Hyperbolic Discounter

Sue is an exponential discounter. Her discount function which illustrates her preference for money at various points in time is characterized as follows:

∂(t) = 1/(1.07)t for t = 0,1,2, ...

Bob on the other hand is a hyperbolic discounter. His discount function is:

∂(t) = 1 for t = 0
= .8/(1.03)t-1 for t = 1,2, ...

a. What would Sue/Bob rather have: $1 today or $1.10 next year? Explain.

Sue’s preference for money

For t = 1, ∂(t)= 1/(1.07)1 = 0.93

P = 1/∂ -1 = 1/0.93 - 1= 1.07 -1 = 7%

Since $1 today or $1.10 next year is 10% increase which is higher than 7% sue will wait until next year.

Bob’s preference for money

For t = 1, ∂(t)= .8/(1.37)1-1 =0.8

P = 1/∂ -1 = 1/0.8 -1= 25%

Since $1 today or $1.10 next year is 10% increase which is lower than Bob’s preference of 25% Bob will prefer to take $1 today.

b. What would Sue/Bob rather have: that? Explain.

Sue’s preference for money

For t = 2, ∂(2)= 1/(1.07)2 = 1/1.1449 = 0.87

P = 1/∂ -1 = 1/0.87 - 1= 1.1449 -1 = 14%

Since $1 next year or $1.10 the year after is 10% increase which is lower than 14% sue will take $1 next year.

Bob’s preference for money

For t = 1, ∂(2)= .8/(1.03)2-1 =0.78

P = 1/∂ -1 = 1/.78 -1= 29%

Since $1 next year or $1.10 the year after is 10% increase which is lower than 29% Bob will take $1 next