Question

A veggie double burger is made up of 2 veggie patties and 3 buns.

Let x1 denote units of veggie patties and x2 denote units of buns. Write down the utility function for veggie patties and buns if I plan to make veggie double burgers out of the two ingredients. What kind of preferences do I have?

What is my marginal utility with respect to veggie patties if I have a disproportionately large number of patties compared to buns, such that I will have leftover veggie patties after I finish making double burgers? What is the marginal rate of substitution of buns for patties in this case?

Answer 1

✓ A veggie double burger is made up of 2 veggie patties and 3 buns.

Let x1 denote units of veggie patties and x2 denote units of buns.

Hence, the veggie double burger is consumed with a fixed ratio of veggie patties (x1) and buns (x2).

Hence, the consumer always consumes 2 veggie patties with 3 buns.

Hence, x1:x2 = 2:3

or, x1/x2 = 2/3

or, 3.x1 = 2.x2

Hence, the utility function is

U(x1, x2) = Min{3.x1, 2.x2}............(1)

The type of preferences you have is called 'Perfect Complement'.

✓ As we know that, the veggie patties and buns are consumed in a fixed proportion, the consumer always consumes 2 veggie patties with 3 buns. If he consumes one extra veggie patties but no extra bun, the proportion is not maintained. Hence, he will not gain any utility. Hence, the marginal utility of consuming one extra veggie patties is zero.

The marginal utility with respect to veggie patties is zero (0).

✓ We know that, Marginal Rate of Substitution or MRS is defined as

The amount of x2 you need to sacrifice in order to get one additional unit of x1 while keeping thr utility constant.

Here, x1 and x2 are always consumed in a fixed proportion. Hence, the consumer can consume one more unit os x1 without sacrificing any x2 while the utility will be constant.

Hence, Marginal Rate of Substitution or MRS will be zero.

The marginal rate of substitution of buns for patties in this case is zero (0).

Hope the solution is clear to you my friend.