a) Show mathematically that for any upward sloping SRMC, SRATC is strictly convex, crosses the SRMC curve at the lowest point on the SRATC curve, and the SRMC curve is rising at that point.
b) Show mathematically that for any U-shaped SRMC, SRAVC is strictly convex, SRAVC crosses the SRMC curve at the lowest point on the SRAVC curve, and the SRMC curve is rising at that point.
c) Why would a firm shut down at price below minimum SRATC rather than minimum SRAVC if its fixed costs of production were avoidable?