Consider a consumer with a choice set that emerges from an exogenous income I. Suppose that, as a result of changes in a consumer's economic circumstances, the budget line rotates outward, with the vertical intercept remaining unchanged but the horizontal intercept shifting to the right. Demonstrate, using the budget line equation, how this could have happened if the price of the good on the horizontal axis did not change?

What will be an ideal response?

The budget equation is x2=I/p2- (p1/p2)x12, with the first term representing the intercept and the term in parenthesis representing the slope. The rotation of the budget that is described implies the intercept remains constant and the slope falls in absolute value. If p1 does not change, this can happen only if I and p2 change by the same factor k --- which then cancels in the first term (leaving the intercept unchanged) and causes the second term to fall in absolute value.