In the budget constraint model, as the quantity of one good consumed increases, what typically happens to the quantity of the other good that can be consumed?

• A. It remains unchanged.
• B. It fluctuates unpredictably.
• C. It increases, regardless of income and prices.
• D. It decreases, given a fixed income and prices.

Answer: (D)

Verified step by step guidance

1. Understand the budget constraint model: it represents all combinations of two goods that a consumer can purchase given their income and the prices of the goods.
2. Express the budget constraint mathematically as \(\text{Income} = P_1 \times Q_1 + P_2 \times Q_2\), where \(P_1\) and \(P_2\) are the prices of goods 1 and 2, and \(Q_1\) and \(Q_2\) are the quantities consumed.
3. Rearrange the equation to solve for \(Q_2\): \(Q_2 = \frac{\text{Income}}{P_2} - \frac{P_1}{P_2} \times Q_1\).
4. Analyze the relationship: as \(Q_1\) (quantity of good 1) increases, the term \(\frac{P_1}{P_2} \times Q_1\) increases, which reduces the maximum possible \(Q_2\) (quantity of good 2) that can be consumed.
5. Conclude that, given fixed income and prices, increasing consumption of one good decreases the quantity of the other good that can be consumed, illustrating the trade-off in the budget constraint.