Properties of Preferences and the MRS

Three quiet assumptions

The slope of indifference

Diminishing MRS and convexity

The zoo of shapes

Why does the transitivity assumption matter so much for the theory of choice?

For $u = x_1 x_2$, what is the marginal rate of substitution at the bundle $(3, 6)$?

A consumer on the curve $x_1 x_2 = 16$ moves from $(2, 8)$ to $(8, 2)$. What happens to the MRS and what does it mean?

A consumer always uses exactly two units of good two with one unit of good one. What do the indifference curves look like and where is a best affordable bundle likely to sit?

For $u = x_1 x_2$ at the bundle $(3, 6)$, compute the marginal rate of substitution in absolute value, and write the number.

On the indifference curve $x_1 x_2 = 16$, if $x_1$ rises from 2 to 4, compute the new level of $x_2$ needed to stay indifferent, and write the number.

Without transitivity, what concrete failure appears in choice behavior?

At the bundle (4, 4) on the curve x1 x2 equals 16, what is the MRS in absolute value?

For a consumer needing exactly two units of good two per unit of good one, where does a best affordable bundle sit?

What does diminishing MRS mean as you slide down and right along an indifference curve?

For u of x1 times x2, compute the absolute MRS at the bundle (6, 3), and write the number.

On x1 x2 equals 16, if x1 rises from 2 to 8, compute how many units of x2 must be surrendered in total, and write the number.