An equal proportionate increase in a consumer's nominal income and the prices of both good… — JAMB UTME

An equal proportionate increase in a consumer's nominal income and the prices of both goods consumed will cause the budget line to shift outward parallel to its original position.

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The statement is False. An equal proportionate increase in nominal income and all commodity prices leaves real purchasing power and the budget line completely unchanged.

The statement is false because multiplying nominal income and all product prices by the same scalar leaves real purchasing power and relative price ratios unchanged, keeping the budget line in its exact original position.

Adım Adım Çözüm

State the standard budget line equation and intercepts

The budget equation is

P_X X + P_Y Y = I

, with horizontal intercept

X = \frac{I}{P_X}

, vertical intercept

Y = \frac{I}{P_Y}

, and slope

-\frac{P_X}{P_Y}

Establishing the mathematical parameters of the budget constraint is necessary to evaluate positional changes.

Apply a proportional scaling factor

k > 1

to nominal income and prices

The new equation becomes

(k P_X) X + (k P_Y) Y = k I

An equal percentage increase scales nominal income and both prices by the same factor

k

Simplify the scaled budget equation and determine the effect on the line

Dividing both sides by

k

yields

P_X X + P_Y Y = I

. The new intercepts

\frac{k I}{k P_X} = \frac{I}{P_X}

and

\frac{k I}{k P_Y} = \frac{I}{P_Y}

are identical to the original intercepts.

Because neither the intercepts nor the slope change, the budget line does not shift outward.

Anahtar Kavram

Homogeneity of the Budget Constraint (Real vs. Nominal Changes)

Tahmini Süre:1m 0s

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