Discounted Utility Model

The Discounted Utility Model, also known as DU models, the generalize motivation is that to answer the case that when we face the options that:

• Option 1: I pay you $100$ pounds today
• Option 2: I pay you $100+x$ pounds in one month

When $x$ is small, we’d like to choose option 1, vice versa.

The conclusion is that we will require a premium to delay the reward. (impatience)

Using the utility thinking method, we denote a ${\delta }_1$ that 1 utility tomorrow is the same as ${\delta }_1$ today.

$$1\ge {\delta }_1\ge 0$$

The key formula:

$$V(U_0,U_1,U_2)=U_0+{\delta }_1{U}_1+{\delta }_2{U}_2$$