Question

Individuals derive utility from​ picnics, p, and kayak​ trips, k. Assuming that an​ individual's utility is ​U(p,k) = k Superscript 0.5k0.5p Superscript 0.5p0.5 and income is​ $100, what is the marginal rate of substitution​ (MRS) between picnics and kayak​ trips? A. MRS​ = minus−1. B. MRS​ = 1. C. MRS​ = minus−one half 1 2 D. There is no substitution because picnics and kayak trips are perfect complements.

Answer 1

B) MRS = 1

Step-by-step explanation:

In this question, we have been given the options as follows:

A) MRS = -1

B) MRS = 1

C) MRS = -1/2

D) There is no substitution because picnics and Kayak trips are perfect complements.

Where, MRS stands for = Marginal Rate of Substitution

First of all, we have to calculate the marginal utility with respect to kayak trips (k) and with respect to picnics (p).

Marginal Utility with respect to P =
`(0.5k^(0.5) )/(p^(0.5) )`

Now, calculate with respect to K

Marginal Utility with respect to K =
`(0.5p^(0.5) )/(k^(0.5) )`

Now, the formula for MRS is as follows:

Marginal Rate of Substitution = (Marginal Utility with respect to P ÷ Marginal Utility with respect to K)

MRS =
`(0.5k^(0.5) )/(p^(0.5) )` ÷
`(0.5p^(0.5) )/(k^(0.5) )` = 1

Hence, the right answer is B) MRS = 1