Consider the owners of Cutitforme, a small lawnmowing service. They can use one of two methods to mow lawns. Method 1 is to purchase a tractor that costs $200 a year to own and then spend $1 (for labor and gas) for every acre of grass cut. Method 2 is to spend $40 on a used push mower that will last one year and then spend $5 (for labor) for every acre of grass cut a) The total cost functions for the two methods can be written as: Method 1: C = 200+q Method 2: C= 40 + 5q where q represent the number of acres of grass cut per year. Briefly explain why this is correct. b) Write down the average total cost function and find the marginal cost for each of the two methods. Explain. c) Assume that the tractor and the push mower have no resale value at the end of the year. i) If the firm expects q = 20, which method should the firm use? Show work. ii) If the firm expects q = 60, which method should the firm use? Show work. iii) What is the smallest number of acres of grass cut per year for which the owners should buy the tractor? Show work. d) What is the minimum efficient scale (MES) if the firm purchases the tractor? Explain your answer. What does this imply for how many acres of grass the Cutitforme company would like to cut if it could charge $6 per acre to all of it customers? Solution (a) A cost function is a mathematical expression which shows the relationship between output level and total cost. It consists fixed cost and variable cost. We have the following cost functions of the two method: Method 1: C = 200+q Method 2: C= 40 + 5q Now, lets see how these twop functions are correct. Method 1: C represents total cost that will incurred by employing method 1 for a year. 200 is fixed cost because it occurs whether the owners of Cutitforme use the tractor or not but purchase it. And 1q represents variable cost because if the owners of Cutitforme mow 1 acre of land they will incurr 1(1) = $1 cost of labor and gas, Similarly if 2 acre gets mowed, 1(2) = $2 will be the cost of labor and gas and so on. Method 2: Again C represents total cost that will incurred by employing method 2 for a year. $40 is fixed cost because it occurs whether the owners of Cutitforme use the push mower or not but purchase it. And 5q represents variable cost because if the owners of Cutitforme mow 1 acre of land they will incurr 5(1) = $5 cost of labor and gas, Similarly if 2 acre gets mowed, 5(2) = $10 will be the cost of labor and gas and so on. (b) We have the following Total cost functions of the two method: Method 1: C = 200+q Method 2: C= 40 + 5q Average Cost (AC) is the unit cost that incurred. And marginal cost(MC) is the additional cost that incurred with an additional output. Here output means acres of mand that get mowed. Hence, AC of method 1: Total Cost / output level = 200+q / q = 200/q + 1 which means per unit cost. AC of method 2 : 40+5q / q = 40/q + 5 which means per unit cost. And MC of method 1 = dTC/dq = d(200+q) / dq = 1 Which means if one more acre lan.

1. Consider the owners of Cutitforme, a small lawnmowing service. They can use one of two
methods to mow
lawns. Method 1 is to purchase a tractor that costs $200 a year to own and then spend $1 (for
labor and gas)
for every acre of grass cut. Method 2 is to spend $40 on a used push mower that will last one
year and then
spend $5 (for labor) for every acre of grass cut
a) The total cost functions for the two methods can be written as:
Method 1: C = 200+q
Method 2: C= 40 + 5q
where q represent the number of acres of grass cut per year. Briefly explain why this is correct.
b) Write down the average total cost function and find the marginal cost for each of the two
methods.
Explain.
c) Assume that the tractor and the push mower have no resale value at the end of the year.
i) If the firm expects q = 20, which method should the firm use? Show work.
ii) If the firm expects q = 60, which method should the firm use? Show work.
iii) What is the smallest number of acres of grass cut per year for which the owners should buy
the
tractor? Show work.
d) What is the minimum efficient scale (MES) if the firm purchases the tractor? Explain your
answer. What
does this imply for how many acres of grass the Cutitforme company would like to cut if it could
charge $6
per acre to all of it customers?
Solution
(a) A cost function is a mathematical expression which shows the relationship between output
level and total cost. It consists fixed cost and variable cost. We have the following cost functions
of the two method:
Method 1: C = 200+q
Method 2: C= 40 + 5q
Now, lets see how these twop functions are correct.
Method 1: C represents total cost that will incurred by employing method 1 for a year. 200 is

2. fixed cost because it occurs whether the owners of Cutitforme use the tractor or not but purchase
it. And 1q represents variable cost because if the owners of Cutitforme mow 1 acre of land they
will incurr 1(1) = $1 cost of labor and gas, Similarly if 2 acre gets mowed, 1(2) = $2 will be the
cost of labor and gas and so on.
Method 2: Again C represents total cost that will incurred by employing method 2 for a year. $40
is fixed cost because it occurs whether the owners of Cutitforme use the push mower or not but
purchase it. And 5q represents variable cost because if the owners of Cutitforme mow 1 acre of
land they will incurr 5(1) = $5 cost of labor and gas, Similarly if 2 acre gets mowed, 5(2) = $10
will be the cost of labor and gas and so on.
(b) We have the following Total cost functions of the two method:
Method 1: C = 200+q
Method 2: C= 40 + 5q
Average Cost (AC) is the unit cost that incurred. And marginal cost(MC) is the additional cost
that incurred with an additional output. Here output means acres of mand that get mowed.
Hence, AC of method 1: Total Cost / output level = 200+q / q = 200/q + 1 which means per unit
cost.
AC of method 2 : 40+5q / q = 40/q + 5 which means per unit cost.
And MC of method 1 = dTC/dq = d(200+q) / dq = 1 Which means if one more acre land get
mowed additional cost will be $1.
MC of method 2: dTC/dq = d(40+5q) / dq = 5 Which means if one more acre land get mowed
additional cost will be $5.
(c) i) If the firm expects q = 20,
TC of method 1 = 200 + (20) = $220 and
TC of method 2 = 40 + 5(20) = $140.
TC of method 2 is less hence method 2 sould be employed.
ii) If the firm expects q = 60,
TC of method 1 = 200 + (60) = $260 and
TC of method 2 = 40 + 5(60) = $340.
TC of method 1 is less hence method 1 sould be employed.
iii) When q = 40.
TC of method 1 = 200 + (40) = $240 and
TC of method 2 = 40 + 5(40) = $240.
Total costs incurred same with both the method. Hence more than 20 acre land mowed will get
TC of method 2 more for which the firm will use tractor. Thus the smallest number of acres of
grass cut per year for which the owners should buy thetractor is 21 acres land.
(d) The minimum efficient scale is defined as the lowest production point at which total average

3. costs (ATC) are minimized.
The minimum efficient scale can be computed by equating average cost (AC) with marginal cost
(MC).
200/q + 1 = 1
q = 0
the minimum efficient scale (MES), if the firm purchases the tractor, is 0 ascre land which means
the tractor will not be used in long run as MES occurs in long run.