If a consumer's nominal income increases by 50\% while the price of good X increases by 50… — JAMB UTME

If a consumer's nominal income increases by $50\%$ while the price of good $X$ increases by $50\%$ and the price of good $Y$ remains constant, the budget line will pivot inward along the vertical axis while keeping its horizontal intercept unchanged.

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Cevap

The statement is False. The budget line pivots outward along the vertical axis while maintaining a fixed horizontal intercept.

The horizontal intercept

(I / P_X)

remains identical because the

50\%

increase in nominal income is exactly offset by the

50\%

increase in the price of good

X

. However, because the price of good

Y

does not change, the

50\%

increase in income allows the consumer to purchase more of good

Y

, shifting the vertical intercept

(I / P_Y)

outward from the origin. Thus, the pivot is outward, making the statement false.

Adım Adım Çözüm

Analyze the formula for the horizontal intercept.

The horizontal intercept is given by

\frac{I}{P_X}

. With a

50\%

increase in both

I

and

P_X

, the new intercept is

\frac{1.5 I}{1.5 P_X} = \frac{I}{P_X}

, which remains unchanged.

Proportionate changes in income and the price of a good cancel each other out for that good's axis intercept.

Analyze the formula for the vertical intercept.

The vertical intercept is given by

\frac{I}{P_Y}

. With a

50\%

increase in

I

and constant

P_Y

, the new intercept is

\frac{1.5 I}{P_Y} = 1.5 \left(\frac{I}{P_Y}\right)

, which increases by

50\%

Higher nominal income with an unchanged price expands the maximum affordable quantity of good

Y

Determine the direction of the rotational pivot and overall budget line movement.

Since the vertical intercept moves further out from the origin while the horizontal intercept stays fixed, the budget line pivots outward along the Y-axis and becomes steeper.

An inward pivot would require a decrease in maximum purchasable

Y

, which contradicts the

50\%

increase in real purchasing power for good

Y

Anahtar Kavram

Rotational Pivot of the Budget Line under Non-Proportionate Price and Income Changes

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