Mary Magnolia wants to open a flower shop, the Petal Pusher, in a new mall. She has her choice of three different floor sizes, 200 square feet, 500 square feet, or 1,000 square feet. The monthly rent will be $1 a square foot. Mary estimates that if she has F square feet of floor space and sells y bouquets a month, her variable costs will be
cv(y) = y³/4F per month.
(a) If she has 200 square feet of floor space, write down her marginal cost function and her average cost function. At what amount of output is average cost minimized? At this level of output, how much is average cost?
(b) If she has 500 square feet, write down her marginal cost function and her average cost function. At what amount of output is average cost minimized? At this level of output, how much is average cost?
(c) If she has 1,000 square feet of floor space, write down her marginal cost function and her average cost function. At what amount of output is average cost minimized? At this level of output, how much is average cost?
(d) Show Mary’s average cost curve and her marginal cost curves if she has 200 square feet. Show her average cost curve and her marginal cost curve if she has 500 square feet. Show her average cost curve and her marginal cost curve if she has 1,000 square feet. Label the average cost curves AC and the marginal cost curves MC.
(e) Show Mary’s long-run average cost curve and her long-run marginal cost curve in your graph. Label them LRAC and LRMC.