Theo's preferences for baseballs are given by the following utility and marginal utility functions.

TU = 402B - 20B²

MU = 402 - 40B

Set up a model (agent, environment, behavior, equilibrium) to derive (write the equation for) Theo's demand curve for baseballs. Show how you will find optimization in levels and differences. Plot Theo's inverse demand curve based on his optimization. If the price of a baseball is $2, how many baseballs will Theo optimally purchase?