Hi,

I have a question on IBC. I was being told that the slope of the budget line equals to -(1+r). Would like to know how do we derive at this? Please assist. Thanks.

That will indeed be the slope, when you assign the vertical axis to next period's consumption, and the horizontal axis to today's consumption.

Remember that in a linear relationship, the line's slope represents the amount by which the vertical variable changes for each unit change in the horizontal variable.

Now think about how next period's consumption must change for a unit increase in today's consumption. To consume one additional unit today, we must either (1) borrow one unit today, which will be repaid next period; or (2) spend today one unit that otherwise would have been invested until next period.

If (1), the loan repayment next period is (1 + r). If (2), by spending that unit today instead of investing it, we'll have (1 + r) fewer units next period (the amount the 'spent' unit would have grown to, had we not spent it).

Either way, for every additional unit we consume this period, we have (1 + r) fewer units available for consumption next period. On the graph, this means that for every unit we move to the right horizontally (additional consumption today), the line's height falls by (1 + r) units. Hence, the slope is negative (1 + r).

Thanks a lot. I fully understand what is going on.