Transcript Chapter 3 PowerPoint Presentation

Chapter 3
Demand Theory
3.1
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The Budget Constraint
 Attainable
consumption bundles are
bundles that the consumer can afford
to buy.
 Attainable consumption bundles
satisfy the following inequality known
as the budget constraint.
p1x1 + p2x2 ≤ M
3.2
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Figure 3.1 Attainable consumption bundles
3.3
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Opportunity Cost, Real Income and
Relative Prices

Rewriting the budget constraint by solving for X2
gives:
x2 = M/p2 – (p1/p2)x1
Where:
M/p2 is real income
P1/P2 is the relative price
The relative price shows that the
opportunity cost of good 1 is P1/P2 units of
good 2. P1/P2 is the absolute value of the slope of
the budget line.
3.4
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Endowments Rather Than Money
Sometimes an endowment of goods is
assumed rather than cash.
 Sally owns apples x10 and eggs x20.
 Her budget constraint is:

p1x1 + p2x2 ≤ p1x10 + p2x20
 Solving for x2:
x2 = (p1x10 + p2x20)/p2 – (p1/p2)/x1
As before, the budget constraint depends upon relative
prices and real income (the endowment).
3.5
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Figure 3.2 The budget line with endowments
3.6
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The Choice Problem
 The
non-satiation assumption implies
that utility maximizing consumption
lies on the budget line.
 The consumer choice problem is:
maximize U(x1, x2) by choice of x1 & x2
subject to constraint p1x1 + p2x2 = M
3.7
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Figure 3.3 Nonsatiation and the utilitymaximizing consumption bundle
3.8
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Demand Functions
X1* = D1(p1,p2, M)
X2* = D2(p1,p2, M)
These equations simply say that the
choice of X1* and X2* depend upon the
prices of all items in the consumption
bundle and the budget devoted to that
bundle.
3.9
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Graphic Analysis of Utility
Maximization
 Assume
indifference curves are
smooth and strictly convex.
 Interior solution is where quantities
of both goods are positive.
 Corner solution is one where the
quantity of one good is positive and
the quantity of the other is zero.
3.10
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Interior Solution

1.
2.
3.11
An interior solution is described by:
P1x1* + P2x2* Ξ M, the optimal
bundle lies on the budget line.
MRS(X1*, X2*) Ξ P1/P2 , the slope of
the indifference curve equals the
slope of the budget line at the
optimal bundle.
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Figure 3.4 The utility-maximizing
consumption bundle
3.12
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Figure 3.5 Essential goods
3.13
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Corner Solutions
A
corner solutions graphically lies not
in the interior between the two axis,
but at a corner where the budget line
intersects one of the two axes.
 For example, if at the point where
the budget line intersects the X2
axis, the budget line is steeper than
the indifference curve, only good 2
will be purchased.
3.14
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Figure 3.6 Inessential goods
3.15
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Excise Tax Versus Lump-Sum Tax
 Given
a choice between a lump sum
tax and an excise tax that raises the
same revenue, the consumer will
choose the lump sum tax (see Figure
3.7).
3.16
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Figure 3.7 Excise versus lump-sum taxes
3.17
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Figure 3.8 Cash transfer versus
in-kind transfers
3.18
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Figure 3.9 Optimal consumption
with endowments
3.19
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Figure 3.10 Normal and inferior goods
3.20
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Figure 3.11 Engel curves
3.21
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Figure 3.12 The consumption response to a
change in the price of another good
3.22
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Consumption Response to a
Change in Price
 The
price-consumption path connects
the utility maximizing bundles that
arise from a change in the price of p1
or p2.
 Note that when p1 changes, M and p2
are assumed to be constant.
Likewise if p2 were to change, M and
p1 are assumed to be constant.
3.23
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Figure 3.13 The price-consumption
path and the demand function
3.24
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Elasticity
 Elasticity
is a measure of
responsiveness of the quantity
demanded for one good to a change
in one of the exogenous variables:
price or income.
 Arc elasticity measures discrete
changes in x1 when there is a
discrete change in p1,p2 or M).
3.25
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Elasticity
 By
allowing changes in the
exogenous variables to approach zero
gives marginal or point elasticity.
 Price elasticity of demand for a good
is the elasticity of quantity consumed
per capita with respect to the price of
the good.
3.26
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Price Elasticity Formula
E11  (x1 / p1)( p1 / x1)
3.27
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Income Elasticity
 The
income elasticity of demand is
the elasticity of quantity consumed
per capita with respect to income per
capita.
3.28
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Income Elasticity Formula
E1m  (x1 / M )( M / x1)
3.29
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Cross Price Elasticity
 The
cross price elasticity of demand
for good 1 with respect to the price
of good 2, is the elasticity of per
capita consumption of good 1 with
respect to p2.
3.30
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Cross Price Elasticity Formula
E1m  (x1 / p 2)( p 2 / x1)
3.31
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