Question

Roger and Zoë spend their vacation time at a nice cottage that they own in the countryside. Farmer Torti lives next door and normally lets his twelve sheep graze in his field. The sheep eat so quickly that it causes them to burp loudly, a very disruptive sound for Roger and Zoë vacationing next door. Torti is willing to remove sheep from the field when Roger and Zoë are there, but his marginal cost of doing so is $1 for the first sheep he removes, $2 for the second sheep, $3 for the third, etc. Roger and Zoë derive a (combined) marginal benefit of $12 for the first sheep Torti removes, $11 for the second sheep he removes, $10 for the third sheep he removes, etc.

a. Calculate the efficient number of sheep in the field if Roger and Zoë stay at the cottage.

b. Calculate the maximum amount Roger and Zoë would be willing to pay Torti to reduce his sheep to the efficient number.

c. Calculate the minimum amount Torti would be willing to accept to reduce his sheep to the efficient number

d. Calculate the range of prices per sheep that Roger and Zoë could pay Torti to achieve the efficient number.

A sound barrier built between the two properties could block 50 percent of the burping sound.

e. Calculate the efficient number of sheep in the field if there were a sound barrier and if Roger and Zoë stay at the cottage.

f. Calculate the total benefit to Roger and Zoë if the sound barrier were there and the corresponding efficient number of sheep were in the field.

g. Calculate the total cost to Torti if the sound barrier were there and the corresponding efficient number of sheep were in the field.

h. Calculate the maximum amount Roger and Zoë would be willing to contribute to the construction of the sound barrier.

i. Calculate the maximum amount Torti would be willing to contribute to the construction of the sound barrier.

Answer 1

a). Calculate the efficient number of sheep in the field if Roger and Zoë stay at the cottage.

The efficient number of sheep is obtained by following the economic decision rule of equating the marginal benefit to the marginal cost (MC = MB).

6 sheep need to be removed from the field, as the marginal cost of removing the 7th sheep is greater than its marginal cost.

Out of his 12 sheep Torti needs to remove 6 sheep and let the other 6 sheep graze in the field

b).Calculate the maximum amount Roger and Zoë would be willing to pay Torti to reduce his sheep to the efficient number.

For removing 6 sheep, the maximum amount that Roger and Zoë would be willing to pay would be equal to total benefit. Total Benefit = Sum of Marginal Benefits.

The maximum amount that Roger and Zoë would be willing to pay is $57

c. Calculate the minimum amount of money Torti would be willing to accept to reduce his sheep to the efficient number.

The minimum amount of money Torti would be willing to accept to reduce his sheep to 6 is equal to his total cost.

Total Cost = Sum of Marginal Cost

The minimum amount Torti would be willing to accept is $21.

d). Calculate the range of prices per sheep that Roger and Zoë could pay Torti to achieve the efficient number.

The mimimum that Roger and Zoë can pay is $21 or $3.5 per sheep, the maximum they can pay is $57 or $9.5 per sheep

$21/6 = $3.5

$57/6 = $9.5

The range of prices per sheep is $3.5 - $9.5