Test 2 Essays – Sections 9 & 10

Section 9

2. Use the figure below of a linear demand curve to answer this set of questions.

  1. 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
  1. At what price is total revenue maximized? (Hint: This may be a price that is not included in your table.)
  2. 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.
  3. 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.

  1. What is Mario’s income elasticity of demand for noodles?
  2. What is Mario’s income elasticity of demand for salmon?
  3. Is either of these goods income elastic for Mario?
  4. Is either of these goods income inelastic for Mario?
  5. From Mario’s perspective, is either of these goods a luxury good? Explain your answer.
  6. From Mario’s perspective, is either of these goods an inferior good? Explain your answer.

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
  1. If the market price is $175, who will buy the good and what is the value of total consumer surplus?
  2. 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?
  3. 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) / Quantity of labor (hours of work) / Quantity of haircuts
10 / 0 / 0
10 / 10 / 15
10 / 20 / 28
10 / 30 / 38
10 / 40 / 44
10 / 50 / 48
  1. 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
Labor (hours
Of work) / Quantity
Of haircuts / FC
($) / VC
($) / AFC
($) / AVC
($) / ATC
($) / TC
($) / MC
($ per unit
Of output)
10 / 0 / 0 / --- / --- / --- / 500
/ / 13.3
10 / 10 / 15 /
10 / 20 / 28 /
10 / 30 / 38
10 / 40 / 44
10 / 50 / 48
  1. Does this production function exhibit diminishing marginal returns to labor? Explain your answer.
  2. 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.
  3. 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.
  4. 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.
  5. 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.

  1. Fill in the table below:

Quantity
Of labor
(units) / Quantity of
capital (units) / Quantity
Of output / VC
($) / FC
($) / AVC
($) / AFC
($) / ATC
($) / TC
($) / MC
($ per unit
Of output)
0 / 5 / 0 / --- / --- / --- /
1 / 5 / 10 /
2 / 5 / 18 / 10 /
3 / 5 / 24 / 15 /
4 / 5 / 28 /
5 / 5 / 30 /
6 / 5 / 31
  1. What is the price of the variable input?
  2. What is the price of the fixed input?
  3. What is the marginal product of the fifth unit of labor?
  4. What is the marginal cost of producing the twenty-fourth 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 / Profit
100 / $200 / $250
200 / 400 / 360
300 / 600 / 530
400 / 800 / 725
500 / 1,000 / 950
  1. What is the market price for a doughnut?
  2. Fill in the profit column of the table. At what level of output does Sarah’s Doughnut Shoppe maximize its profits?
  3. 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
Doughnuts / Total
Revenue / Total
Cost / Marginal
Cost / Marginal
Revenue / Profit
100 / $200 / $250
200 / 400 / 360
300 / 600 / 530
400 / 800 / 725
500 / 1,000 / 950
  1. What is the relationship between marginal revenue and marginal cost at the profit-maximizing 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.

  1. 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
  1. At what price is total revenue maximized? (Hint: This may be a price that is not included in your table.)
  2. 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.
  3. 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.

  1. What is Mario’s income elasticity of demand for noodles?
  2. What is Mario’s income elasticity of demand for salmon?
  3. Is either of these goods income elastic for Mario?
  4. Is either of these goods income inelastic for Mario?
  5. From Mario’s perspective, is either of these goods a luxury good? Explain your answer.
  6. 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
  1. If the market price is $175, who will buy the good and what is the value of total consumer surplus?
  2. 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?
  3. 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) / Quantity of labor (hours of work) / Quantity of haircuts
10 / 0 / 0
10 / 10 / 15
10 / 20 / 28
10 / 30 / 38
10 / 40 / 44
10 / 50 / 48
  1. 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
Labor (hours
Of work) / Quantity
Of haircuts / FC
($) / VC
($) / AFC
($) / AVC
($) / ATC
($) / TC
($) / MC
($ per unit
Of output)
10 / 0 / 0 / --- / --- / --- / 500
/ / 13.3
10 / 10 / 15 /
10 / 20 / 28 /
10 / 30 / 38
10 / 40 / 44
10 / 50 / 48
  1. Does this production function exhibit diminishing marginal returns to labor? Explain your answer.
  2. 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.
  3. 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.
  4. 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.
  5. 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) / Quantity of
Labor (hours
Of work) / Quantity
Of haircuts / FC
($) / VC
($) / AFC
($) / AVC
($) / ATC
($) / TC
($) / MC
($ per unit
Of output)
10 / 0 / 0 / 500 / 0 / --- / --- / --- / 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
/ 20.0
10 / 30 / 38 / 500 / 600 / 13.2 / 15.8 / 28.9 / 1,100
/ 33.3
10 / 40 / 44 / 500 / 800 / 11.4 / 18.2 / 29.5 / 1,300
/ 50.0
10 / 50 / 48 / 500 / 1,000 / 10.4 / 20.8 / 31.8 / 1,500

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
Capital (units) / Quantity of labor
(hours of work) / Quantity
Of haircuts / Marginal product of labor
(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.

  1. Fill in the table below:

Quantity
Of labor
(units) / Quantity of
capital (units) / Quantity
Of output / VC
($) / FC
($) / AVC
($) / AFC
($) / ATC
($) / TC
($) / MC
($ per unit
Of output)
0 / 5 / 0 / --- / --- / --- /
1 / 5 / 10 /
2 / 5 / 18 / 10 /
3 / 5 / 24 / 15 /
4 / 5 / 28 /
5 / 5 / 30 /
6 / 5 / 31
  1. What is the price of the variable input?
  2. What is the price of the fixed input?
  3. What is the marginal product of the fifth unit of labor?
  4. What is the marginal cost of producing the twenty-fourth unit of output?

5. a.

Quantity
Of labor
(units) / Quantity of
capital (units) / Quantity
Of output / VC
($) / FC
($) / AVC
($) / AFC
($) / ATC
($) / TC
($) / MC
($ per unit
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.

  1. The price of the fixed input is $2 per unit because the fixed cost is $10 when 5 units of capital are hired.
  1. 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.
  1. 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
  1. What is the market price for a doughnut?
  2. Fill in the profit column of the table. At what level of output does Sarah’s Doughnut Shoppe maximize its profits?
  3. 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
Doughnuts / Total
Revenue / Total
Cost / Marginal
Cost / Marginal
Revenue / Profit
100 / $200 / $250
200 / 400 / 360
300 / 600 / 530
400 / 800 / 725
500 / 1,000 / 950
  1. What is the relationship between marginal revenue and marginal cost at the profit-maximizing 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
Doughnuts / Total
Revenue / Total
Cost / Marginal
Cost / Marginal
Revenue / Profit
100 / $200 / $250 / -$50
/ $1.10 / $2
200 / 400 / 360 / 40
/ 1.70 / 2
300 / 600 / 530 / / 70
/ 1.95 / 2
400 / 800 / 725 / 75
/ 2.25 / 2
500 / 1,000 / 950 / 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.