1 Budget Constraints Free Online FlashCards

What does a budget constraint describe?

A budget constraint describes the combinations of goods a consumer can afford; it does not determine which affordable bundle the consumer prefers.

What bundles belong to the budget set?

The budget set is all nonnegative bundles whose total cost does not exceed income: $B=\{(x,y):x\geq0,\ y\geq0,\ p_xx+p_yy\leq I\}$.

What does the budget line represent?

The budget line is the boundary of the budget set: $p_xx+p_yy=I$. Bundles on it use all available income.

Which bundles are affordable relative to the budget line?

Bundles on or below the budget line are affordable; bundles beyond it cost more than the consumer can spend.

When can a consumer choose a bundle inside the budget line?

If unspent income can be saved freely, bundles strictly inside the budget set are also possible.

How can the two-good budget line be written in terms of $y$?

Solving the budget-line equation for $y$ gives $y=\frac{I}{p_y}-\frac{p_x}{p_y}x$.

What does the vertical intercept $\frac{I}{p_y}$ mean?

The vertical intercept is $\frac{I}{p_y}$, the maximum quantity of good $y$ affordable when the consumer buys no $x$.

What trade-off does the budget-line slope show?

The slope is $-\frac{p_x}{p_y}$. Its magnitude gives the units of $y$ that must be given up to afford one more unit of $x$.

In the coffee-and-sandwich example, what is the trade-off for one more coffee?

With income $\$20$, coffee at $\$4$ per cup, and sandwiches at $\$2$ each, the budget line is $y=10-2x$. One extra coffee requires giving up two sandwiches.

How does a change in income affect the budget line when prices stay fixed?

With prices unchanged, higher income shifts the budget line outward in parallel and raises both intercepts proportionally; lower income shifts it inward.

What happens when the price of one good changes, with income and other prices fixed?

Changing one good’s price pivots the line: that good’s intercept changes while the other intercept stays fixed. A higher price lowers its maximum affordable quantity.

What happens to the budget set when all prices and income change by the same proportion?

If all prices and income change by the same proportion, the budget set remains unchanged because every bundle has the same affordability as before.