Summary Exercise Solutions Illustrated | Intermediate Microeconomics | VUB | 2025/26

2026




INTERMEDIATE MICROECONOMICS
SUMMARY EXERCISE SOLUTIONS


KOEN HANEGREEFS
VUB

,Chapter 2: Budget Constraint
Exercise 2.1
Solution:

Input: x₁ = 100 units; x₂ = 50 units; p₁ = €2; p₁’ = €3; p₂ = €4

Budget constraint: m = p₁ · x₁ + p₂ · x₂

• Initial prices: m = 2 · 100 + 50 · 4 = €400
• New prices: m = 3 · 100 + 50 · 4 = €500

Answer: Jan’s income should increase by €100.



Exercise 2.2
Solution:

Input: x₁ = 8, x₂ = 8; x₁’ = 10, x₂’ = 4; p₁ = €0.50

Budget constraint: m = p₁ · x₁ + p₂ · x₂

Both bundles (8, 8) and (10, 4) are on the budget line: - m = 8 · 0.5 + 8 · p₂ = 6 - m = 10 · 0.5 + 4 · p₂

Solving: m = 6; p₂ = 0.25

Budget line equation: 6 = 0.5x₁ + 0.25x₂

Intercepts: - x₁ = 6/0.5 = 12 - x₂ = 6/0.25 = 24

Answer: Amy gets €6 of pocket money per week.




Ex. 2.2 — Amy’s budget line

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,Exercise 2.3
Solution A:

Input: m = 60,000; p₁ (x₁ ≤ 1,000 m³) = €15; p₁ (x₁ > 1,000 m³) = €10; p₂ = €10

Budget constraints: - If x₁ ≤ 1,000: 60,000 = 15x₁ + 10x₂ - If x₁ > 1,000: 60,000 = 15 · 1,000 + 10(x₁ - 1,000) +
10x₂
So: 55,000 = 10x₁ + 10x₂

Key points: - When x₁ = 0: x₂ = 6,000 - When x₁ = 1,000: x₂ = 4,500 (kink point) - When x₂ = 0: x₁ = 5,500

Answer: The budget line has a kink at (1,000, 4,500).




Ex. 2.3a — Budget set with quantity discount

Solution B:

Input: Same as (a) but with €6,000 connection costs

Budget constraints: - If x₁ ≤ 1,000: 60,000 = 6,000 + 15x₁ + 10x₂
So: 54,000 = 15x₁ + 10x₂ - If x₁ > 1,000: 60,000 = 6,000 + 15 · 1,000 + 10(x₁ - 1,000) + 10x₂
So: 49,000 = 10x₁ + 10x₂

Key points: - When x₁ = 0: x₂ = 5,400 - When x₂ = 0: x₁ = 4,900

Answer: The budget line shifts down (parallel shift) due to the fixed connection cost.




Ex. 2.3b — Budget set with €6,000 connection fee (parallel shift)


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, Exercise 2.4
Solution 1: Unconditional lump-sum subsidy

Input: m = 60,000; subsidy = €10,000

Budget constraint: 60,000 + 10,000 = C + O
So: 70,000 = C + O

Answer: The budget line shifts outward uniformly. Maximum C = 70,000 or maximum O = 70,000.



Solution 2: Conditional subsidy (minimum purchase requirement)

Input: m = 60,000; subsidy = €10,000 if C ≥ €30,000

Budget constraints: - When C < €30,000: 60,000 = C + O - When C ≥ €30,000: 70,000 = C + O

Key points: - Kink point at C = 30,000, O = 30,000 - Maximum C without subsidy = 60,000 - Maximum C with
subsidy = 70,000

Answer: Non-convex budget set due to discontinuity at C = €30,000.



Solution 3: Proportional price subsidy (50% discount on computers)

Input: m = 60,000; subsidy = 50% on computers

Budget constraint: 60,000 = 0.5C + O

Key points: - Maximum O = 60,000 - Maximum C = 120,000

Answer: Effective price of computers falls to €0.50. Budget line becomes flatter.



Solution 4: Price subsidy with cap (50% discount, max €10,000 subsidy)

Input: m = 60,000; subsidy = 50% on computers (max = €10,000)

Transition point: Subsidy cap reached at C = €20,000 (subsidy = 0.5 × 20,000 = €10,000)

Budget constraints: - When C ≤ €20,000: 60,000 = 0.5C + O - When C > €20,000: 60,000 = 0.5 · 20,000 + (C -
20,000) + O
So: 70,000 = C + O

Key points: - Kink at C = 20,000, O = 50,000 - Maximum C = 70,000 - Slope changes from -0.5 to -1 at kink

Answer: Budget line has a kink at C = €20,000.




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