A new branch of "Elon Musk Dance School" just opened in your city. Nobody knows how good the dance instruction at the school is except its head. Hiring good dance instructors is expensive (and hiring bad ones is cheap). Assume that it is common knowledge that , the quality of the dance instruction, is drawn from a uniform distribution on [0, 1]. It costs the school a to pay the dance instructors for each pupil they take, where a (1/2, 1). The tuition p it charges must at least cover the pay of dance instructors. Assume the school has no other costs. A pupil's utility from enrolling at the school is p, where p is the price of tuition. If they do not enrol at the school, their utility is zero. Assume that it is competitive to get into the dance school, so a pupil's expected payoff will be zero in equilibrium.

(a) What is the equilibrium tuition p of Elon Musk Dance School? What will be the expected quality of the dance instruction there?

(b) Now, suppose Elon Musk Dance School posts a promotional video and shows off some of the moves its namesake has learned at the school. Thus, each potential pupil learns that the quality of dance instruction is at least > 0. What is the equilibrium tuition in this case?