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The Economic Theory of Choice
Lecture 1.5: The Economic Theory of ChoiceInvestment Analysis
Fall 2012
Anisha Ghosh
Tepper School of BusinessCarnegie Mellon University
November 1, 2012
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.
Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
Th E i Th f Ch i
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
Th E i Th f Ch i
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
The Economic Theory of Choice
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The Economic Theory of Choice
Two Key Ingredients
Any decision problem involves:
Identification of theset of feasible alternatives.Aselection criterionfor choosing among the availablealternatives.And, finally, thesolutionof the problem.
The individual solutions can often be aggregated to
describe equilibrium conditions that prevail in the
marketplace.
We first consider a decision problem under certainty.Later in the course, we will study the more realistic case of
the optimal selection of risky assets.
The Economic Theory of Choice
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The Economic Theory of Choice
Example
An investor will receive an income of $10, 000 at the end ofyears 1 and 2 with certainty.
The only investment available is a savings account withinterest rate r=5%. The investor can also borrow money at
a 5% rate.
Question
How much should the investor save and how much should heconsume each year?
The Economic Theory of Choice
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The Economic Theory of Choice
Example
An investor will receive an income of $10, 000 at the end ofyears 1 and 2 with certainty.
The only investment available is a savings account withinterest rate r=5%. The investor can also borrow money at
a 5% rate.
Question
How much should the investor save and how much should heconsume each year?
The Economic Theory of Choice
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The Economic Theory of Choice
Example
An investor will receive an income of $10, 000 at the end ofyears 1 and 2 with certainty.
The only investment available is a savings account withinterest rate r=5%. The investor can also borrow money at
a 5% rate.
Question
How much should the investor save and how much should heconsume each year?
The Economic Theory of Choice
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The Economic Theory of Choice
The Opportunity SetThe options open to the investor
The set of feasible consumption patterns in periods 1 and 2 lie along
the straight line known as theopportunity set.
The Economic Theory of Choice
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y
The Opportunity SetThe options open to the investor
Point B the investor saves nothing and consumes$10, 000 in eachperiod.
Point A the investor saves all his income and consumes nothing in
period 1 in the second period, he consumes:
C2 = 10, 000
Period 2s income
+ 10, 000
Period 1s income
+ 500
interest on period 1s income
= $20, 500
Point C the investor consumes everything in period 1 and nothing in
the second period his consumption in period 1 is:
C1 = 10, 000
Period 1s income
+ 10, 000
1.05
Maximum amount that can be borrowed against Period 2s income
= $19, 524
The Economic Theory of Choice
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y
The Opportunity SetThe options open to the investor
Point B the investor saves nothing and consumes$10, 000 in eachperiod.
Point A the investor saves all his income and consumes nothing in
period 1 in the second period, he consumes:
C2 = 10, 000
Period 2s income
+ 10, 000
Period 1s income
+ 500
interest on period 1s income
= $20, 500
Point C the investor consumes everything in period 1 and nothing in
the second period his consumption in period 1 is:
C1 = 10, 000
Period 1s income
+ 10, 000
1.05
Maximum amount that can be borrowed against Period 2s income
= $19, 524
The Economic Theory of Choice
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The Opportunity SetThe options open to the investor
Point B the investor saves nothing and consumes$10, 000 in eachperiod.
Point A the investor saves all his income and consumes nothing in
period 1 in the second period, he consumes:
C2 = 10, 000
Period 2s income
+ 10, 000
Period 1s income
+ 500
interest on period 1s income
= $20, 500
Point C the investor consumes everything in period 1 and nothing in
the second period his consumption in period 1 is:
C1 = 10, 000
Period 1s income
+ 10, 000
1.05
Maximum amount that can be borrowed against Period 2s income
= $19, 524
The Economic Theory of Choice
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The Opportunity SetThe options open to the investor
The set of feasible consumption patterns in periods 1 and 2 lie along
the straight line known as theopportunity set.
The Economic Theory of Choice
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The Opportunity Set contd.The options open to the investor
The set of feasible consumption patterns in periods 1 and 2 lie along
the straight line ABC.
This is because the amount consumed in period 2 is the income,
$10, 000, earned in period 2 plus the period 2 value of the savings inperiod 1:
C2 = 10, 000+ (10, 000C1) (1.05)
= 20, 500 1.05C1
This is the equation of the straight line in Figure 1.1
The Economic Theory of Choice
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The Opportunity Set contd.The options open to the investor
The set of feasible consumption patterns in periods 1 and 2 lie along
the straight line ABC.
This is because the amount consumed in period 2 is the income,
$10, 000, earned in period 2 plus the period 2 value of the savings inperiod 1:
C2 = 10, 000+ (10, 000C1) (1.05)
= 20, 500 1.05C1
This is the equation of the straight line in Figure 1.1
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The Economic Theory of Choice
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Definitions
PRESENT VALUE (PV)
The amount you realize at the initial date borrowing against
all future receipts. The PVof a cash flow of $Ctreceived atthe end of year t is
Ct(1 +r)t
FUTURE VALUE (FV)
The amount you realize at the terminal date lending allintermediate cash flows. The FVof$100 at the end of yeart is
100(1 +r)t
The Economic Theory of Choice
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Indifference Curves
Indifference curves represent the investors preference for consumption
in the two periods.
The Economic Theory of Choice
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Indifference Curves contd.
The investor is equally happy with or "indifferent" between all possible
patterns of consumption along the same indifference curve.
The investor is assumed to prefer more to less he prefers to be on
indifference curves higher up and to the right.
The indifference curves are convex each additional dollar of
consumption forgone in period 1 requires greater consumption in period
2 in order for the investor to remain indifferent.
The Economic Theory of Choice
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Indifference Curves contd.
The investor is equally happy with or "indifferent" between all possible
patterns of consumption along the same indifference curve.
The investor is assumed to prefer more to less he prefers to be on
indifference curves higher up and to the right.
The indifference curves are convex each additional dollar of
consumption forgone in period 1 requires greater consumption in period
2 in order for the investor to remain indifferent.
The Economic Theory of Choice
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Indifference Curves contd.
The investor is equally happy with or "indifferent" between all possible
patterns of consumption along the same indifference curve.
The investor is assumed to prefer more to less he prefers to be on
indifference curves higher up and to the right.
The indifference curves are convex each additional dollar of
consumption forgone in period 1 requires greater consumption in period
2 in order for the investor to remain indifferent.
The Economic Theory of Choice
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The Solution
The optimum consumption pattern for the investor is determined by the point
at which an indifference curve is tangent to the opportunity set.