Question

The town where Beth’s Lawn Mowing Service is located (see Problems 8.1 and 8.2) is subject to sporadic droughts and monsoons. During periods of drought, the price for mowing lawns drops to $15 per acre, whereas during monsoons, it rises to $25 per acre.
a. How will Beth react to these changing prices?
b. Suppose that weeks of drought and weeks of monsoons each occur half the time during a summer. What will Beth’s average weekly profit be?

c. Suppose Beth’s kindly (but still greedy) father offers to eliminate the uncertainty in Beth’s profits by agreeing to trade her the weekly profits

Answer 1

Answer: question not complete

c. Suppose Beth’s kindly (but still greedy) father offers to eliminate the uncertainty in Beth’s profits by agreeing to trade her the weekly profits based on a stable price of $20 per acre in exchange for the profits Beth actually makes. Should she take the deal?

d. Graph your results and explain them intuitively. Solution to this is in the picture attached

Explanation:

During the period of drought, the rate of mowing is $15 per acre, while, in the period of monsoons, the rate is $25 per acre.

a). Beth's supply function will be

q = 5P - 50

If P =15

q = 5 x 15 - 50

= 75-50

= 25

If P = 25

q = 5 x 25 - 50

= 125 - 50

= 75

b). The periods of both drought and monsoon will last for equal number of weeks in the summer. The average weekly profit will be:

If P = 15

π = P x q - C

= 15 x 25 - 362.5

= 375 - 362.5

= 12.5

If P =25

π = P x q - C

= 25 x 75 - 1362.5

= 1875 - 1362.5

= 512.5

The average weekly profit will be

=12.5 + 512.5 / 2

=525 / 2

= 262.5

c). Father offer a price of $20 irrespective of the season and the quantity will be:

q = 5 x 20 - 50

= 50

The profits in this case will be

π = P x q - C

= 20 x 50 - 800

= 200

This is less than the average profits in the other cases, hence, this offer will make her worse off.