Question
Explain why the budget line is downward sloping.

Answer

The budget line is downward sloping because a consumer can increase the consumption of good 1 only by decreasing the consumption of good 2. The consumer have limited income which is can spend to those goods between good 1 and good 2.
The slope of the budget line is $\frac{-\text{P}_1}{\text{P}_2}=\frac{\triangle\text{x}^2}{\triangle\text{x}_1},$ which implies the rate of exchange or the rate at which good 2 can be substituted for good 1.

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