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(Solved) Chapter 2: Individual Choice Purpose: Develop a model to describe how individuals make choices.allocate scarce resources. Start with a simple model,...

Ex. 3: Calculating Value of the Marginal Product

in the given question

Chapter 2:

Individual Choice

Purpose: Develop a model to

describe how individuals make

choicesâ€¦.allocate scarce resources. Start with a simple model, then allow

for more complex decisions. Assumption that always holds:

Individuals are rational -- always

make the best choice. Key Concepts of the

Model Total Utility (TU) â€“ an individualâ€™s total

satisfaction/ happiness

- Utils: measure of utility.

Marginal Utility (MU) â€“ a change in TU

resulting from a change in the quantity

(Q)â€¦â€¦ Formula: MU = Î”TU/Î”Q.

Diminishing MU â€“ an assumption that

MU diminishes with additional units

consumed. Ex.1: Decision with One

Option (No Scarcity) Following table shows the total utility

Jack derives from each slice of pizza

he eats. Determine Jackâ€™s marginal utility for

each slice of pizza. Fill in MU column. If pizza is free, when should Jack stop

eating pizza? Ex.1: Decision With One

Option (No Scarcity) Decision Rule With One

Option (No Scarcity)

Jack should consume pizza up to the

point where his TU is maximized (no

utility left to gain from the additional

unit). Decision rule: MU=0 (making a

decision at the margin). Referred to as satiation or bliss point. Ex. 2: Decision With N

Options (No Scarcity)

Following graphs represent the MU

for each hour spent doing two

activities:

- Which activity is initially more satisfying?

- Which activity is more sustainable

overtime?

- How should you allocate your time if

your time is not scarce? Ex. 2: Decision With

N Options (N=2)

MU of Activity 1

90

80

70

60

50

40

30

20

10

0 MU of Activity 2 90

81

70 50 25 0 1 2 3 4 5 6 7 8 9 90

80

70 65

60

50

40

30

20

10

0

1 64 62 59 55 50

43

30

15 2 3 4 5 Figure 2A and 2B

(Hours on Horizontal Axes; MU on Vertical Axes) 6 7 8 9 10 Decision Rule with N

Choices (No Scarcity) If time is not scarce, consume until

fully satiated from each choice: MU1/hr=0 & MU2/hr=0 & MU3/hr=0 &...& MUn/hr=0 If consuming a good, $ replaces

time: MU1/$=0 & MU2/$=0 &...& MUn/$=0

Decision rule:

MU1.= MU2=MU3=â€¦â€¦â€¦=MUn=0. (Note: Can drop unit of resource) Ex. 2: Decision With N

Options and Scarcity Must find optimal allocation -allocation of scarce resources that

maximizes oneâ€™s total utility. Back to Ex. 2: Suppose you have only

10 hours to spend between both

activities. Find the optimal allocation

of your 10 hours. Ex 2: Decision With N

Options and Scarcity

Activity 1 Activity 2

Hrs MU1 TU1 MU2 TU2

1

2

3

4

5

6

7

8

9

10 90

81

70

50

25

0 90

171

241

291

316

316 65

64

62

59

55

50

43

30

15

0 65

129

191

250

305

355

398

428

443

0 Allocation: 10 Hours

H1, H2 TU1+TU2=

Net

TU

Gains/ Losses Decision Rule with N

Choices and Scarcity Equal Marginal Principle â€“ the best

allocation is always found where the

marginal utilities are equal across

options. Decision Rule: MU1/unit = MU2/unit =â€¦...= MUn/unit = X.

Note: X>0 implies scarcity; may drop X and

unit. Adding Production

into Decision Model

How should we best use our

productive resources (such as labor)? Point of production: We produce to

consume and consume to maximize

utility. Thus, we produce to maximize

our utility. Must decide optimal allocation of our

productive resources. Adding Production

into Decision Model Marginal Product (MP) â€“ a change in output

(Q) due to each additional unit of a

resource.

MP (of labor, N) = Î”Q/Î”N

o Assume MP diminishes.

Value of the Marginal Product (V) â€“ can be

measured as the utility derived from each

additional unit of a productive resource. Combines MP and MU Ex. 3: Calculating Value

of the Marginal Product

Max goes fishing every weekend.

Table A: Marginal product for each of his

labor hours spent fishing

o Table B: Maxâ€™s marginal utility derived

from each fish he consumes

o Table C: Fill in Max's value of the

marginal product (V) for each hour spent

fishing.

o Ex. 3: Calculating Value

of the Marginal Product Ex. 3: Calculating Value

of the Marginal Product Decision Rule:

Production of One Good In ex. 3, there is only one good (fish)

to produce. Assuming Max does not

face scarcity, the only decision is

when to stop fishing. Decision Rule: V=0

Produce until the value for an additional unit of a productive resource equals zero Ex. 4: Decision to

Produce N Options

On camping trips, Joe does the

following daily tasks: fishes, chops

firewood, gathers berries, and

fetches water. If Joe is not

constrained by time, then:

VFish= VWood= Vcooks=VCleans=0.

Use the information in the table on next

slide to find his satiation point. Ex. 4: Decision to

Produce N Options

Table 4. J oeâ€™s Value of the Marginal Product (V) for

Daily Tasks

(Total Utility in Parenthesis)

V

V

V

Labor

V

Picking

Chopping Cleaning

Hours

Fishing

Berries

Firewood Campsite

1st

90 (90)

40 (40)

40 (40)

180 (180)

2nd

160 (250)

50 (90)

60 (100)

60 (240)

3rd

180 (430) 150 (240) 30 (130)

10 (250)

4th

60 (490)

170 (410) 10 (140)

0 (250)

5th

20 (510)

60 (470)

5 (145)

0 (250)

6th

0 (510)

5 (475)

0 (145)

0 (250)

7th

0 (510)

0 (475)

0 (145)

0 (250) Decision Rule with

Production (No Scarcity)

If Joe does not face scarcity, then he

needs to decide when to stop

producing. Joe will stop at the point where there is

no additional utility to be gained. Decision Rule: V1= V2= V3=â€¦â€¦â€¦â€¦..= Vn=0. Ex. 4: Produce N

Options and Scarcity

Back to Ex. 4:

â€¢ Is it reasonable to believe Joe can

reach his satiation point each day? â€¢ If Joe is constrained by 13 hours of

daylight, how should he allocate his

time? â€¢ What if Joe has 14 hours of daylight? Several Options,

Production, and Scarcity

The optimal allocation is reached

when there is no other opportunity

that offers higher utility. Decision rule:

V1= V2= V3=â€¦â€¦â€¦..= Vn=X (X>0). If constraints change, must find a

new allocation. Decisions with Future

Consequences Our important decisions in life tend to

be intertemporal-- have

consequences across time, such as

the decision to go college. Two concepts aid in decisions that

affect our future: Present Value and

Discount rate. Decisions with Future

Consequences

Present Value (PV) -- value of future

utility put into todayâ€™s value -- allows

comparisons across time. Discount rate (DR)â€“ measures oneâ€™s

willingness to wait for future utility.

-- Low DR - more willing to wait.

-- High DR - less willing to wait. Discount rate can change overtime. Decision Rule For

Intertemporal Choices

Decision rule:

PV1 = PV2 = PV3 =â€¦â€¦â€¦.= PVn. V: value of marginal product â€“

utility derived from each unit of a

productive resource P: present value â€“ todayâ€™s value

of future utility Adding Risk to the

Decision Rule Risks (E) -- events that may affect oneâ€™s

decision; given the individualâ€™s perceived

probability

Decision rule:

EPV1 = EPV2 = EPV3 =â€¦â€¦= EPVn.

â€œExpected Present Valueâ€

V: value of MP â€“ utility derived from resources

P: present value â€“ value of future utility

E: expected â€“ adjustment for perceived risk

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