Consider the following principal-agent problem. The principal is a monopoly coffee shop owner, and the agent is a custom

[answerhappygod]

Consider the following principal-agent problem. The principal is
a monopoly coffee shop owner, and the agent is a customer who is
equally likely (β= 0.5) to be a coffee addict (‘high’ type with θ𝐻
= 40) or a regular Joe (‘low’ type with θ𝐿= 20). Suppose
v(q)=2q0.5 represents the agents’ benefit function
from qounce of coffee. Also suppose the price of
coffee is p cents per ounce
(i.e., linear price), and marginal cost of producing
coffee is c = 5 cents per ounce.
a) If the barista can observe agents’ type (i.e., no adverse
selection), set-up the agents’ maximization problem and derive
their coffee demand functions q*H and
q*L as a function of price p.
(3𝐩𝐨𝐢𝐧𝐭𝐬)
b) Set-up the principal’s maximization problem and solve for the
optimal price p*. (4𝐩𝐨𝐢𝐧𝐭𝐬)
c) Calculate the values of q*H and
q*L and the principal’s expected profit at that
price (p*). (3𝐩𝐨𝐢𝐧𝐭𝐬)