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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

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Chapter 2:
Individual Choice
Purpose: Develop a model to
describe how individuals make
choices….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) – an individual’s total
satisfaction/ happiness
- Utils: measure of utility.
Marginal Utility (MU) – a change in TU
resulting from a change in the quantity
(Q)…… Formula: MU = ΔTU/ΔQ.
Diminishing MU – 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 Jack’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=………=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 one’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 – the best
allocation is always found where the
marginal utilities are equal across
options. Decision Rule: MU1/unit = MU2/unit =…...= 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) – a change in output
(Q) due to each additional unit of a
resource.
MP (of labor, N) = ΔQ/ΔN
o Assume MP diminishes.
Value of the Marginal Product (V) – 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: Max’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 oe’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=…………..= Vn=0. Ex. 4: Produce N
Options and Scarcity
Back to Ex. 4:
• Is it reasonable to believe Joe can
reach his satiation point each day? • If Joe is constrained by 13 hours of
daylight, how should he allocate his
time? • 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=………..= 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 today’s value -- allows
comparisons across time. Discount rate (DR)– measures one’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 =……….= PVn. V: value of marginal product –
utility derived from each unit of a
productive resource P: present value – today’s value
of future utility Adding Risk to the
Decision Rule Risks (E) -- events that may affect one’s
decision; given the individual’s perceived
probability
Decision rule:
EPV1 = EPV2 = EPV3 =……= EPVn.
“Expected Present Value”
V: value of MP – utility derived from resources
P: present value – value of future utility
E: expected – adjustment for perceived risk

 


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