Individual Consumer Choice • Utility • Preference

Individual Consumer Choice
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Utility
Preference Ranking
Budget Constraint (relative prices, market tradeoff)
Indifference Curve (marginal rate of substitution, individual tradeoff)
Price & Income Changes
Income & Substitution Effects
Demand Curve, Engel Curve
Elasticity
Applications
Bundle:
Budget Constraint:
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Income = M
Y
PX & PY
X
Y
M = $1000
X
2
PX = $1 PY = $2
More Examples:
• Food & Shelter, Corn & Barley
• Good X & Composite Good (all other goods, Money)
• Leisure vs. Work (income)
• Future Consumption vs. Present Consumption
Back to good X and good Y.
PX
or
How does the budget constraint change if……
PY
or
M
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or
Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint.
2. Draw her new budget constraint if Px falls to $10 per unit, give the equation and label the slope and intercepts.
3. Now suppose the Px rises to $30 per unit, do the same.
Y
X
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Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint
2. Draw her new budget constraint if Py falls to $5 per unit, give the equation and label the slope and intercepts.
3. Now suppose the Py rises to $20 per unit, do the same.
Y
X
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Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint.
2. Draw her new budget constraint if her weekly income rises to $2000, give the equation and label the slope and
intercepts.
3. Now suppose her weekly income falls to $500, do the same.
Y
X
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Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint.
2. Draw her new budget constraint if Px falls to $10 per unit and her weekly income rises to $2000, give the
equation and label the slope and intercepts.
3. Now suppose the Py falls to $5 per unit, do the same.
Y
X
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Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint.
2. Draw her new budget constraint if all prices double and her income also doubles, give the equation and label the
slope and intercepts.
Y
X
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Josephine has a weekly income of $1000 Units of X cost $20 each
Units of Y cost $10 each
1. Draw her budget constraint, label the slope and intercepts, and write the equation of the budget constraint.
2. Draw her new budget constraint if all prices are cut in half and her income is also cut in half, give the equation
and label the slope and intercepts.
Y
X
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Suppose we now want to leave the world of 2 goods. We can create a composite good representing all other goods.
Purchasing Power
For example:
apples
M($)
apples
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Suppose:
M = 200
Pa = $4
Pa = $2
Pa = $1
Draw Budget Constraints
M($)
apples
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Suppose:
Pa = $1
M = $50
M = $100
M = $200
Draw Budget Constraints
M($)
apples
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Quantity Discount (See HW 5)
The Gigawatt Power Company charges $0.10 per kilowatt-hour (kw hr) for the 1st 1000 kw hrs of power purchased
each month, but charges only $0.05/kw hr for all additional power consumed in the month.
Graph the budget constraint for a consumer with $400 monthly income.
monthly
income
400
300
200
100
1
2
3
4
5
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6
7
Q
1000s of kw hrs/month
Consumption Penalty (Lump Sum Tax)
The Gigawatt Power Company charges $0.10 per kilowatt-hour (kw hr) for all power consumption. Graph the
budget constraint for a consumer with $400 monthly income.
Now the government now charges a lump sum penalty of $100 for any power over 1000 kw hrs per month. Illustrate
how the budget constraint will change because of this policy.
monthly
income
400
300
200
100
1
2
3
4
5
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6
7
Q
1000s of kw hrs/month
Food Stamps (In Kind Transfer of Food)
Graph the budget constraint for a consumer with $400 monthly income where the consumer chooses between food
and all other goods and the price of food is given by Pf.
Now alter the budget constraint if the government starts a food stamp program where individuals with incomes of
$400 and under receive $100 in food stamps per month
monthly
income
500
400
300
200
100
Q
units of food
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Labor vs. Leisure
Daily Income
Labor (hours)
Leisure (hours)
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Income Taxes
reduce the net wage by some % amount
tax = t
for example 20% = 0.02
Draw the new budget constraint
Daily Income
Slope = -W
24*W
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Labor (hours)
Leisure (hours)
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AFDC (TANF)
The government provides a grant of $G per month to individuals with zero income (those who don’t work). If they
work at all, the grant is taken away dollar for dollar (a tax rate of 100% on income until the grant is taxed away)
Monthly Income
Slope = -W
Slope = 0
720*W
G
720 - G/W
Labor (hours)
720
Leisure (hours)
The grant will be completely taxed away when you have worked enough hours to pay back the amount G. $ for $
payback means you need to earn G, meaning the break even point occurs at G/W hours of work.
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Present Consumption vs. Future Consumption
Save:
Borrow:
C1
all
tomorrow
Y1 + s*(1+r)
s*(1+r)
b = borrow
C1 = Y1
s = save
b*(1+r)
Y1 - b*(1+r)
Y0 - s
C0 = Y0
Y0 + b
all today
C0
steep budget line means a lot of future income must be given up to get more present income, high interest rate.
steep budget line means a lot of future income can be earned by giving up a little present income, high interest rate.
flat budget line means a little future income must be given up to get more present income, a low interest rate.
flat budget line means only a little future income can be earned by giving up a lot present income, low interest rate.
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How does the consumer make his choice?
Maximize Utility
Choose the best bundle subject to income constraint
Marginal Utility Theory
2 goods
Equi-marginal Principle
How to choose between X & Y given a budget?
MU X
PX
MU Y
PY
Income M
X & Y
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prices & income
Problem…..how to measure Utility?
Preference Ordering: A scheme whereby the consumer ranks
Indifference Curve A set of bundles
Indifference Map: A representative sample
Important Properties
-Completeness (possible to rank all possibilities)
-More is better (non-satiation, exhaust budget)
-Transitivity A > B & B > C then A > C
A>B>C
-Convexity (mixtures are preferred to extremes, corner solutions, declining MRS)
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Completeness
Enables the consumer to rank all possible combinations of goods & services
More is Better
Other things equal, more of a good is preferred to less of a good
Non-satiation (budget constraints/disposable income)
Transitivity
If A > B &
B > C , Then
A > C (not C > A)
Steak > Hamburger > Hot Dogs
Convexity (convex to the origin)
Mixtures of goods are preferred to extremes (balance)
Declining marginal rate of substitution (MRS)
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Generating equally preferred bundles (indifference curve)
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From an identical bundle “A”
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Marginal Rate of Substitution
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Diminishing Marginal Rate of Substitution (MRS)
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Maximizing Utility Subject to a Budget Constraint
E:
A:
Recall our earlier result from choosing
MU X PX
=
MU Y
PY
F:
X&Y
MU S
P
= S
MU F PF
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Can we reconcile these two terms?
MU S PS
=
MU F PF
MRS =
∆F PS
=
∆S PF
We need to show that
MU S ∆F
=
MU F ∆S
Consider giving up Food for Shelter
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*Solution to optimal bundle may not always be a tangency
MRS < Ps/Pf : When the MRS (food for shelter) is always less than the slope of the budget constraint (price ratio)
The best the consumer can do is to buy all food and no shelter (shelter is too expensive for this consumer’s tastes)
MRS > Ps/Pf : When the MRS (food for shelter) is always more than the slope of the budget constraint (price ratio)
The best the consumer can do is to buy all shelter and no food (food is too expensive for this consumer’s tastes)
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Special Cases
Draw
1. Perfect Substitutes (1 for 1, 2 for 1, 1 for 2…..)
Constant trade off
2. Perfect Complements (1 with 1, 1 with 2, 2 with 1…..)
Consumed in fixed proportion
3. Things you don’t like at all (more is not preferred, lexicographic)
For a given amount of chocolate, you don’t care if you have 1, 2, 3, or any additional amount of broccoli
4. Normal case
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MRS = 2 (coke for Jolt)
If Pj/Pc = 4/3 = 1.33 the consumer will choose all Jolt
For example: Pj = 1.33
Pc = 1
M = $20
MRS = 2 (coke for Jolt)
If Pj/Pc < 2
If Pj/Pc > 2
If Pj/Pc = 2
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Cash Aid
vs
Food Stamps
If income is $400 or less
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$100 in Food stamps
or
$100 Cash
Consumption Today vs. Consumption Tomorrow
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