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AU / Economics / ECON 2020 / What is the satisfaction a consumer obtains from the consumption of a

What is the satisfaction a consumer obtains from the consumption of a

What is the satisfaction a consumer obtains from the consumption of a

Description

School: Auburn University
Department: Economics
Course: PRINCIPLES OF MICROECONOMICS
Professor: William finck
Term: Fall 2016
Tags: Econ, Economics, economic, micro, Microecon, Microeconomic, and Microeconomics
Cost: 50
Name: ECON 2020 Exam 3 Study Guide
Description: This is a study guide based off of the study materials provided. It also includes the answers to the problem set as well as the breakdown of the test.
Uploaded: 10/12/2016
44 Pages 288 Views 10 Unlocks
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ECON 2020 Exam 3 Study Guide


What is the satisfaction a consumer obtains from the consumption of a good or service?



TERMS:  

∙ Utility – the satisfaction a consumer obtains from the consumption of  a good or service

∙ Total utility – the total satisfaction a person derives from consuming  some specific quantity; TU increases as Qd increases; TU = ∑MU ∙ Marginal utility – the additional utility a consumer derives from an  additional unit of a good

∙ Law of Diminishing Marginal Utility – As QD rises -> MU falls; NOTE: As  MU falls, willingness to pay falls as well

∙ Budget constraint/line – line that shows the different consumption  bundles a consumer can purchase with a specific money income. ∙ Consumption bundle – the combination of goods and services  consumed by an individual


What is the total satisfaction a person derives from consuming some specific quantity?



If you want to learn more check out What does gdp tell you about a country?

∙ Optimal consumption bundle – the bundle that maximizes total utility ∙ Indifference curves – a line that shows the consumption bundles that  yield the same amount of total utility We also discuss several other topics like What are the derived traits of plants called?
Don't forget about the age old question of Is american indian the same as native american?

∙ Marginal rate of substitution – the ratio of the marginal utility of one  good to the marginal utility of another; MRS = MUx/MUy

∙ Principle of Diminishing Marginal Rate of Substitution (MRS) – the  more of good X a person consumes in proportion to good Y, the less  the consumer is willing to substitute for X; MRS decreases as Qx  increases 

∙ Perfect substitutes – goods for which the marginal rate of substitution  is constant, no matter how much of each is consumed


What is the additional utility a consumer derives from an additional unit of a good?



∙ Perfect complements – goods that a consumer will consume in the  same ratio regardless of their relative price

∙ Implicit cost – the forgone income from employing resources in their  next-best use.

∙ Plant capacity – the size of the building and amount of capital  equipment

∙ Marginal product of labor – the additional output produced by one  more unit of labor; MPL = ∆Q / ∆L

∙ Economies of scale/increasing returns to scale – as q rises, LRATC falls ∙ Diseconomies of scale/decreasing returns to scale – as q rises, LRATC  rises We also discuss several other topics like What is monism in psychology?

CONCEPTS:

Utility Facts: 

∙ Utility is measured in utils.

∙ We CANNOT compare the utils assigned to a good by multiple people. ∙ We CAN compare the utils assigned to multiple goods by one person. o If you hear “Utility” and there is no word in front of it, it is total  utility.

Total Utility and Quantity Demanded: 

∙ Total Utility increases as Quantity Demanded increases Marginal Utility and Quantity Demanded: 

∙ As Quantity Demanded rises, Marginal Utility falls

Marginal Utility and Willingness to Pay: 

∙ As Marginal Utility falls, willingness to pay falls as well Don't forget about the age old question of What is also involved in information gathering and investigations?

o Ex:  

Quantity

1

2

3

4

5

6

TU

15

28

39

48

55

60

MU

15

13

11

9

7

5

Factors That Change the Budget Line: If you want to learn more check out What is the definition of a dynamic (unpredictable) world?

1. Income – a change in incomes causes a shift of the budget line 2. Price of Y – a change in the price causes a rotation of the budget line 3. Price of X – a change in the price causes a rotation of the budget line

2

Utility-Maximization (Optimal) Consumption: 

∙ Optimal consumption bundle – the bundle that maximizes total utility ∙ Find the optimal consumption bundle using the following information: o Consumer income = $24

o Px = $3

o Py = $2

Optimal Consumption

Qx

TUx

MUx

MUx/Px

Qy

TUy

MUy

MUy/Py

1

39

39

13 

1

30

30

15

2

75

36

12 

2

58

28

14

3

108

33

11

3

84

26

13

4

135

27

4

108

24

12

5

159

24

5

128

20

10

6

180

21

7

6

146

18

9

7

198

18

6

7

162

16

8

Possible Optimal Bundles

⮚ Use the INCOME formula on possible optimal bundles to determine if  all $ spent:

∙ 1 X and 3 Y: (1 * 3) + (3 * 2) = $9

∙ 2 X and 4 Y: (2 * 3) + (4 * 2) = $14

∙ 4 X and 6 Y: (4 * 3) + (6 * 2) = $24

o Optimal = 4 unites of X and 6 units of Y

o TU of bundle = 135 + 146 = 281 utils

Properties of (Most) Indifference Curves: 

1. ICs are downward sloping

2. ICs farther from the origin represent a greater level of TU 3. ICs never cross

4. ICs are bowed inward

3

Special Indifference Curves: 

∙ Perfect substitutes – goods for which the marginal rate of substitution  is constant, no matter how much of each is consumed

∙ Perfect complements – goods that a consumer will consume in the  same ratio regardless of their relative price

Perfect Substitutes

∙ Example: A consumer has $55 to spend on bundles containing Exxon  and Chevron gasoline. Px = $2.75 and Pc = $2.50

4

Perfect Complements

∙ A consumer has $24 to spend on bundles containing ham and bread.  Ph = $6 and Pb = $2

Economic vs. Accounting Profit: 

1. Accounting ∏ = TR – Explicit cost

2. Economic ∏ = TR – Economic cost

▪ These are used to get total cost

∙ Economic cost includes the implicit cost, which for a producer is the  forgone income from employing resources in their next-best use. ∙ Example:

o TR = $15,000

o Explicit cost = $11,000

o Implicit cost = $4,000

o Finding Account and Economic Profits

Solution:

5

∙ Accounting ∏ = 15000 – 11000 = $4,000

∙ Economic ∏ = 15000 – (11000 + 4000) = $0

Normal Profit: 

1. The firm is doing just as well as it could in another industry 2. Accounting profit = Implicit Cost

3. Economic profit = $0

Short Run vs. Long Run: 

∙ Short run – an amount of time insufficient to allow plant capacity to  vary. Also, firms may shutdown production, but they cannot exit the  market.

∙ Long run – all costs are variable; entry and exit are possible

Fixed Costs vs. Variable Costs: 

∙ Fixed Costs:

1. Cannot be varied in the short run

2. Do not changes as output changes

3. Still exist when output falls to zero

4. Usually associated with capital

∙ Variable costs – costs that change as output changes; go to zero  during shutdown

Law of Diminishing Marginal Returns:

6

∙ As successive units of a variable resource are added to a fixed  resource, the marginal product of the variable resource eventually  decreases.

∙ LDMR explains why the short run cost curves eventually increase as  output increases.

∙ Only applies in short run (no fixed resources in long run)

Factors That Shift Cost Curves: 

1. Input Prices – input prices and cost curves move together 2. Regulation/Taxes – taxes and costs move together

3. Technology – as technology improves, costs fall

GRAPHS:

Budget Line: 

∙ NOTE: the price of a consumption bundle cannot exceed the  consumer’s total income

∙ Income = (Qx * Px) + (Qy * Py)

o Example: Assume a consumer with $24 to spend is choosing  between $4 hot dogs and $2 chicken fingers

o If the consumer is at a bundle on the budget line, the only way  to consume more of one good is to give up some of the other Opportunity Cost of X = max Qy / max Qx = Px/Py

7

Factors that Change the Budget Line

1. Income

∙ A change in income causes a shift of the budget line 2. Price of Y

∙ A change in price causes a rotation of the budget line

8

3. Price of X

∙ A change in the price causes a rotation of the budget line *Will be a definite answer. SO DON’T CHOOSE “A and B” or “A and  C” as an answer on the test.

9

Indifference Curves: 

MC, ATC, and AVC: 

Q

TFC

TVC

TC

MC

AFC

AVC

ATC

0

240

0

240

----- 

-----

----- 

-----

1

240

50

290

50 

240

50 

290

2

240

90

330

40 

120

45 

165

3

240

120

360

30 

80

40 

120

4

240

160

400

40 

60

40 

100

5

240

240

480

80 

48

48 

96

∙ What is ∏ for a firm with these costs selling 5 units for a price of  $100?

o ∏ = TR – TC = (5 * 100) – 480 = $20

o MC, AVC, and ATC are needed for a graph

10

???? Market gets capital letter, firm gets lower case letter VERY IMPORTANT: ATC and AVC must cross MC at their minimum!

Shifts of LR Cost Curves: 

Long Run Costs

11

∙ Know explanation for the shape of the curves.

Change in LR Costs

FORMULAS/EQUATIONS:

Marginal utility = Δ TU 

Total utility = Σ MU 

Income: 

Income = (Qx * Px) + (Qy * Py)

Opportunity Cost (2): 

Opportunity Cost of X = max Qy / max Qx = Px/Py

Opportunity Cost of Good X = Quantity of Y / Quantity of X Marginal Utility Per Dollar: 

Marginal Utility Per Dollar = MU / P

Utility-Maximization Rule: 

MUx / Px = MUy / Py

12

Marginal Rate of Substitution (slope of IC): 

∙ Slope = ∆Qy / ∆Qx

∙ Along an IC:

∆TUx + ∆TUy = 0

∙ This can be rewritten as:

MUx * ∆Qx + MUy * ∆Qy = 0 Or:

MUx * ∆Qx = -MUy * ∆Qy

∙ Dividing both sides by Qx and by –MUy:

∆Qy / ∆Qx = -MUx / MUy

Marginal Rate of Substitution

∙ Marginal rate of substitution – the ratio of the marginal utility of one  good to the marginal utility of another; MRS = MUx/MUy

Relative Price (Slope of Budget Line): 

∙ Relative price – the ratio of the price of one good to the price of the  other; RP = Px / Py

∙ NOTE: slope of budget line = -Px / Py

13

∙ Thus, we can find the optimal bundle by setting MRS = RP or  MUx/MUy = Px/Py 

Relative Price Rule: 

∙ At the optimal consumption bundle, MRS = RP

Bundle

Qx

MUx

Qy

MUy

MRS

A

2

2500

60

100

25

B

3

2000

40

200

10

C

5

1000

24

500

2

D

6

750

20

750

1

∙ If Px = $50 and Py = $5, what is the optimal bundle?

∙ SOLUTION: MRS = RP

∙ MRS = MUx / MUy

∙ RP = Px / Py = 50 / 5 = 10

∙ Optimal Bundle = B

Profit (general): 

∏ = Total Revenue – Total Cost

TR = P * Q

Economic Profit: 

Economic ∏ = TR – Economic cost

Accounting Profit: 

Accounting ∏ = TR – Explicit cost

Total Cost: 

Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC) Average Fixed Cost: 

Average Fixed Cost = TFC / Q

Average Variable Cost:

14

Average Variable Cost = TVC / Q Average Total Cost: 

Average Total Cost = TC / Q = AFC + AVC Marginal Cost (2): 

Marginal Cost = ∆TC / ∆Q

MC = Wage / MPL

Marginal Product of Labor: 

MPL = ∆Q / ∆L

Total Product:  

Q = ΣMPL

15

Problem Set 3 Answers

1a. What is the opportunity cost of a movie ticket?  

Opp. Cost of X = max Qy / max Qx = 12/4 = 3

1b. If the consumer has $36 to spend at BL1, what is the price of a movie  ticket?  

Income = Px * Qx + Py * Qy

36 = 4Px + 0

Px = $9

1c. What would a movement from BL1 to BL2 represent?  If both endpoints are decreasing, income is decreasing

A decrease in income from $36 to $27

16

2. Let X and Y represent two goods with identical prices in a consumption  bundle with unknown quantities of each. If the marginal utility of the last  unit of X consumed is less than the marginal utility from the last unit of Y,  then how should the consumer alter the quantities of X and Y to reach  

optimal consumption? (Assume the consumer is currently spending all  income.)

Optimal: MUx/Px = MUy/Py

MUx must increase and MUy must decrease

Buy less X and more Y

3a. Find the optimal consumption bundle. (Remember the optimal  consumption rule: all income must be spent and MUx/Px = MUy/Py.)  

[Must fill in chart to answer questions]

Qx

TUx

Mux

MUx/Px

Qy

TUy

MUy

MUy/Py

1

18

18 

1

32 

32 

8

2

30 

12

6*

2

56

24 

6*

3

40 

10 

5

3

72

16 

4*

4

48

8

4*

4

80 

8

2

Blue* – numbers that are possible optimal consumption bundles Green – numbers that were filled in

17

#1 – 2X and 2 Y = (2*2) + (2*4) = 4 + 8 = $12

#2 – 4X and 3Y = (4*2) + (3*4) = 8 + 12 = $20

3b. Find the total utility derived from the entire purchase. Px = $2 Py = $4 and income = $20

TU of 4X = 48

TU of 3 Y = 72

TU = 48 + 72 = 120 utils

3c. Graph the consumer’s budget line and draw an indifference curve that is  tangent at the optimal bundle. Label the optimal bundle with a “1”, then  label with a “2” any point on the IC to the left of the optimal bundle.  

3d. What is the opportunity cost of one unit of good Y?  

Opp. Cost: max Qx/ max Qy = 10/5 = 2 or Py/Px = 4/2 = 2 3e. Which point (1 or 2) has the higher MRS?

18

Point 2

3f. TRICK QUESTION: Which point (1 or 2) yields a higher level of total  utility?  

Neither, they are on the same indifference curve

4.

MRS

4

1

1

1/2

4a. Using the relative price rule, find the optimal bundle if the price of X is  $4 and the price of Y is $2.

RP = 4/2 =2

Optimal bundle = B

19

4b. Find the optimal bundle if the price of Y rises to $8.  

MRS

4

1

1

1/2

RP = 4/8 = ½

Optimal bundle = D

5a. A consumer considers good X and good Y to be perfect substitutes. If the  price of good X is $4, the price of good Y is $8, and the consumer has $48 to  spend, how many units of each good will be in the consumer’s optimal  bundle?  

Optimal bundle = Income / Low P

Optimal = 48/4 = 12

12 units of X and 0 units of Y

5b. If the consumer instead considers the goods to be perfect complements,  then how many units of each good will be in the consumer’s optimal  bundle?  

Optimal bundle = Income / (Px + Py)

Optimal = 48/ (4 + 8) = 4

4 units of X and 4 units of Y

6a. If you can complete this table, then you have mastered all of the cost  concepts.

20

Q

TFC

TVC

TC

MC

AFC

AVC

ATC

0

60

0

60

-----

-----

-----

-----

1

60

40

100

40

60

40

100

2

60

60

120

20

30

30

60

3

60

90

150

30

20

30

50

4

60

140

200

50

15

35

50

5

60

240

300

100

12

48

60

6b. Find the profit of a firm with the above costs if it sells 5 units at a price of  $80 each.  

∏ = TR – TC = (5*80) – 300 = 400 – 300 = $100

7. Complete the table. Don't forget that in this case MC = W/MPL.  

K

L

W

Q

MPL

MC = W/MPL

1

0

12

0

-----

-----

1

1

12

2

2

6

1

2

12

6

4

3

1

3

12

9

3

$4

EXAM BREAKDOWN:

Chapter 8 and 9 questions – 16

Chapter 11 questions – 9

21

Problem Set questions – 12 Math questions – 9

Graphs – 3 (7 questions)

Draw your own graph – 3 max Evil multiple choice questions – 6 Theme – Step Brothers

22

ECON 2020 Exam 3 Study Guide

TERMS:  

∙ Utility – the satisfaction a consumer obtains from the consumption of  a good or service

∙ Total utility – the total satisfaction a person derives from consuming  some specific quantity; TU increases as Qd increases; TU = ∑MU ∙ Marginal utility – the additional utility a consumer derives from an  additional unit of a good

∙ Law of Diminishing Marginal Utility – As QD rises -> MU falls; NOTE: As  MU falls, willingness to pay falls as well

∙ Budget constraint/line – line that shows the different consumption  bundles a consumer can purchase with a specific money income. ∙ Consumption bundle – the combination of goods and services  consumed by an individual

∙ Optimal consumption bundle – the bundle that maximizes total utility ∙ Indifference curves – a line that shows the consumption bundles that  yield the same amount of total utility

∙ Marginal rate of substitution – the ratio of the marginal utility of one  good to the marginal utility of another; MRS = MUx/MUy

∙ Principle of Diminishing Marginal Rate of Substitution (MRS) – the  more of good X a person consumes in proportion to good Y, the less  the consumer is willing to substitute for X; MRS decreases as Qx  increases 

∙ Perfect substitutes – goods for which the marginal rate of substitution  is constant, no matter how much of each is consumed

∙ Perfect complements – goods that a consumer will consume in the  same ratio regardless of their relative price

∙ Implicit cost – the forgone income from employing resources in their  next-best use.

∙ Plant capacity – the size of the building and amount of capital  equipment

∙ Marginal product of labor – the additional output produced by one  more unit of labor; MPL = ∆Q / ∆L

∙ Economies of scale/increasing returns to scale – as q rises, LRATC falls ∙ Diseconomies of scale/decreasing returns to scale – as q rises, LRATC  rises

CONCEPTS:

Utility Facts: 

∙ Utility is measured in utils.

∙ We CANNOT compare the utils assigned to a good by multiple people. ∙ We CAN compare the utils assigned to multiple goods by one person. o If you hear “Utility” and there is no word in front of it, it is total  utility.

Total Utility and Quantity Demanded: 

∙ Total Utility increases as Quantity Demanded increases Marginal Utility and Quantity Demanded: 

∙ As Quantity Demanded rises, Marginal Utility falls

Marginal Utility and Willingness to Pay: 

∙ As Marginal Utility falls, willingness to pay falls as well

o Ex:  

Quantity

1

2

3

4

5

6

TU

15

28

39

48

55

60

MU

15

13

11

9

7

5

Factors That Change the Budget Line: 

1. Income – a change in incomes causes a shift of the budget line 2. Price of Y – a change in the price causes a rotation of the budget line 3. Price of X – a change in the price causes a rotation of the budget line

2

Utility-Maximization (Optimal) Consumption: 

∙ Optimal consumption bundle – the bundle that maximizes total utility ∙ Find the optimal consumption bundle using the following information: o Consumer income = $24

o Px = $3

o Py = $2

Optimal Consumption

Qx

TUx

MUx

MUx/Px

Qy

TUy

MUy

MUy/Py

1

39

39

13 

1

30

30

15

2

75

36

12 

2

58

28

14

3

108

33

11

3

84

26

13

4

135

27

4

108

24

12

5

159

24

5

128

20

10

6

180

21

7

6

146

18

9

7

198

18

6

7

162

16

8

Possible Optimal Bundles

⮚ Use the INCOME formula on possible optimal bundles to determine if  all $ spent:

∙ 1 X and 3 Y: (1 * 3) + (3 * 2) = $9

∙ 2 X and 4 Y: (2 * 3) + (4 * 2) = $14

∙ 4 X and 6 Y: (4 * 3) + (6 * 2) = $24

o Optimal = 4 unites of X and 6 units of Y

o TU of bundle = 135 + 146 = 281 utils

Properties of (Most) Indifference Curves: 

1. ICs are downward sloping

2. ICs farther from the origin represent a greater level of TU 3. ICs never cross

4. ICs are bowed inward

3

Special Indifference Curves: 

∙ Perfect substitutes – goods for which the marginal rate of substitution  is constant, no matter how much of each is consumed

∙ Perfect complements – goods that a consumer will consume in the  same ratio regardless of their relative price

Perfect Substitutes

∙ Example: A consumer has $55 to spend on bundles containing Exxon  and Chevron gasoline. Px = $2.75 and Pc = $2.50

4

Perfect Complements

∙ A consumer has $24 to spend on bundles containing ham and bread.  Ph = $6 and Pb = $2

Economic vs. Accounting Profit: 

1. Accounting ∏ = TR – Explicit cost

2. Economic ∏ = TR – Economic cost

▪ These are used to get total cost

∙ Economic cost includes the implicit cost, which for a producer is the  forgone income from employing resources in their next-best use. ∙ Example:

o TR = $15,000

o Explicit cost = $11,000

o Implicit cost = $4,000

o Finding Account and Economic Profits

Solution:

5

∙ Accounting ∏ = 15000 – 11000 = $4,000

∙ Economic ∏ = 15000 – (11000 + 4000) = $0

Normal Profit: 

1. The firm is doing just as well as it could in another industry 2. Accounting profit = Implicit Cost

3. Economic profit = $0

Short Run vs. Long Run: 

∙ Short run – an amount of time insufficient to allow plant capacity to  vary. Also, firms may shutdown production, but they cannot exit the  market.

∙ Long run – all costs are variable; entry and exit are possible

Fixed Costs vs. Variable Costs: 

∙ Fixed Costs:

1. Cannot be varied in the short run

2. Do not changes as output changes

3. Still exist when output falls to zero

4. Usually associated with capital

∙ Variable costs – costs that change as output changes; go to zero  during shutdown

Law of Diminishing Marginal Returns:

6

∙ As successive units of a variable resource are added to a fixed  resource, the marginal product of the variable resource eventually  decreases.

∙ LDMR explains why the short run cost curves eventually increase as  output increases.

∙ Only applies in short run (no fixed resources in long run)

Factors That Shift Cost Curves: 

1. Input Prices – input prices and cost curves move together 2. Regulation/Taxes – taxes and costs move together

3. Technology – as technology improves, costs fall

GRAPHS:

Budget Line: 

∙ NOTE: the price of a consumption bundle cannot exceed the  consumer’s total income

∙ Income = (Qx * Px) + (Qy * Py)

o Example: Assume a consumer with $24 to spend is choosing  between $4 hot dogs and $2 chicken fingers

o If the consumer is at a bundle on the budget line, the only way  to consume more of one good is to give up some of the other Opportunity Cost of X = max Qy / max Qx = Px/Py

7

Factors that Change the Budget Line

1. Income

∙ A change in income causes a shift of the budget line 2. Price of Y

∙ A change in price causes a rotation of the budget line

8

3. Price of X

∙ A change in the price causes a rotation of the budget line *Will be a definite answer. SO DON’T CHOOSE “A and B” or “A and  C” as an answer on the test.

9

Indifference Curves: 

MC, ATC, and AVC: 

Q

TFC

TVC

TC

MC

AFC

AVC

ATC

0

240

0

240

----- 

-----

----- 

-----

1

240

50

290

50 

240

50 

290

2

240

90

330

40 

120

45 

165

3

240

120

360

30 

80

40 

120

4

240

160

400

40 

60

40 

100

5

240

240

480

80 

48

48 

96

∙ What is ∏ for a firm with these costs selling 5 units for a price of  $100?

o ∏ = TR – TC = (5 * 100) – 480 = $20

o MC, AVC, and ATC are needed for a graph

10

???? Market gets capital letter, firm gets lower case letter VERY IMPORTANT: ATC and AVC must cross MC at their minimum!

Shifts of LR Cost Curves: 

Long Run Costs

11

∙ Know explanation for the shape of the curves.

Change in LR Costs

FORMULAS/EQUATIONS:

Marginal utility = Δ TU 

Total utility = Σ MU 

Income: 

Income = (Qx * Px) + (Qy * Py)

Opportunity Cost (2): 

Opportunity Cost of X = max Qy / max Qx = Px/Py

Opportunity Cost of Good X = Quantity of Y / Quantity of X Marginal Utility Per Dollar: 

Marginal Utility Per Dollar = MU / P

Utility-Maximization Rule: 

MUx / Px = MUy / Py

12

Marginal Rate of Substitution (slope of IC): 

∙ Slope = ∆Qy / ∆Qx

∙ Along an IC:

∆TUx + ∆TUy = 0

∙ This can be rewritten as:

MUx * ∆Qx + MUy * ∆Qy = 0 Or:

MUx * ∆Qx = -MUy * ∆Qy

∙ Dividing both sides by Qx and by –MUy:

∆Qy / ∆Qx = -MUx / MUy

Marginal Rate of Substitution

∙ Marginal rate of substitution – the ratio of the marginal utility of one  good to the marginal utility of another; MRS = MUx/MUy

Relative Price (Slope of Budget Line): 

∙ Relative price – the ratio of the price of one good to the price of the  other; RP = Px / Py

∙ NOTE: slope of budget line = -Px / Py

13

∙ Thus, we can find the optimal bundle by setting MRS = RP or  MUx/MUy = Px/Py 

Relative Price Rule: 

∙ At the optimal consumption bundle, MRS = RP

Bundle

Qx

MUx

Qy

MUy

MRS

A

2

2500

60

100

25

B

3

2000

40

200

10

C

5

1000

24

500

2

D

6

750

20

750

1

∙ If Px = $50 and Py = $5, what is the optimal bundle?

∙ SOLUTION: MRS = RP

∙ MRS = MUx / MUy

∙ RP = Px / Py = 50 / 5 = 10

∙ Optimal Bundle = B

Profit (general): 

∏ = Total Revenue – Total Cost

TR = P * Q

Economic Profit: 

Economic ∏ = TR – Economic cost

Accounting Profit: 

Accounting ∏ = TR – Explicit cost

Total Cost: 

Total Cost (TC) = Total Fixed Cost (TFC) + Total Variable Cost (TVC) Average Fixed Cost: 

Average Fixed Cost = TFC / Q

Average Variable Cost:

14

Average Variable Cost = TVC / Q Average Total Cost: 

Average Total Cost = TC / Q = AFC + AVC Marginal Cost (2): 

Marginal Cost = ∆TC / ∆Q

MC = Wage / MPL

Marginal Product of Labor: 

MPL = ∆Q / ∆L

Total Product:  

Q = ΣMPL

15

Problem Set 3 Answers

1a. What is the opportunity cost of a movie ticket?  

Opp. Cost of X = max Qy / max Qx = 12/4 = 3

1b. If the consumer has $36 to spend at BL1, what is the price of a movie  ticket?  

Income = Px * Qx + Py * Qy

36 = 4Px + 0

Px = $9

1c. What would a movement from BL1 to BL2 represent?  If both endpoints are decreasing, income is decreasing

A decrease in income from $36 to $27

16

2. Let X and Y represent two goods with identical prices in a consumption  bundle with unknown quantities of each. If the marginal utility of the last  unit of X consumed is less than the marginal utility from the last unit of Y,  then how should the consumer alter the quantities of X and Y to reach  

optimal consumption? (Assume the consumer is currently spending all  income.)

Optimal: MUx/Px = MUy/Py

MUx must increase and MUy must decrease

Buy less X and more Y

3a. Find the optimal consumption bundle. (Remember the optimal  consumption rule: all income must be spent and MUx/Px = MUy/Py.)  

[Must fill in chart to answer questions]

Qx

TUx

Mux

MUx/Px

Qy

TUy

MUy

MUy/Py

1

18

18 

1

32 

32 

8

2

30 

12

6*

2

56

24 

6*

3

40 

10 

5

3

72

16 

4*

4

48

8

4*

4

80 

8

2

Blue* – numbers that are possible optimal consumption bundles Green – numbers that were filled in

17

#1 – 2X and 2 Y = (2*2) + (2*4) = 4 + 8 = $12

#2 – 4X and 3Y = (4*2) + (3*4) = 8 + 12 = $20

3b. Find the total utility derived from the entire purchase. Px = $2 Py = $4 and income = $20

TU of 4X = 48

TU of 3 Y = 72

TU = 48 + 72 = 120 utils

3c. Graph the consumer’s budget line and draw an indifference curve that is  tangent at the optimal bundle. Label the optimal bundle with a “1”, then  label with a “2” any point on the IC to the left of the optimal bundle.  

3d. What is the opportunity cost of one unit of good Y?  

Opp. Cost: max Qx/ max Qy = 10/5 = 2 or Py/Px = 4/2 = 2 3e. Which point (1 or 2) has the higher MRS?

18

Point 2

3f. TRICK QUESTION: Which point (1 or 2) yields a higher level of total  utility?  

Neither, they are on the same indifference curve

4.

MRS

4

1

1

1/2

4a. Using the relative price rule, find the optimal bundle if the price of X is  $4 and the price of Y is $2.

RP = 4/2 =2

Optimal bundle = B

19

4b. Find the optimal bundle if the price of Y rises to $8.  

MRS

4

1

1

1/2

RP = 4/8 = ½

Optimal bundle = D

5a. A consumer considers good X and good Y to be perfect substitutes. If the  price of good X is $4, the price of good Y is $8, and the consumer has $48 to  spend, how many units of each good will be in the consumer’s optimal  bundle?  

Optimal bundle = Income / Low P

Optimal = 48/4 = 12

12 units of X and 0 units of Y

5b. If the consumer instead considers the goods to be perfect complements,  then how many units of each good will be in the consumer’s optimal  bundle?  

Optimal bundle = Income / (Px + Py)

Optimal = 48/ (4 + 8) = 4

4 units of X and 4 units of Y

6a. If you can complete this table, then you have mastered all of the cost  concepts.

20

Q

TFC

TVC

TC

MC

AFC

AVC

ATC

0

60

0

60

-----

-----

-----

-----

1

60

40

100

40

60

40

100

2

60

60

120

20

30

30

60

3

60

90

150

30

20

30

50

4

60

140

200

50

15

35

50

5

60

240

300

100

12

48

60

6b. Find the profit of a firm with the above costs if it sells 5 units at a price of  $80 each.  

∏ = TR – TC = (5*80) – 300 = 400 – 300 = $100

7. Complete the table. Don't forget that in this case MC = W/MPL.  

K

L

W

Q

MPL

MC = W/MPL

1

0

12

0

-----

-----

1

1

12

2

2

6

1

2

12

6

4

3

1

3

12

9

3

$4

EXAM BREAKDOWN:

Chapter 8 and 9 questions – 16

Chapter 11 questions – 9

21

Problem Set questions – 12 Math questions – 9

Graphs – 3 (7 questions)

Draw your own graph – 3 max Evil multiple choice questions – 6 Theme – Step Brothers

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