Term 1 Week 3: MRS

Question 1

What is the MRS (3)

Answer 1

-The Marginal Rate of Substitution is the rate at which the consumer is willing to substitute one G/S for another
-∆x₂/∆x₁ , with ∆x₁ being small,
-The MRS is the slope of an indifference curve and negative due to monotonicity

Question 2

How can we work out the MRS using Marginal Utilities (4,1)

Answer 2

-Marginal utility is the change in utility following a small change in one of the goods
-To work out marginal utility, you partially differentiate the utility function with respect to the variable you’re interested in
-since ∆U = MU1∆x1, to keep utility constant (same IC), if x1 rises then x2 falls, and thus ∆U = MU1∆x1 – MU2∆x2 = 0
-Rearranging this shows you how MRS = ∆x2/∆x1 and so MRS = MU1/MU2

-The MRS is found by partially differentiating the utility function for each variable, then doing the x/y

Question 3

How does the MRS change for different utility functions (3)

Answer 3

-For perfect substitutes U(x, y) = ax + by, MRS = a/b
-For perfect complements, U(x, y) = min{ax, by), MRS = -infinity (vertical portion), 0 (horizontal) or undefined (kink),
-For Cobb Douglas U(x, y) = x^a, y^1-a, MRS = (a/1-a)(y/x)

Question 4

What does a diminishing MRS mean (2)

Answer 4

-A diminishing MRS is how the curve gets flatter in absolute terms
-The more of a good you have, the more willing you are to sacrifice it to gain an additional unit of another good

Question 5

What are homothetic tastes (3)

Answer 5

-Homothetic tastes are when the consumers preference depend solely on the ratio of good 1 to good 2
-Homothetic tastes give rise to indifference maps, where the MRS is constant along any ray from the origin
-When income rises, demand rises by the same proportion

Question 6

What are Quasilinear tastes (3)

Answer 6

-Quasilinear tastes are where tastes are linear in one good, but may not be in the other
-Consumption does not vary with income, leading to indifference curves that are vertical translates of one another, where MRS is constant from any vertical line
-U(x, y) = V(x) + y

Question 7

What is the elasticity of substitution (3)

Answer 7

-The elasticity of substitution measures how responsive the bundle of goods along an IC is to changes in the MRS
-σ = (percentage change in x2/x1)/%change in MRS)
-For perfect substitutes, σ = infinity, for perfect complements, σ = 0, for cobb-douglas, σ = 1