3.Consider a coffee shop that has two types of customers: lawyers and doctors. The demand for espresso by lawyers is given by QL= 18 –3P, where P Is measured in dollars and Q Is measured in ounces. The demand for espresso by doctors is given by QD= 10 –2P. There are equal numbers of lawyers and doctors. The marginal cost of an ounce of espresso is $2. (a)Suppose that the coffee shop can identify which customer is a doctor and which is a lawyer. The shop will offer each type of customer a specific size cup of espresso for some total price. How many ounces of espresso will lawyers be offered, and at what total price? How many ounces of espresso will doctors be offered, and at what total price? (HINT: you should find that lawyers are offered a 12 ounce drink for $48, and doctors are offered a 6 ounce drink for $21. Lawyers and doctors are both tired and rich!) (b)Suppose that the shop owner can no longer distinguish the lawyers from the doctors (e.g., the doctors don’t put on their white coats before getting their espresso).Suppose the shop still offers the two options you found in part (a). That is, each customer has the option of paying $21 for 6 ounces or $48 for 12 ounces. How will the customers respond? (c)Keeping the drink sizes the same (6 ounces and 12 ounces), how should the coffee shop owner change the total prices of the two drinks so that lawyers will buy the lawyer option and doctors will buy the doctors option, and profits are maximized? (d)Describe qualitatively how the coffee shop owners should change the drink sizes (and then the prices) to increase profits even further, while still ensuring that lawyers will buy the lawyer option and doctors will buy the doctors option. (e)Suppose that the coffee shop owner could only charge a single, uniform two-part tariff to all customers. That is, both lawyers and doctors pay the same cover charge Cand per-ounce price p. Describe qualitatively what C and p should be if the shop owner maximizes profits. Can you put upper and / or lower bounds on Cand/or p?