Lecture 4 - MRS, Marginal Utility

Question 1

What does MRS1,2(x1, x2) denote?

Answer 1

the marginal rate of substitution of good 2 for good 1 at the point (x1, x2)

Question 2

If c(t) is the amount of change in x2 to compensate exactly for the change of t in x1, then (x1, x2) ∼ _____?

Answer 2

(x1, x2) ∼ (x1 + t, x2 + c(t))

Question 3

What does c(0) equal, and why?

Answer 3

• c(0) = 0
• as not change in x1 requires no change in x2

Question 4

Why does MRS1,2(x1, x2) equal the gradient of the tangent of the IC at (x1, x2)?

Answer 4

as it tells us how many units of x2 the consumer is willing to sacrifice for an additional unit of x2

Question 5

Show why MRS1,2(x1, x2) equals lim t→0 (c(t)/t)

Answer 5

MRS1,2(x1, x2) = lim t→0 (((x2 + c(t)) - x2) / ((x1 + t) - t))

Question 6

As well as MRS1,2(x1, x2), what does lim t→0 (c(t)/t) equal? (in words)

Answer 6

• the derivative of c with respect to t at the point 0
• as it equals lim t→0 ((c(t) - c(0))/t), as c(0) = 0