relationship between Uh and Qh in context of utilities

[Akwasi]

Hello all, please can somebody explain to me the difference between Uh and Qh in the context of utility in section 5.2 in asm. I have read this for like six times but i am not getting it. Forgive me if you think this is trivial, but i really need somebody to explain this to me in the simplest of terms.
Also why is Qh = pUh and Qh + Ql = 1/(1+r).
Thanks in advance.

[psu602]

Originally Posted by Akwasi

Hello all, please can somebody explain to me the difference between Uh and Qh in the context of utility in section 5.2 in asm. I have read this for like six times but i am not getting it. Forgive me if you think this is trivial, but i really need somebody to explain this to me in the simplest of terms.
Also why is Qh = pUh and Qh + Ql = 1/(1+r).
Thanks in advance.

U is the value of a dollar, in terms of Utility.

Utility theory says that a dollar gained is not as valuable as a dollar lost. To illustrate what Utility theory is, let's assume you make $25k per year. Consider the following scenarios:

-Your salary increases by $25k (to $50k total)
-Your salary decreases by $25k (to nothing)

The amount of "happiness" in scenario 1 is LESS dramatic than the amount of "unhappiness" in scenario 2. Insurance exists because of Utility Theory.

Back to your question, Q is the probability of receiving that dollar times it's value (in utility). U is just the value of it, with no probability involved.

[mathmajor]

You really don't need to understand the "usefulness" idea to get Q vs. U.

Basically, U is the buying power of $1 at the end of the year. Uh is the amount gained if the "H" state happens, and Ul is if the "L" state happens. Qh is the present value of prob(H)*Uh. Qh can be thought of as Uh's contribution to the PV of the expected value. Added together, these should add to the present value of $1, or 1/(1+r).

[actuary_aspire]

Originally Posted by mathmajor

You really don't need to understand the "usefulness" idea to get Q vs. U.

Basically, U is the buying power of $1 at the end of the year. Uh is the amount gained if the "H" state happens, and Ul is if the "L" state happens. Qh is the present value of prob(H)*Uh. Qh can be thought of as Uh's contribution to the PV of the expected value. Added together, these should add to the present value of $1, or 1/(1+r).

Uh is the utility now of getting 1$ in the up state, so Qh is just prob(H)*Uh.