Question

Beth’s Lawn Mowing Service acts as a monopoly.  The prevailing market price equation is given by P = 20 - 0.2q where q represents one acre of lawn. Cost equations are as follows: 

Total Cost = 0.1q² + 10q + 50

Marginal Cost = 0.2q + 10

a)      How many acres should Beth choose to mow in order to maximize profits?
b)      Calculate Beth’s maximum weekly profits/losses.

Answer 1

(a)

Profit is maximized when MR = MC.

TR = P x q = 20q - 0.2q²

MR = dTR/dq = 20 - 0.4q

20 - 0.4q = 0.2q + 10

0.6q = 10

q = 16.67

(b)

P = 20 - (0.2 x 16.67) = 20 - 3.33 = 16.67

TR = 16.67 x 16.67 = 277.89

TC = 0.1 x 16.67 x 16.67 + 10 x 16.67 + 50 = 27.79 + 166.7 + 50 = 244.49

Profit = TR - TC = 277.89 - 244.49 = 33.4