Peter sells pigeon pies from a pushcart in High Park. He is the only supplier. His costs are zero due to abundance of raw materials available in the park.

a) If the inverse demand for pigeon pies is p(y) = 100 y, write an expression for his marginal revenue.

b) Calculate the level of output that maximizes Peter's profits. What will be the price per pie?

c) Imagine the demand shifts to p(y) = 75 (y/2). Write an expression for his new marginal revenue.

d) Calculate the new level of output that maximizes Peter's profits. What will be the new price per pie?