State Officials Are Establishing a Deposit/refund System for Batteries $\quad$

State officials are establishing a deposit/refund system for batteries. Marginal costs and benefits have been estimated to be:
MPC = 5 + 0.5Q $\quad$$\quad$ MPB = MSB = 20 - 0.5Q
MSC = 5 + 0.7Q,
where Q is in millions, and the marginal cost and benefit values are in dollars per battery.
a. Determine the deposit/refund amount that achieves an efficient solution.
b. Explain the economics of why the refund might be set higher than the deposit.