3 Utility and Marginal Utility Free Online FlashCards

What does it mean for utility to be ordinal?

In standard consumer theory, utility is usually ordinal: the ranking of bundles matters, not the numerical size of utility differences.

What does equal utility for two bundles indicate?

Equal utility values indicate indifference between the bundles in that utility representation.

What does a strictly increasing utility transformation preserve?

A strictly increasing transformation preserves the ranking of bundles, so it represents the same preferences even though utility numbers change.

Under $u(x,y)=xy$, how do $(2,6)$ and $(3,4)$ compare?

Both bundles have utility $12$, so they are indifferent in this representation.

What is marginal utility?

Marginal utility is the change in represented utility from a small increase in one good, holding other goods fixed.

For $U(q)=10q-q^2$, what is $MU(q)$, and what are its values at $q=1$ and $q=3$?

Here $MU(q)=10-2q$, so marginal utility is $8$ at $q=1$ and $4$ at $q=3$.

What is diminishing marginal utility?

Diminishing marginal utility means marginal utility falls as consumption increases; utility can still rise while each additional unit adds less than the previous one.

Is diminishing marginal utility a universal, representation-independent rule?

Diminishing marginal utility is common but not universal. It can depend on the utility representation, so it is not by itself a representation-independent fact about preferences.

How is the indifference-curve slope related to marginal utilities?

The indifference-curve slope is $\left.\frac{dy}{dx}\right|_{u=\text{constant}}=-\frac{MU_x}{MU_y}$. The ratio describes the local trade-off between the goods.

What is the indifference-curve slope for $u(x,y)=xy$?

For $u(x,y)=xy$, $MU_x=y$ and $MU_y=x$, so the indifference-curve slope is $-\frac{y}{x}$.

What happens to marginal utility and the MRS under a strictly increasing transformation?

A strictly increasing transformation can change marginal-utility values, but where derivatives exist and marginal utilities are nonzero, it preserves their ratio and thus the marginal rate of substitution.

Why does $v(x,y)=\ln x+\ln y$ represent the same preferences as $u(x,y)=xy$?

For positive $x$ and $y$, $v(x,y)=\ln x+\ln y=\ln(xy)$ represents the same preferences as $u(x,y)=xy$, because the logarithm is strictly increasing.