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4 Utility Maximization Free Online FlashCards

Study 4 Utility Maximization with 12 free online flashcards. Review key terms, definitions, and concepts with this interactive flashcard deck.

12 cards

Front

What does utility maximization mean?

Back

It is choosing the most-preferred bundle among those the consumer can afford.

Front

What is the budget set?

Back

The budget set is every bundle satisfying $p_xx+p_yy\le m$ .

Front

What does the budget line represent?

Back

The budget line is the boundary $p_xx+p_yy=m$ , where the consumer spends all income.

Front

What are the budget line's intercepts and slope?

Back

The intercepts are $m/p_x$ on the $x$ -axis and $m/p_y$ on the $y$ -axis; the slope is $-p_x/p_y$ .

Front

When does a consumer use the full budget?

Back

With locally nonsatiated preferences, the optimum uses the full budget.

Front

What defines an interior solution?

Back

An interior solution has positive quantities of both goods: $x^*>0$ and $y^*>0$ .

Front

What tangency condition holds at a smooth interior optimum?

Back

At a smooth interior optimum, $\mathrm{MRS}_{xy}=\frac{MU_x}{MU_y}=\frac{p_x}{p_y}$ .

Front

How can the interior optimum condition be expressed per dollar?

Back

Marginal utility per dollar is equal across goods: $\frac{MU_x}{p_x}=\frac{MU_y}{p_y}$ .

Front

Does tangency alone guarantee a maximum?

Back

No. It identifies a candidate interior optimum, but preferences and feasibility must also be checked.

Front

For $U(x,y)=\sqrt{xy}$ , $m=12$ , $p_x=2$ , and $p_y=1$ , what is the optimum?

Back

The optimum is $(x^*,y^*)=(3,6)$ , satisfying $2(3)+6=12$ .

Front

What is a corner solution?

Back

A corner solution has zero units of at least one good, such as $x^*>0$ and $y^*=0$ .

Front

For $U(x,y)=3x+y$ , $m=12$ , $p_x=2$ , and $p_y=1$ , which bundle is optimal?

Back

The consumer spends all income on $x$ , choosing $(x^*,y^*)=(6,0)$ , because $x$ gives more utility per dollar.

4 Utility Maximization Free Online FlashCards

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