3) Consider variable cost and marginal cost. Assume the VC curve is smooth and continuous. (Like normal)

a) Write AVC as a function of VC and Q.

b) Demonstrate, with calculus, that MC=AVC if AVC is at a minimum.

c) If MC=AVC, does that necessarily imply that AVC is at a local minimum?

d) Suppose a profit maximizing firm is producing at a quantity where AVC is at a unique minimum. If the firm faces a horizontal demand curve, is this firm earning positive profits?