Question

Why is the budget line downward sloping? Explain.

Hint:

Budget line: PxX+PyY=M gives slope -Px/Py; fixed income forces a trade-off between the two goods.

Answer 1

Step 1: Write the budget equation:
For two goods X and Y, a consumer with income M spends: $P_xX + P_yY = M$.

Step 2: Rearrange to see the slope:
Solving for Y: $Y = \dfrac{M}{P_y} - \dfrac{P_x}{P_y}X$. This is a straight line whose slope is $-\dfrac{P_x}{P_y}$, which is negative since both prices are positive.

Step 3: Give the economic reasoning:
With a fixed money income and fixed prices, the consumer faces a strict trade-off: buying more units of X necessarily means less money is left for Y, so Y purchased must fall. This inverse (trade-off) relationship between the quantities of the two goods is exactly what produces a negatively (downward) sloping line.

Final Answer:
The budget line slopes downward because, given a fixed income, buying more of one good is only possible by giving up some of the other good — its slope equals $-P_x/P_y$.