Question 1: Nonlinear Pricing (6 points) Amy is the owner of an independent cinema. She is deciding on a pricing strategy for selling movie tickets. The following table shows the WTP for 3 representative customers (in dollars), for up to 4 cinema visits in a month. In your calculations, assume that the per-unit variable cost is zero. Number of movies watched per month 1st Movie 2nd Movie 3rd Movie 4th Movie Customer 1 18 12 WTP for each Customer Customer 2 20 11 10 7 Customer 3 13 12 10 9 8 5 a. If Amy were to charge one single price, what is the optimal price she should charge? (2 points) b. If Amy were to design a 2-block pricing, that is, charge P1 for each of the first 2 movies, followed by a lower price of P2 for each of the next 2 movies, what are the optimal P1 and P2, and the resultant profits? Assume that for each movie, customers will only purchase if the price is equal to or less than the WTP. (2 points) c. If Amy were to design a 4-block pricing, that is, charge P1 for the first movie, followed by a lower price of P2 for the second movie, followed by a lower price of P3 for the third movie, and finally a lower P4 for the fourth movie, what are the optimal P1, P2, P3 and P4, and the resultant profits? Assume that for each movie, customers will only purchase if the price is equal to or less than the WTP. (2 points)