $60, country imports.
Qd at P=30: 30 = 80 − Q → Qd = 50
Qs at P=30: 30 = 20 + 2Q → 10 = 2Q → Qs = 5
Imports = 50 − 5 = 45
CS = ½(80 − 30)(50) = ½(50)(50) = $1,250
PS = ½(30 − 20)(5) = ½(10)(5) = $25
Total = $1,250 + $25 = $1,275
Part (d) — $20 tariff (domestic price = $50)
Qs = 15 | Qd = 30 | Imports = 15 | CS = $450 | PS = $225 | Tariff Rev = $300 | DWL = $300
Qd at P=50: 50 = 80 − Q → Qd = 30
Qs at P=50: 50 = 20 + 2Q → Qs = 15
Imports = 30 − 15 = 15
CS = ½(80 − 50)(30) = ½(30)(30) = $450
PS = ½(50 − 20)(15) = ½(30)(15) = $225
Tariff Revenue = $20 × 15 = $300
DWL = left Δ + right Δ
Left = ½(20)(15 − 5) = ½(20)(10) = $100
Right = ½(20)(50 − 30) = ½(20)(20) = $200
Total DWL = $100 + $200 = $300
Check: $450 + $225 + $300 + $300 = $1,275 = free-trade total surplus ✓
| Free Trade | With Tariff | Change |
|---|
| CS | $1,250 | $450 | −$800 |
| PS | $25 | $225 | +$200 |
| Tariff Revenue | — | $300 | +$300 |
| DWL | — | $300 | −$300 |
| Total | $1,275 | $1,275 | $0 |
Multiple Choice — Figure 8-2
D: P = 12 − 1.5Q | S: P = 1.5Q | Pre-tax eq: Q=4, P=$6 | Post-tax: Q=2, Pb=$9, Ps=$3 | Tax=$6
1. The tax causes quantity sold to…
D decrease by 2 units.
Pre-tax Q = 4 (where D and S cross at P=$6). Post-tax Q = 2 (at points E and F). Decrease = 4 − 2 = 2.
2. The tax causes the price paid by buyers to…
B increase by $3.
Pre-tax: buyers paid $6. Post-tax: buyers pay $9 (point E). Change = $9 − $6 = +$3.
3. The deadweight loss from the tax is…
B $6.
DWL = ½(tax)(ΔQ) = ½($6)(4 − 2) = ½(6)(2) = $6.
True / False — Ch. 8
4. When a tax is imposed on buyers, CS and PS both decrease.
A True
A tax creates a wedge between what buyers pay and sellers receive. Buyers pay more (CS falls) and sellers receive less (PS falls), regardless of which side the tax is legally imposed on.
5. Taxes cause DWL because they prevent buyers and sellers from realizing some gains from trade.
A True
The tax reduces quantity traded below the efficient level, preventing some mutually beneficial trades that would have occurred at the no-tax equilibrium.
6. The more inelastic are demand and supply, the greater is the DWL of a tax.
B False
It’s the opposite. More elastic curves → greater quantity response → larger DWL triangle. Inelastic curves mean quantity barely changes, so DWL is small.
7. The DWL of a tax rises even more rapidly than the size of the tax.
A True
DWL ∝ t² (proportional to the square of the tax). Double the tax → quadruple the DWL. So DWL grows faster than the tax itself.
Scenario 8-3
QD = 200 − P | QS = 3P | Tax T = 40 on buyers | New demand: QD = 200 − (P + 40) = 160 − P
8. If T = 40, what is the deadweight loss?
DWL = $600
Pre-tax eq: 200 − P = 3P → P = 50, Q = 150
Post-tax: 160 − P = 3P → 160 = 4P → Ps = 40, Q = 120
Pb = 40 + 40 = $80
DWL = ½(T)(ΔQ) = ½(40)(150 − 120) = ½(40)(30) = $600
Check surpluses: Pre-tax CS=11,250 + PS=3,750 = 15,000. Post-tax CS=7,200 + PS=2,400 + TaxRev=4,800 + DWL=600 = 15,000 ✓
Multiple Choice — Figure 9-2 (Tricycles)
Autarky eq: Q=360, P=$57 | World price = $33 | At P=$33: Qs=200, Qd=520
9. With trade, the price of tricycles is…
A $33, with 200 produced domestically and 320 imported.
At world price $33: domestic supply = 200, domestic demand = 520.
Imports = 520 − 200 = 320.
10. With trade, consumer surplus is…
C $20,280.
CS = ½(111 − 33)(520) = ½(78)(520) = (78)(260) = $20,280.
Multiple Choice — Figure 9-3 (Roses)
World price = $2 | Tariff = $2 (domestic price rises to $4)
At P=$2: Qs=200, Qd=600 (imports=400) | At P=$4: Qs=300, Qd=500 (imports=200)
11. The tariff on roses causes imports to…
C decrease by 200.
Imports before tariff: 600 − 200 = 400
Imports after tariff: 500 − 300 = 200
Change: 400 − 200 = decrease of 200.
12. The deadweight loss from the tariff is…
B $200.
Left Δ (production inefficiency): ½(300 − 200)($4 − $2) = ½(100)(2) = $100
Right Δ (consumption inefficiency): ½(600 − 500)($4 − $2) = ½(100)(2) = $100
Total DWL = $100 + $100 = $200
True / False — Ch. 9
13. Economists view free trade as a way to raise living standards both at home and abroad.
A True
Free trade allows countries to specialize according to comparative advantage, increasing total output and welfare. Both importing and exporting countries see net gains (total surplus rises), even though some groups within each country may be worse off.
14. In Jumanji, the domestic price of coffee (no trade) is below the world price. Importer or exporter?
Jumanji will be an exporter of coffee.
Domestic price < world price means Jumanji can produce coffee cheaply relative to the world.
When trade opens, domestic price rises to the world price.
At the higher price: Qs increases, Qd decreases → Qs > Qd → excess is exported.
15. Tariffs cause DWL because they move the domestic price closer to the no-trade equilibrium, reducing gains from trade.
A True
A tariff raises the domestic price from the world price toward the autarky price. This reduces the volume of trade and eliminates some mutually beneficial exchanges, creating deadweight loss.
Quick Reference
| # | Answer | Key Value |
|---|
| 1a | P=35, Q=240 | |
| 1b | CS=10,800; PS=3,600 | |
| 1c | Pb=50, Ps=30, Q=200 | |
| 1d | CS=7,500; PS=2,500; TaxRev=4,000 | DWL=400 |
| 2a | P=$60, Q=20 | |
| 2b | CS=$200; PS=$400 | |
| 2c | Qs=5, Qd=50, Imports=45 | CS=$1,250; PS=$25 |
| 2d | Qs=15, Qd=30, Imports=15 | CS=$450; PS=$225; TariffRev=$300; DWL=$300 |
| MC 1 | D — decrease by 2 units |
| MC 2 | B — increase by $3 |
| MC 3 | B — $6 |
| T/F 4 | A — True |
| T/F 5 | A — True |
| T/F 6 | B — False (inelastic = less DWL) |
| T/F 7 | A — True (DWL ∝ t²) |
| SC 8 | DWL = $600 |
| MC 9 | A — $33, 200 domestic + 320 imported |
| MC 10 | C — $20,280 |
| MC 11 | C — decreases by 200 |
| MC 12 | B — $200 |
| T/F 13 | A — True |
| SA 14 | Exporter (domestic price < world price) |
| T/F 15 | A — True |