Duffy derives utility from only two goods: milk and cookies. He only consumes milk and cookies in fixed proportions: he likes to have 4 cookies with each glass of milk. Duffy has income of $270, the price of milk is $1 per glass, and the price of a cookie is $2.
a. Determine and graph Duffy’s budget constraint (put milk on the horizontal axis).
b. Write a utility function consistent with Duffy’s preferences for milk and cookies.
c. Graph an indifference curve of Duffy’s. Plot and label particular points on the indifference curve. Be sure to label your diagram completely.
d. What quantities of milk and cookies will maximize Duffy’s utility given his budget constraint. Explain how you know this is the optimal solution.