Question 3 of 26intermediate💡 UnderstandShort Answer3 marks

Explain why the budget line is downward sloping.

Correct Answer

The budget line represents all bundles of goods that cost the consumer her entire income at prevailing market prices. It is downward sloping because a consumer has a fixed income; to consume more of one good, she must reduce the consumption of the other good to keep total expenditure equal to her income.

Mathematically, the budget constraint is given by p1x1+p2x2=Mp_1 x_1 + p_2 x_2 = M. For any two points on the budget line, a change in consumption must satisfy p1Δx1+p2Δx2=0p_1 \Delta x_1 + p_2 \Delta x_2 = 0. Rearranging this, we get the slope Δx2Δx1=−p1p2\frac{\Delta x_2}{\Delta x_1} = -\frac{p_1}{p_2}. Since prices (p1,p2p_1, p_2) are positive, the slope is negative, confirming that the budget line is downward sloping. This indicates that the consumer can substitute one good for another at the price ratio.

Exercise: EXERCISES | Q: 3
For More Understanding

Explanation

The answer is derived from the 'Derivation of the Slope of the Budget Line' section in the provided text. It uses the mathematical relationship p1Δx1+p2Δx2=0p_1 \Delta x_1 + p_2 \Delta x_2 = 0 to demonstrate the negative slope (−p1/p2-p_1/p_2). The explanation connects the mathematical slope to the economic logic of a fixed income constraint mentioned in the text: to buy more of one good, the consumer must give up some of the other good.

Solution Steps

  1. Step 1: State the budget constraint equation: p1x1+p2x2=Mp_1 x_1 + p_2 x_2 = M.

  2. Step 2: Consider changes in consumption (Δx1,Δx2\Delta x_1, \Delta x_2) which leads to p1Δx1+p2Δx2=0p_1 \Delta x_1 + p_2 \Delta x_2 = 0.

  3. Step 3: Rearrange to find the slope: Δx2Δx1=−p1p2\frac{\Delta x_2}{\Delta x_1} = -\frac{p_1}{p_2}.

  4. Step 4: Conclude that since prices are positive, the slope is negative, making the line downward sloping.

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