John is planning ahead for retirement in a two-period world. When John is young he will earn $1 million, and when John is old and retired he will be given $50,000 from Social Security. If the interest rate between the two time periods is 7 percent, what is the slope of John's budget constraint when considering the consumption possibilities between the two periods if consumption when young is graphed on the horizontal axis and consumption when old is graphed on the vertical axis?
A)-0.89
B)-1.05
C)-1.07
D)-1.12

Question

Quizplus · Accepted Answer

The slope of John's budget constraint is equal to the opportunity cost of consuming one unit of consumption when young in terms of the units of consumption John could have when old.

Let's denote the consumption John has when young as C1 and the consumption John has when old as C2. John's budget constraint can be written as:

C2 = (1 + r)C1 + 50,000

where r is the interest rate between the two time periods, which is given as 7% or 0.07 in decimal form.

To find the slope of this equation, we need to solve for C2 in terms of C1:

C2 = 0.07C1 + 1,050,000

The slope of the budget constraint is the coefficient of C1, which is 0.07.

We want the opportunity cost of consuming one unit of consumption when young in terms of the units of consumption John could have when old, so we need to compute the reciprocal of the slope:

1/0.07 = 14.29

This means that John could have 14.29 units of consumption when old for every unit of consumption he foregoes when young.

However, the question asks for the slope of John's budget constraint when consumption when young is graphed on the horizontal axis and consumption when old is graphed on the vertical axis. In this case, we need to reverse the roles of C1 and C2 in the budget constraint equation and solve for C1 in terms of C2:

C1 = (1/1.07)(C2 - 50,000)

The slope of the budget constraint is the coefficient of C2, which is 1/1.07 = 0.9346, but since we want the slope in terms of consumption when young on the horizontal axis and consumption when old on the vertical axis, we need to take the reciprocal of the slope:

1/0.9346 = 1.07

Therefore, the slope of John's budget constraint when considering the consumption possibilities between the two periods is -1.07.

John Is Planning Ahead for Retirement in a Two-Period World