Test 2 Essays – Sections 9 & 10
Section 9
2. Use the figure below of a linear demand curve to answer this set of questions.
a. Based on the above figure, fill in the following table:
Price Quantity Demanded Total Revenue
$0
1
2
3
4
5
6
7
8
9
10
11
b. At what price is total revenue maximized? (Hint: This may be a price that is not
included in your table.)
c. Suppose the price is initially $6, but it then decreases to $5. Calculate the
elasticity of demand between these two points on the demand curve using the
midpoint method.
d. Based on your calculations in part (c), describe the relationship between the
absolute value of the percentage change in the quantity demanded and the
absolute value of the percentage change in price moving from a price of $6 to a
price of $5.
5. When Mario’s income increases by 10%, his consumption of noodles decreases from
100 units a year to 70 units a year, while his consumption of salmon increases from 20
units a year to 60 units a year.
What is Mario’s income elasticity of demand for noodles?
What is Mario’s income elasticity of demand for salmon?
Is either of these goods income elastic for Mario?
Is either of these goods income inelastic for Mario?
From Mario’s perspective, is either of these goods a luxury good? Explain your
answer.
f. From Mario’s perspective, is either of these goods an inferior good? Explain your
answer.
a.
b.
c.
d.
e.
7. The following table expresses the amount people are willing to pay to buy a new
music-playing device. Use this information to answer this series of questions.
Name of person Price willing to pay
Joe
$100
Mary
200
Lucinda
150
Pete
50
Mario
300
a. If the market price is $175, who will buy the good and what is the value of total
consumer surplus?
b. Suppose the market price is $175, but a decision is made to allocate the two units
of the good that are demanded at that price to Mario and Lucinda. What is the
value of total consumer surplus in this case?
c. Why does the reallocation of the good in part (b) reduce the value of consumer
surplus? What are the implications of the reduction in consumer surplus that
occurs when the good is not allocated to those buyers who place the highest value
on it?
Section 10
3. The following table provides the short-run production function for Sherry’s Hair Salon.
Sherry uses only two inputs, labor and capital, to produce her output of stylish haircuts.
The price of labor is $20 an hour, and the price of capital is $50 per unit.
Quantity of capital (units)
10
10
10
10
10
10
Quantity of labor (hours
of work)
0
10
20
30
40
50
Quantity of haircuts
0
15
28
38
44
48
a. Complete the following table of Sherry’s costs, given the above information.
Round your calculations to one place past the decimal point.
Quantity
Of
capital
(units)
10
Quantity
of
Labor
(hours
Of work)
0
Quantity
Of
haircuts
0
FC VC AFC AVC ATC TC
($) ($) ($)
($)
($)
($)
---
---
---
MC
($ per
unit
Of
output)
500
13.3
10
10
15
10
20
28
10
30
38
10
40
44
10
50
48
b. Does this production function exhibit diminishing marginal returns to labor?
Explain your answer.
c. Graph the total cost function for Sherry’s Hair Salon. Measure total cost on the
vertical axis and the quantity of haircuts on the horizontal axis. Describe how
increasing the quantity of haircuts affects the slope of the total cost curve.
d. Graph the marginal cost function for Sherry’s Hair Salon using the midpoint
method. Measure marginal cost on the vertical axis and the quantity of haircuts
on the horizontal axis. Describe the slope of the MC curve, and then explain why
the MC is sloped this way.
e. In a new graph, draw Sherry’s Hair Salon AFC curve. Measure average fixed
cost on the vertical axis and the quantity of haircuts on the horizontal axis. In
your graph, indicate the area that corresponds to fixed cost if 15 haircuts are
currently being produced.
f. In a new graph, sketch Sherry’s Hair Salon ATC, AVC, AFC, and MC curves.
Measure cost per unit on the vertical axis and the quantity of haircuts on the
horizontal axis. What must be true about the relationship between the ATC and
MC curves?
5. The table below provides some information about Stella’s Delight, a business that
Stella owns. Stella uses labor and capital as her only inputs in the production of her
product.
a. Fill in the table below:
b.
Quantity Quantity of Quantity
Of labor
capital
Of
(units)
(units)
output
0
5
0
1
5
10
2
5
18
3
5
24
4
5
28
5
5
30
6
c.
d.
e.
f.
VC FC AVC AFC ATC TC
($) ($) ($)
($)
($) ($)
---
---
---
10
15
5
31
What is the price of the variable input?
What is the price of the fixed input?
What is the marginal product of the fifth unit of labor?
What is the marginal cost of producing the twenty-fourth unit of output?
MC
($ per
unit
Of
output)
7. The table below provides information about Sarah’s Doughnut Shoppe, a small firm
operating in a perfectly competitive industry. Use this information to answer the next set
of questions.
Quantity of doughnuts Total revenue Total cost
100
$200
$250
200
400
360
300
600
530
400
800
725
500
1,000
950
Profit
a. What is the market price for a doughnut?
b. Fill in the profit column of the table. At what level of output does Sarah’s
Doughnut Shoppe maximize its profits?
c. Calculate Sarah’s Doughnut Shoppe’s marginal cost and marginal revenue for
each level of output. Use the table below to organize your results.
Quantity of
Total
Total Marginal Marginal
Doughnuts Revenue Cost
Cost
Revenue
100
$200
$250
200
400
360
300
600
530
400
800
725
500
1,000
950
Profit
d. What is the relationship between marginal revenue and marginal cost at the profitmaximizing level of output for Sarah’s Doughnut Shoppe? Explain the meaning
of this relationship and how it relates to profitability.
Answers:
Test 2 Essays – Sections 9 & 10
Section 9
2. Use the figure below of a linear demand curve to answer this set of questions.
a. Based on the above figure, fill in the following table:
Price Quantity Demanded Total Revenue
$0
1
2
3
4
5
6
7
8
9
10
11
b. At what price is total revenue maximized? (Hint: This may be a price that is not
included in your table.)
c. Suppose the price is initially $6, but it then decreases to $5. Calculate the
elasticity of demand between these two points on the demand curve using the
midpoint method.
d. Based on your calculations in part (c), describe the relationship between the
absolute value of the percentage change in the quantity demanded and the
absolute value of the percentage change in price moving from a price of $6 to a
price of $5.
2. a.
Price Quantity Demanded Total Revenue
$0
11
$0
1
10
10
2
9
18
3
8
24
4
7
28
5
6
30
6
5
30
7
4
28
8
3
24
9
2
18
10
1
10
11
0
0
b. From the table, we can see that total revenue equals $30 when the price is $5 or
when the price is $6. At a price of $5.50-the midpoint of the demand curve-we find that
total revenue equals $30.25. For a linear demand curve, total revenue is maximized at
the mid-point of the demand curve.
(5-6)
(6+5)
c. Price elasticity of demand =
2 =1
(5-6)
(6+5)
2
d. When the price elasticity of demand equals one, the absolute value of the percentage
change in the quantity demanded equals the absolute value of the percentage change
in the price.
5. When Mario’s income increases by 10%, his consumption of noodles decreases from
100 units a year to 70 units a year, while his consumption of salmon increases from 20
units a year to 60 units a year.
a.
b.
c.
d.
What is Mario’s income elasticity of demand for noodles?
What is Mario’s income elasticity of demand for salmon?
Is either of these goods income elastic for Mario?
Is either of these goods income inelastic for Mario?
e. From Mario’s perspective, is either of these goods a luxury good? Explain your
answer.
f. From Mario’s perspective, is either of these goods an inferior good? Explain your
answer.
5. a. Income elasticity of demand for noodles = -30% = -3
10%
b. Income elasticity of demand for salmon = 200% = 20
10%
c. Salmon
d. Neither good is income inelastic because neither good has an income elasticity of
demand value that is positive but is less than one.
e. Salmon is a luxury good because the value of the income elasticity of demand for
salmon is greater than one. As Mario’s income increases, his demand for salmon
increases at an even faster rate.
f. Noodles are an inferior good because as Mario’s income increases his demand for
noodles decreases. A negative value for the income elasticity of demand indicates that
the good is an inferior good.
7. The following table expresses the amount people are willing to pay to buy a new
music-playing device. Use this information to answer this series of questions.
Name of person Price willing to pay
Joe
$100
Mary
200
Lucinda
150
Pete
50
Mario
300
a. If the market price is $175, who will buy the good and what is the value of total
consumer surplus?
b. Suppose the market price is $175, but a decision is made to allocate the two units
of the good that are demanded at that price to Mario and Lucinda. What is the
value of total consumer surplus in this case?
c. Why does the reallocation of the good in part (b) reduce the value of consumer
surplus? What are the implications of the reduction in consumer surplus that
occurs when the good is not allocated to those buyers who place the highest value
on it?
7. a. At a market price of $175, Mario and Mary will buy the good because they are the
only potential consumers who are willing to pay a price that is equal to or greater than
the market price. The value of consumer surplus is $150. (Mario receives consumer
surplus of $125, while Mary receives consumer surplus of $25.)
b. Mario has a consumer surplus of $300 - $175, or $125, while Lucinda’s consumer
surplus is equal to $150 - $175, or -$25. The total consumer surplus is therefore $100
when the two units are allocated to Mario and Lucinda.
c. Consumer surplus is reduced when the good is reallocated because the good goes to
consumers who place a lower value on the good. This type of reallocation, away from
the market’s allocation, results in a failure to maximize consumer surplus.
Section 10
3. The following table provides the short-run production function for Sherry’s Hair Salon.
Sherry uses only two inputs, labor and capital, to produce her output of stylish haircuts.
The price of labor is $20 an hour, and the price of capital is $50 per unit.
Quantity of capital (units)
10
10
10
10
10
10
Quantity of labor (hours
of work)
0
10
20
30
40
50
Quantity of haircuts
0
15
28
38
44
48
a. Complete the following table of Sherry’s costs, given the above information.
Round your calculations to one place past the decimal point.
Quantity
Of
capital
(units)
Quantity
Of
haircuts
10
Quantity
of
Labor
(hours
Of work)
0
10
10
15
10
20
28
10
30
38
10
40
44
10
50
48
0
FC VC AFC AVC ATC TC
($) ($) ($)
($)
($)
($)
---
---
---
MC
($ per
unit
Of
output)
500
13.3
b. Does this production function exhibit diminishing marginal returns to labor?
Explain your answer.
c. Graph the total cost function for Sherry’s Hair Salon. Measure total cost on the
vertical axis and the quantity of haircuts on the horizontal axis. Describe how
increasing the quantity of haircuts affects the slope of the total cost curve.
d. Graph the marginal cost function for Sherry’s Hair Salon using the midpoint
method. Measure marginal cost on the vertical axis and the quantity of haircuts
on the horizontal axis. Describe the slope of the MC curve, and then explain why
the MC is sloped this way.
e. In a new graph, draw Sherry’s Hair Salon AFC curve. Measure average fixed
cost on the vertical axis and the quantity of haircuts on the horizontal axis. In
your graph, indicate the area that corresponds to fixed cost if 15 haircuts are
currently being produced.
f. In a new graph, sketch Sherry’s Hair Salon ATC, AVC, AFC, and MC curves.
Measure cost per unit on the vertical axis and the quantity of haircuts on the
horizontal axis. What must be true about the relationship between the ATC and
MC curves?
3. a.
Quantity
Of
capital
(units)
10
Quantity
of
Labor
(hours
Of work)
0
Quantity
Of
haircuts
FC
($)
0
500
VC
($)
0
AFC AVC ATC
($)
($)
($)
---
---
---
TC
($)
MC
($ per
unit
Of
output)
500
13.3
10
10
15
500
200 33.3
13.3
46.7
700
15.4
10
20
28
500
400 17.9
14.3
32.1
900
10
30
38
500
600 13.2
15.8
28.9
1,100
10
40
44
500
800 11.4
18.2
29.5
1,300
10
50
48
500 1,000 10.4
20.8
31.8
1,500
20.0
33.3
50.0
b. A production function exhibits diminishing marginal returns to labor if, as labor is
increased while holding all other inputs constant, the level of total output increases but
at a decreasing rate. The marginal product of labor for this production function is
summarized in the table below. As you can see from the table, the production does
exhibit diminishing marginal returns to labor.
Quantity of
Quantity of labor Quantity
Marginal product of labor
Capital (units) (hours of work)
Of haircuts (haircuts per hour of work)
10
0
0
1.5
10
10
15
1.3
10
20
28
1.0
10
30
38
0.6
10
40
44
0.4
10
50
48
c.
As the quantity of haircuts increases, TC increases at an increasing rate due to the
diminishing marginal returns to labor.
d.
As output gets larger, the effect of diminishing marginal returns to the variable input
causes MC to increase.
e.
f,
5. The table below provides some information about Stella’s Delight, a business that
Stella owns. Stella uses labor and capital as her only inputs in the production of her
product.
a. Fill in the table below:
Quantity Quantity of Quantity
Of labor
capital
Of
(units)
(units)
output
0
5
0
1
5
10
2
5
18
3
5
24
4
5
28
5
5
30
6
5
31
VC FC AVC AFC ATC TC
($) ($) ($)
($)
($) ($)
---
10
15
b. What is the price of the variable input?
---
---
MC
($ per
unit
Of
output)
c. What is the price of the fixed input?
d. What is the marginal product of the fifth unit of labor?
e. What is the marginal cost of producing the twenty-fourth unit of output?
5. a.
Quantity Quantity of
Quantity VC FC AVC AFC ATC TC
MC
Of labor capital (units) Of output ($) ($) ($)
($)
($) ($) ($ per unit
(units)
Of output)
0
5
0
0
10
------10
0.50
1
5
10
5
10 0.50 1.00 1.50 15
0.63
2
5
18
10 10 0.56 0.56 1.11 20
0.83
3
5
24
15 10 0.42 0.42 1.04 25
1.25
4
5
28
20 10 0.36 0.36 1.07 30
2.50
5
5
30
25 10 0.33 0.33 1.17 35
5.00
6
5
31
39 10 0.32 0.32 1.29 40
b. The price of the variable input is $5 per unit because the variable cost is $15 when 3
units of labor are hired.
c. The price of the fixed input is $2 per unit because the fixed cost is $10 when 5 units
of capital are hired.
d. The marginal product of the fifth unit of labor equals the change in total output
divided by the change in the amount of labor when the firm increases its use of
labor from 4 units to 5 units, or (2 units of output)/(1 unit of labor), for a marginal
product of 2.
e. The marginal cost of producing the twenty-fourth unit of output is the change in
total cost divided by the change in output, or ($5)/(6 units of output), for a marginal
cost of $0.83.
7. The table below provides information about Sarah’s Doughnut Shoppe, a small firm
operating in a perfectly competitive industry. Use this information to answer the next set
of questions.
Quantity of doughnuts Total revenue Total cost
Profit
100
$200
$250
200
400
360
300
600
530
400
800
725
500
1,000
950
a. What is the market price for a doughnut?
b. Fill in the profit column of the table. At what level of output does Sarah’s
Doughnut Shoppe maximize its profits?
c. Calculate Sarah’s Doughnut Shoppe’s marginal cost and marginal revenue for
each level of output. Use the table below to organize your results.
Quantity of
Total
Total Marginal Marginal
Doughnuts Revenue Cost
Cost
Revenue
100
$200
$250
200
400
360
300
600
530
400
800
725
500
1,000
950
Profit
d. What is the relationship between marginal revenue and marginal cost at the profitmaximizing level of output for Sarah’s Doughnut Shoppe? Explain the meaning
of this relationship and how it relates to profitability.
7. a. Because total revenue equals price times quantity sold, we can use this equation to
find the price of a doughnut. When TR = $200, Q = 100 and price is $2. When TR =
$400, Q = 200 and price is $2. In a perfectly competitive industry the price the firm
sells its product for stays constant and is the market price.
b. According to the table, Sarah’s Doughnut Shoppe maximizes its profits when it
produces 400 doughnuts.
Quantity of doughnuts Total revenue Total cost
Profit
100
$200
$250
-$50
200
400
360
40
300
600
530
70
400
800
725
75
500
1,000
950
50
c.
Quantity of
Total
Total Marginal Marginal
Doughnuts Revenue Cost
Cost
Revenue
100
$200
$250
$1.10
$2
200
400
360
1.70
2
300
600
530
1.95
2
400
800
725
2.25
2
500
1,000
950
Profit
-$50
40
70
75
50
d. At the profit-maximizing level of output, MR = MC (or very close to it). Because
marginal revenue is also the price of a doughnut, marginal cost is the price of a
doughnut. When MR = MC, the addition to total revenue selling an additional unit of
the good is the addition to total cost from producing an additional unit of the good.
When MR < MC, fewer units of the good should be produced and sold in order to profit
maximize.