What happens when both supply and demand rise equally?

There is two types of increase for supply.

1) Movement along the demand curve (upwards or downwards) which is subjected to the shifting of the demand curve

2) Shift of the supply curve.

For the first case, the supply curve does not shift but there is increased production to meet the new market demand. Supply will increase as there is a upward movement along the supply curve, and until the new market equilibrium is achieved.

For the second case, Supply shifts right and hence the upward movement along the demand curve.