Problem 4 A well-known restaurant, Casa Chuchi, works with two types of customers: 1000 people are of type 1, who always pay with credit card (American Excess) and 2000 individuals are of type 2, and they always pay cash. The respective individual demand functions are 1 g1 = 10 o, d. q: = 1_Pz We will assume that the unit cost of "producing\" (prepare and serve food) of Casa Chuchi is constant and equal to , where = 10. a) Calculate and compare (monopoly) prices that the restaurant will charge if Casa Chuchi can differentiate between the two types of consumers. That is, if they can set different prices for each type of customer (depending on who pays cash or by card). Get prices, quantities and profits. b) Suppose now that Casa Chuchi cannot charge different prices depending on the type of payment (cash or card). That is, if prices are the same for all customers, what would be the (linear price) solution that maximizes the profits of Casa Chuchi? Get prices, quantities and profits. c) What if they could charge non-linear prices, but one single tariff? Compute Casa Chuchi's profits in all scenarios and discuss. d) In the real context of restaurants, would it make sense to set non-linear prices in this or in other cases? What about discrimination strategies in general