Q.In the earlier example, a consumer had an income of Rs. 600 to spend on X (Rs. 60 per unit) and Y (Rs. 40 per unit). Suppose his income now rises to Rs. 900, with both prices unchanged. Write the new budget line equation, find the new intercepts, and state whether the slope changes.

Only the income term in the budget equation changes; substitute the new income and find the new intercepts, keeping prices (and hence the slope) the same.

With income now $M=900$ and prices unchanged ($P_x=60,\ P_y=40$), the new budget line equation is:

New X-intercept ($y=0$): $60x=900 \Rightarrow x=15$ units.

New Y-intercept ($x=0$): $40y=900 \Rightarrow y=22.5$ units.

Both intercepts have increased in exactly the same proportion as income did (income rose from 600 to 900, a factor of 1.5; the X-intercept rose from 10 to 15, and the Y-intercept from 15 to 22.5 — both also a factor of 1.5). The slope, $-\dfrac{P_x}{P_y}=-\dfrac{60}{40}=-1.5$, is UNCHANGED, since neither price changed — only income did. Graphically, the new budget line is a straight line PARALLEL to the old one, shifted outward (further from the origin), reflecting th …

Assuming the slope must also change whenever the budget line shifts is a common misconception — the slope depends ONLY on the price ratio Px/Py, so it …