Question

shutdown point and break even point can be equal in some situations

Answer 1

True

The shutdown point is at the minimum of average variable cost, while the break even point is at the minimum of average total cost. Since the AVC is below the ATC, the quantity level at shut down point is less than the quantity level at break even point, since MC (marginal cost) curve is upward sloping. However, if there are no fixed cost, ie if FC=0, then we would have TC=VC, ie ATC=AVC. In that case, both points coincide with each other, as both curve would have a common minimum point, and we would have quantity level for shutdown point and breakeven point be the same or equal.

But, if FC is not zero, and since MC has positive slope but is never veritcal at least in the short run, there is no way both points are equal.