Question

I will not be graded on this question if you could please show your work! thanks

4. Mary Magnolia wants to open a flower shop. She has to choose between 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 k square feet of floor space and sells y bouquets a month, her variable costs will be cv(y) = y²/k per month. (a) If she has 200 square feet of floor space, what is her marginal cost? and her average cost function? (b) If she has 200 square feet of floor space, at what amount of output is average cost minimized? At this level of output, how much is the average cost? (c) If she has 500 square feet of floor space, what is her marginal cost? and her average cost function? (d) If she has 500 square feet of floor space, at what amount of output is average cost minimized? At this level of output, how much is the average cost? 3 (e) If she has 1000 square feet of floor space, what is her marginal cost? and her average cost function? (1) If she has 1000 square feet of floor space, at what amount of output is average cost minimized? At this level of output, how much is the average cost?

Answer 1

Solution.

Following is the solution of the question with explanation of first two parts. All other parts can be solved in similar manner by substituting the values in the formulas given in the explanation and final answer.

Second Order condition 22 (AC) > 0 [This implies that AC is minimised ay at this level of output 400 >o [: output will always remain yo positive Average Cost (AC) at y = AC = y + 200 y $2 200 200 AC =

With the help of above explanation, the other 4 parts can be solved by substituting the values of k i.e floor area. Follwoing is the final answer for each part.

	Case I              (Part a and b)	Case II                  (Part c and d)	Case III (Part e and f)
Mary's flower shop	(200 sq. feet)	(500 sq. feet)	(1000 sq. feet)
Variable Cost function	y2/200	y2/500	y2/1000
FIxed Cost	$200	$500	$1000
Total cost function	y2/200 + 200	y2/500 + 500	y2/1000 + 1000
Marginal Cost function	y/100	y/250	y/500
Average Cost Function	y/200 + 200/y	y/500 + 500/y	y/1000 + 1000/y
Output at minimised Average cost	200 units	500 units	1000 units
Minimum Average cost	$ 2	$ 2	$ 2