Question

The table below represents Sue's preferences for bottled water and soft drinks, the combination of which yields the same level of utility.

Calculate Sue's marginal rate of substitution of soft drinks for bottled water at each rate of consumption of water (or soft drinks). Relate the marginal rate of substitution to marginal utility.

Short answer

marginal rate of substitution of soft drinks for bottled water at each rate of consumption of water are

A -$0$, B- $0.8$, C-$0.6$, D-$0.4$, E-$0.2$

Step-by-step solution

Given Information

The marginal rate of replacement or MRS alludes to the rate at which one great can be filled in for the other great holding utility steady. At the end of the day, it is the rate at which the shopper will compromise one great for the other keeping utility fixed.

Explanation

We know,

Soft drink's marginal utility = $M{U}_S$

Bottled water marginal utility = $M{U}_W$

Marginal rate of substitution MRS = role="math" localid="1652254990012" $-\frac{\text{Units of goods sacrificed}}{\text{Units of goods gained}}=-\frac{M{U}_S}{M{U}_W}$

At point A, MRS is $0$as there is nothing before point A.

At point B MRS = $MRS=-\frac{-4}{5}=0.8$

At point C MRS = $MRS=-\frac{-3}{5}=0.6$

At point D MRS = $MRS=-\frac{-2}{5}=0.4$

At point E MRS = $MRS=-\frac{-1}{5}=0.2$