4 Utility Maximization Online Quiz Questions

If preferences are locally nonsatiated, an optimal affordable bundle uses the full budget.

The budget line contains every bundle the consumer can afford, including bundles strictly inside the budget.

What is the name for the collection of all bundles that satisfy $p_xx+p_yy\le m$?

A consumer faces prices $p_x=3$ and $p_y=2$. What is the slope of the budget line when $x$ is on the horizontal axis and $y$ is on the vertical axis?

For differentiable preferences, satisfying the tangency condition by itself guarantees that a bundle is a utility maximum.

Select all statements that correctly describe the smooth tangency condition for an interior solution.

For $U(x,y)=\sqrt{xy}$, income $m=12$, and prices $p_x=2$ and $p_y=1$, the interior tangency condition implies $y=2x$. What is the optimal quantity $y^*$?

With utility $U(x,y)=3x+y$, income $m=12$, and prices $p_x=2$, $p_y=1$, which bundle maximizes utility?

When applying a practical method to identify a utility-maximizing bundle, select all steps that can be necessary.

For $U(x,y)=\sqrt{xy}$, income $m=20$, and prices $p_x=4$ and $p_y=1$, find the smooth interior optimum. Show how the tangency condition and budget constraint determine $(x^*,y^*)$.

A consumer has income $m=18$ and faces price $p_x=3$. If all income is spent on good $x$, what is the quantity at the budget line’s $x$-intercept?

For perfect substitutes, if the goods provide equal utility per dollar, what can be said about bundles on the budget line?

A consumer has utility $U(x,y)=2x+y$, income $m=10$, and prices $p_x=2$ and $p_y=1$. Which listed bundle solves the consumer’s utility-maximization problem?

A consumer’s preferences have the property that, near any bundle, there is a bundle the consumer prefers. What preference property implies that an optimum uses the full budget?

A consumer’s budget line is based on prices $p_x=3$ and $p_y=2$. What is its slope when $x$ is on the horizontal axis and $y$ is on the vertical axis?

For $U(x,y)=\sqrt{xy}$, the marginal rate of substitution is $\text{MRS}_{xy}=y/x$. What is $\text{MRS}_{xy}$ at $(x,y)=(2,8)$? Enter the numerical ratio.

At a consumer’s current bundle, $MU_x=12$, $p_x=4$, $MU_y=10$, and $p_y=2$. If the consumer can reallocate a small amount of spending, which change can increase utility?

A consumer's income doubles while the prices of goods $x$ and $y$ remain fixed. Describe in one concise phrase how the budget line changes.