How to Calculate Barry's Utility Function
What is Barry's utility function?
Given that Barry only drinks coffee with 1/2 teaspoon of sugar and his utility is not increased by consuming more coffee or sugar in a different ratio.
Barry's utility function is U = x₁ + 2x₂
Barry's utility function is U = x₁ + 2x₂, where x₁ represents coffee and x₂ represents sugar. The utility gained from consuming coffee is equal to the amount of coffee consumed, and the utility gained from consuming sugar is twice the amount of sugar consumed.
To calculate Barry's utility function, we use the given information that he only drinks coffee with 1/2 teaspoon of sugar. This means his satisfaction or utility is derived from the specific ratio of coffee to sugar he consumes.
The utility function is represented as U = x₁ + 2x₂, where x₁ represents the amount of coffee consumed and x₂ represents the amount of sugar consumed. Since Barry's utility is not affected by consuming more coffee or sugar in a different ratio, the coefficients in the utility function reflect this.
For example, if Barry drinks 2 cups of coffee, the utility function would be calculated as follows:
U = 2 + 2(1/2) = 3
Therefore, Barry's utility function U = x₁ + 2x₂ captures his satisfaction from consuming coffee and sugar in the specific ratio he prefers.