The only way Sarah entertains herself is to go to the movies, where she always buys two bags of popcorn.

(a) Let M and P represent the quantities of movies and popcorn Sarah consumes, let pm and pc be their prices and let I be the amount that Sarah has budgeted for entertainment. What is Sarah’s utility function for entertainment?

(b) Find Sarah’s demand functions for movies and popcorn.

(c) If Sarah’s entertainment budget is $60 per month and pm=$10 and pc=$2.50, how many movies would Sarah go to each month on average and how many bags of popcorn would she buy?

(d) Suppose the price of popcorn went up to $5 per bag. What would Sarah’s consumption pattern be now? How much of the change in consumption of each good would you attribute to the substitution effect and how much to the income effect?

(e) Find Sarah’s compensated demand function for popcorn and draw her ordinary and compensated demand curves on the same graph.

(f) Starting with I=$60 per month and pm=$10 and pp=$2.50, find the compensating and equivalent variations of a change in the price of popcorn to $5.

Please answer (e) and (f).