Utility Functions and Ordinality

A thermometer with no units

Checking invariance

The workhorse families

Curves from utility, utility from curves

Bundle A has utility 6 and bundle B has utility 3 under $u = x_1 x_2$. Which claims are meaningful?

Which MRS does $v = \ln x_1 + \ln x_2$ have, and how does it relate to the MRS of $u = x_1 x_2$?

For quasilinear utility $u = v(x_1) + x_2$, what is the geometric signature of the indifference map?

Why do economists so often work with $v = a \ln x_1 + b \ln x_2$ instead of $u = x_1^a x_2^b$?

For $u = x_1^2 x_2^3$ at the bundle $(2, 3)$, compute the MRS in absolute value, and write the number.

Under $u = x_1 x_2$ the bundle $(4, 5)$ has utility 20. Compute the value of $v = \ln u$ at that bundle, rounded to two decimals, and write the number.

Under u of x1 x2, bundle A scores 6 and bundle B scores 3. Which claim is meaningful?

Starting from u of x1 x2, which rewrite preserves every preference?

For u of v(x1) plus x2, what geometric property do the indifference curves have?

What convenience does v equal a ln x1 plus b ln x2 buy over its exponential parent?

For u of x1 times x2 cubed at the bundle (1, 3), compute the absolute MRS, and write the number.

For u of x1 times x2, compute the absolute MRS at the bundle (5, 2), and write the number as a decimal.