Come up with an example of a utility function $($i$.$e$.,$ a mathematical expression$)$ that

accurately represents this preference relation.

$($b$)$ Draw the consumer$$s indifference curve for three different levels of utility. Place pep$-$

peroni $($p$)$ on the x$-$axis and anchovies $($a$)$ on the y$-$axis. Label the axes and the utility

levels.

$($c$)$ Do the indifference curves have a positive, zero, or negative slope? Explain.

$($d$)$ To which direction does the utility increase? Draw the arrows on the graph and explain

it in words.

$($e$)$ Draw the consumer$$s utility function as a function of pepperoni only, holding fixed the

amount of anchovies at three different levels. Make sure you label the axes and each

curve with the specific amount of anchovies consumed.

$($f$)$ Using your previous graph, can you tell if the marginal utility of pepperoni is increasing,

decreasing, or constant as the consumer eats more pepperoni? Can you tell if the marginal

utility of pepperoni is positive, negative, or zero as the consumer eats more pepperoni?

Explain.

$($g$)$ Draw the consumer$$s marginal utility function of pepperoni, holding fixed the amount of

anchovies at a certain level. Do not forget to label the axes. How does this graph relate

to the questions in part $($f$)?$ Explain.

$($h$)$ Now, draw the consumer$$s utility function as a function of anchovies only, holding fixed

the amount of pepperoni at three different levels. Make sure you label the axes and each

curve with the specific amount of pepperoni consumed.

$($i$)$ Using your previous graph, can you tell if the marginal utility of anchovies is increasing,

decreasing, or constant as the consumer eats more anchovies? Can you tell if the marginal

utility of anchovies is positive, negative, or zero as the consumer eats more anchovies?

Explain.

$($j$)$ Draw the consumer$$s marginal utility function of anchovies, holding fixed the amount of

pepperoni at a certain level. Do not forget to label the axes. How does this graph relate

to the questions in part $($i$)?$ Explain.

$($k$)$ Calculate the marginal rate of substitution function or MRS$.$ Does this consumer$$s pref$-$

erences exhibit a diminishing marginal rate of substitution of pepperoni for anchovies?

Explain.