Which of the following combinations is unattainable for a consumer given their budget line?

• A. A combination that lies inside the budget line
• B. A combination that lies on the budget line
• C. A combination where the consumer spends exactly their entire budget
• D. A combination that lies outside the budget line

Answer: (D)

Verified step by step guidance

1. Understand the concept of a budget line: it represents all combinations of goods that a consumer can purchase by spending their entire budget. Mathematically, it is expressed as \(P_x Q_x + P_y Q_y = M\), where \(P_x\) and \(P_y\) are prices of goods \(x\) and \(y\), \(Q_x\) and \(Q_y\) are quantities, and \(M\) is the consumer's total budget.
2. Identify what it means for a combination to lie inside the budget line: this means the consumer spends less than their total budget, so \(P_x Q_x + P_y Q_y < M\). Such combinations are attainable because the consumer can afford them without exhausting their budget.
3. Recognize that combinations on the budget line satisfy \(P_x Q_x + P_y Q_y = M\), meaning the consumer spends their entire budget exactly. These combinations are attainable and represent the consumer's maximum purchasing power.
4. Analyze combinations outside the budget line: these satisfy \(P_x Q_x + P_y Q_y > M\), meaning the consumer would need more money than they have to afford these combinations. Therefore, these are unattainable given the budget constraint.
5. Conclude that the unattainable combinations for a consumer are those that lie outside the budget line, as they require spending beyond the consumer's available budget.