Please help!

Suppose that Peppa Pig has the following utility function: u(x, y) = x + 2 ln y. The two goods' prices are respectively px = 1 and py = p. Good y must be nonnegative: y 0. Peppa's income is I > 0. Suppose that x R. That is, x can take any value on the real line.

(a) Find Peppa's optimal bundle (x , y ). Please justify and briefly explain your solution approach. Show your work.

(b) From your answer to part (a), how does y depend on her income? Suppose that Peppa now earns one more dollar, that is, her income is I + 1. How does this affect her utility?

(c) Suppose that now there is a non-negativity constraint on x, that is, x 0. How does Peppa's Marshallian demand change? When is the new non-negativity constraint on good x irrelevant? Show your work and explain briefly.