Problem $3(30$ points$).$

Priya, a college student, has two options for meals: eating at the dining hall for $\backslash$$$6$ per meal, or eating a cup of Ramen soup for $\backslash (\backslash$$ $1\mathrm{.}50\backslash )$ per meal. Her weekly food budget is $\backslash$$$60.$

$1.$ Draw the budget constraint showing the trade$-$off between dining$-$hall meals and cups of soup. Assuming that Priya spends equal amounts on both goods, draw an indifference curve showing the optimum choice. Label the optimum as point A$.$

$2.$ Suppose the price of a cup of soup rises to $\backslash$$$2.$ Using your diagram from part $($a$),$ show the consequences of this change in price. Assume that Priya now spends only $30$ percent of her income on dining$-$hall meals. Label the new optimum as point $\backslash ($ B $\backslash ).$

$3.$ What happened to the quantity of soup consumed because of this price change? What does this result say about the income and substitution effects? Explain.

$4.$ Use points A and B to draw Priya's demand curve for cups of soup. What is this type of good called?