Alex consumes only lemons and sugar. For each lemon he requires exactly 2 spoons of sugar. He doesn't like more sugar on his lemons, and he won't eat lemons with less sugar. What is Alex's optimal consumption bundle?Write down the precise quantities of each good.(Assume that the price of each lemon is 20 and the price of a spoon of sugar is 1. Alex has 44 to spend on lemons and sugar)
Alex's preferences of sugar and lemons can be expressed in form of a utility function as:
where $x$ is sugar and $y$ is lemons.This function tells us we need at least 2 spoons of sugar to consume 1 lemon.
we need a minimum of 2 sugars initally so we can say $x=2$ for 1 lemon so $y=1$
Plugging those values into our budget constraint:
Notice how we end up having 3 left over, however with the budget constraint and preferences provided our consumption bundle will be 2 sugars and 1 lemon.