Paying for extracirricular activities

[mango]

We share 50/50 custody of my step-daughter and have no support order. In the order it states parents agree to pay for one-half of the childs school-related activites. The child decided to take up flute, (5th grade) and the mother went out and bought a $800 flute with no discussion to the father. Then she sends the receipt to the father and expects payments. He has 2 other kids and needs to live a little more frugile then one with one child would. He had access to 2 second-hand flutes and offered them instead, sicne she is a beginner. She refused, and said the child has been using the new one and prefers it. Does he have an obligation to pay on demand whatever she chooses to purchase without discussion?