Calculate the price and output if the supply continues

Question

Problem

Powerbank Co. has established a business to supply large-capacity battery to EV manufacturers. It demand and supply functions are

P^d = 20 - 0.05 Q^d
P^s = 5 + 0.05 Q^s

1. Calculate the profit-maximising price and output if PowerBank enjoys an effective monopoly in the market.

2. Calculate the price and output if the competition makes the market become perfectly competitive.

3. Calculate the price and output if the supply continues to be competitive but Tesla becomes the only buyer of large-capacity car batteries in the market.

4. Calculate the price and output if Powerbank regains all market share and Tesla continues to be the single buyer of large-capacity car batteries.