3 Budget-Constrained Consumer Choice Free Online FlashCards

What is the budget constraint for goods $x$ and $y$?

The consumer’s affordable choices satisfy $p_xx+p_yy\leq m$, with $x,y\geq 0$.

What does the budget set contain?

The budget set is the collection of all bundles the consumer can afford.

What does the budget line represent?

The budget line contains bundles that spend all available income: $p_xx+p_yy=m$.

What are the budget line’s intercepts?

The vertical intercept is $\frac{m}{p_y}$, the maximum quantity of $y$; the horizontal intercept is $\frac{m}{p_x}$, the maximum quantity of $x$.

What does the budget line’s slope mean?

Its slope is $-\frac{p_x}{p_y}$. This is the quantity of $y$ the consumer gives up to gain one unit of $x$ while keeping spending unchanged.

How do income and a single price change affect the budget line?

With prices unchanged, higher income shifts the budget line outward in parallel. A change in one good’s price rotates it around the other good’s intercept.

What does a utility function represent?

A utility function represents a preference ranking: a higher utility value means a bundle is preferred. Utility is generally ordinal, not an objective measure of satisfaction.

What does an indifference curve show?

An indifference curve joins bundles that provide the same utility. If both goods are desirable, curves farther from the origin represent preferred bundles.

What is marginal utility?

Marginal utility is the change in utility from a small increase in one good’s consumption, holding the other good fixed.

What does the marginal rate of substitution measure?

The marginal rate of substitution is $\mathrm{MRS}_{xy}=\frac{MU_x}{MU_y}$. It describes how much $y$ the consumer will give up for a small increase in $x$ while remaining equally satisfied.

What condition characterizes an interior consumer optimum?

The consumer chooses the highest-utility bundle among those satisfying the budget constraint. At an interior optimum, the indifference curve is tangent to the budget line, so $\mathrm{MRS}_{xy}=\frac{p_x}{p_y}$.

What must be equal across goods at an interior optimum?

At an interior optimum, $\frac{MU_x}{p_x}=\frac{MU_y}{p_y}$: the last dollar spent on either good yields the same marginal utility.