Worksheet 3 Answers
Production
Total Production (TP, Q) , Marginal Production (MP), Average Production (AP)
TP is an increasing function
Marginal production is a decreasing function. Law of diminishing marginal returns.
MP = ∆TP/ ∆L , AP = TP/ L
Costs
Costs (TC = VC + FC)
FC is variable in the long run, in the long run TC=VC.
FC=TC when Q=0.
TC, Marginal Cost (MC) and Average cost (AC)
MC = ∆TC/ ∆Q, AC = TC/ Q
AVC=VC/Q, AFC=FC/Q. ATC=AVC+AFC.
Problem 1
A firm’s cost curves are given by the following table
Q
TC
TFC
0
$100
$100
1
130
100
2
150
100
3
160
100
4
172
100
5
185
100
6
210
100
7
240
100
8
280
100
TVC
AVC
1
ATC
MC
9
330
100
230
10
390
100
290
a. Complete the table
b. Graph AVC, ATC, and MC on the same graph. What is the relationship between AVC and MC
curves, what is the relationship between ATC and MC curves?
1- See the table
Q
TC
TFC
TVC
AVC
ATC
MC
0
$100
$100
0
-
-
-
1
130
100
30
30
130
30
2
150
100
50
25
75
20
3
160
100
60
20
53.33333 10
4
172
100
72
18
43
12
5
185
100
85
17
37
13
6
210
100
110
18.33333 35
25
7
240
100
140
20
34.28571 30
8
280
100
180
22.5
35
9
330
100
230
25.55556 36.66667 50
10
390
100
290
29
39
40
60
2- See the graph. When MC is below AVC, AVC is declining and when MC is above
AVC, AVC is rising. Rising MC intersects AVC at the minimum point of AVC.
Similar relation appears between MC and ATC
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Relationship MC and AC:

When MC<ATC then ATC decreases.

When MC= ATC, ATC is minimum

When MC>ATC, ATC increases
Same relationship holds between MC and AVC

When MC<AVC then AVC decreases.

When MC= AVC, AVC is minimum

When MC>AVC, AVC increases
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Problem 2
1- What is the average fixed cost of producing two units of output?
2- What is the value of TVC and AVC at output level of 3
3- What is MC at output level of 3
1- From the graph above the TC curve starts at 500 thus $500 is the TFC  AFC at
two units of output is 500/2 = $250
2- Total variable costs are 500 from the graph, and average variable cost are 500/3
3- MC = change in TC/ change in Q = 1000-850 / 3-2 = 150/1 = 150
Or MC at output 3 is (TVC at 3 – TVC at 2) / (3-2). At output 2 TC = 850 
TVC = TC – TFC = 850 – 500 = 350 and TVC at output 3 is 500  MC at output
3 is (500 – 350)/1 = 150
Problem 3
Nehmie is a financial consultant who works at a consultant office in Beirut where he used to
get an annual salary of $50,000. Due to economic instability in the country, Nehmie decided
to quit his job and move to Dubai to start a new business on his own. He planned to open a
restaurant serving Lebanese cuisine. Nehmie has to pay a sum of $25000 per year for rent,
electricity, phones, water, and other services. Nehmie hires two Lebanese cookers
(Mohammad and Barakat) where they will get an annual salary of $15,000 each. He also
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hired seven waiters for which he will be paying an annual salary of $10,000 each. Nehmie
also has to pay an annual sum of $35,000 for food ingredients....
Assuming that Nehmie receives 5000 customers where each customer orders one meal for
$35.
1- Calculate Nehmie’s Accounting profit?
2- Calculate Nehmie’s economic profit?
3- Should Nehmie invest in his new business or not? Explain
1- Accounting profit = TR – TC where TC are explicit costs only
Explicit costs = 25000 + 15000*2 + 10000*7 + 35000 = $160,000
TR = 5000*35 = $175,000
Accounting profit is 175000 – 160000 = 15000
2- Economic profit is TR – TC where TC = Explicit cost + implicit cost and
Implicit cost is 50000  TC = 160000 + 50000 = $210,000
Economic profit is 175000 – 210000 = - 35000
3- Nehmie should not invest in this business since his economic profit is
negative.
Problem 4
Coffee King Starbucks Raises Its Prices
Starbucks is raising its prices because the wholesale price of milk has risen 70 percent
and there’s a lot of milk in Starbucks lattes.
Source: USA Today, July 24, 2007
Is milk a fixed factor of production or a variable factor of production? Describe how
the increase in the price of milk changes Starbucks’ short-run cost curves.
Milk is a variable factor of production. The increase in the price of milk shifts
Starbucks’ short-run AVC, ATC, MC, TC, and TVC curves upward.
Problem 5
Bill’s Bakery has a fire and Bill loses some of his cost data. The bits of paper that he
recovers after the fire provide the information in the following table (all the cost
numbers are dollars).Bill asks you to come to his rescue and provide the missing data
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in the five spaces identified as A, B, C, D, and E.
𝐹𝐶
𝐴𝐹𝐶 = 𝑇𝑃
𝑄
. FC=120*10= 1200
𝐴: AFC=FC/TP= 1200/20 = 60
130 =
40𝐷 − 3900
10
40D-3900=1300 , 40D=1300+3900=5200, D=5200/40= 130
E=6600-5200/10 = 140
TP
AFC
AVC
ATC
10
120
100
220
MC
TC
2200
80
20
A=60 B=90
150
3000
90
30
40
90
130
3900
130
40
30
C=100 D=130
5200
E=140
50
24
108
132
6600
130= 40D-(130)(30)/ 40-30
Then 130 =
40𝐷−3900
10
40 D -3900 = 1300
40D=1300+3900
40D=5200
D=5200/40 = 130
ATC = 130 AFC = 30 , AVC = 130 – 30 = 100
E = 132*50 – 130*40 / 10
E = 140
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A is the average fixed cost, AFC, when the output is 20. Average fixed cost equals total fixed
cost divided by output, or AFC = TFC ÷ Q. Rearranging gives TFC = AFC × Q. So the total
fixed cost for the problem equals $120 × 10, which is $1,200. A equals $1,200, TFC, divided
by 20, Q, which is $60.
B is the average variable cost, AVC, when output is 20. Use the result that AFC + AVC =
ATC by rearranging to give AVC = ATC  AFC, so average variable cost equals $150  $60,
which is $90.
D is the average total cost, ATC, when output, Q, equals 40. Average total cost equals total
cost divided by output, or ATC = TC ÷ Q. Rearranging gives TC = ATC × Q. So the total
cost when 30 units are produced is $130 × 30, which is $3,900. Marginal cost, MC, equals
the change in total cost divided by the change in quantity, or MC = TC ÷ Q. Rearranging
gives TC = MC × Q, so the change in total cost between Q = 30 and Q = 40 is $130 × 10,
or $1,300. Therefore the total cost when Q equals 40 is $3,900 + $1,300, or $5,200. The
average total cost when Q is 40 is $5,200 ÷ 40, or $130.
C is the average variable cost, AVC, when output, Q, equals 40. Use the result that AFC +
AVC = ATC by rearranging to give AVC = ATC  AFC. As a result, average variable cost
equals $130  $30, or $100.
E is the marginal cost, MC, when output increases from 40 units to 50 units. Marginal cost,
MC, equals the change in total cost divided by the change in quantity, or MC = TC ÷ Q.
To calculate marginal cost, the total cost when output is 40 and the total cost when output is
50 are needed. Average total cost equals total cost divided by output, or ATC = TC ÷ Q.
Rearranging gives TC = ATC × Q. So the total cost when 40 units are produced is $130 × 40,
which is $5,200 and total cost when 50 units are produced is $132 × 50, which is $6,600. So
the marginal cost equals ($6,600  $5,200) ÷ 10, which equals $140.
Problem 6
ABC checks its costs of Production. The below graph illustrates the cost functions and the
Total production function of the company.
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ABC pays its workers $ 20 per day. Assume that ABC pays $ 10 to rent a machine and $
10 to insure the merchandises against the risk of fire per day.
a- Compute the firm’s Total Fixed costs. Does the graph illustrate the short-run production
or the long-run production? Why? A
b- At which level of output is AVC at its minimum level ? At which level of output is ATC
at its minimum level ?
c- At Q = 25 units, compute Total Cost, TVC and AFC. Can you determine the number of
workers hired at 25 units produced? Q = 25, TC = 13*25 = 325
VC =TC-FC = 325-20 = 305 , AFC = FC/Q = 20 / 25 = 0.8 , AVC = VC/Q = 305/25 =
12.2
d- At Q=10 units, compute AFC. Whats happens to AFC as the quantity of output increases
from 10 to 25 units? What feature of the above graph illustrates it?
e- At what level of output does the law of diminishing marginal returns begin? Explain
a- TFC = Rent + Insurance = $ 10 + $ 10 = $ 20
Since we have fixed costs, then we are studying the short-run production
b- Q = 20 units ( Min AVC) MC intersects AVC from below
Q = 25 units ( Min ATC) MC intersects ATC from below
c- ATC = TC/Q  TC = ATC x Q  TC = 13 x 25 = $ 325
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TC = TFC + TVC  TVC = 325 – 20 = $ 305
AFC= TFC/Q= 20/25=$0.8
The number of workers hired= TVC/wage=305/20= 15 workers hired (approximately)
d- At Q=10 units, AFC= TFC/Q=20/10=$2
AFC falls as output rises (the decreasing gap between ATC and AVC illustrates it)
e- MP begins to fall at the same output level where MC begins to rise, at Q=10 units
Problem 7
PART A
Workers
Total Products
MP
(Bushels of corn)
0
0 bushels
-
1
10
10
2
25
15
3
32
7
4
37
5
1. What is the marginal product MPL of the second worker?
MPPL = Δ Output / Δ Workers = units of output = (25-10) / (2-1) = 15
2. At what point do diminishing returns start?
When MPL starts to decrease, with the 3rd worker.
3. Suppose FC = $50 when output is zero. What is the fixed cost when output is 10
units?
FC = $50
PART B
Fixed cost = 1200
Average variable cost = 4 , AVC= VC/ Q . VC = AVC*Q
1. Calculate total cost if 300 units are produced.
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TC = FC + VC = 1200 + 4*300 = 2400
2. Graph total cost as a function of Q ( Q=0, 300, & 600)
TC = 1200 + 4 Q
Q=0, TC = 1200 / at Q=300, TC = 2400 / At Q=600 , TC = 3600
3. Graph average cost as a function of Q ( Q=0, 300, & 600)
AC = TC/Q
at Q=0, no answer / at Q=300, AC =2400/300 = 8 . at Q=600
AC=3600/600= 6 / at Q=100, TC = 1600 then AC = 1600/100= 16
Problem 8
L
TP (Q)
MP
AP
0
0
-
-
1
100
A=100
B= 100
2
170
C= 70
D=85
3
E= 230
60
F= 76.66
4
G = 280
H= 280-230 = 50
70
a) Fill in the missing values in the table.
MP = ∆TP/∆L
AP = TP / L . TP= AP*L = 70*4 = 280
b) Explain the relationship between MP and TP and the relationship between MP and
AP.
TP and MP: TP is the accumulation of MP. We notice that MP is a decreasing
function as Labor increases, each additional unit of labor produces less than the
previous unit.
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MP and AP:
When MP>AP, AP increases
When MP=AP, AP is maximum and when MP<AP, AP decreases.
c) When does diminishing marginal returns start?
Diminishing marginal returns started at the second employee.
d) Is labor a variable or a fixed factor of production?
Labor is a variable factor of production. It is increasing in the table. Capital is the
fixed factor of production that cannot be changed in the short run, it can only be
changed in the long run.
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