A firm's production function is as the following: q = min{M, L1/2}. M is the number of machines, L is the amount of labor that it uses. The price of labor is $1, and the price of machines is $2 per unit.

1. Is it true that if average production cost is increasing, a firm's technology exhibits decreasing returns to scale? (If yes, show the proof. If not, show a counter example)
2. Is it true that if a firm's technology exhibits decreasing returns to scale, average production cost is increasing? (If yes, show the proof. If not, show a counter example)