Eaton Micro 6e Ch03

© 2005 Pearson Education Canada Inc.3.1

Chapter 3Chapter 3

Demand TheoryDemand Theory


The Budget ConstraintThe Budget Constraint

Attainable consumption bundles are Attainable consumption bundles are bundles that the consumer can afford bundles that the consumer can afford to buy.to buy.

Attainable consumption bundles Attainable consumption bundles satisfy the following inequality known satisfy the following inequality known as the budget constraint.as the budget constraint.

pp11xx11 ++ pp22xx22 ≤ M ≤ M


Figure 3.1 Attainable consumption bundlesFigure 3.1 Attainable consumption bundles


Opportunity Cost, Real Income and Opportunity Cost, Real Income and Relative PricesRelative Prices

Rewriting the budget constraint by solving for XRewriting the budget constraint by solving for X2 2

gives:gives:x2 = M/p2 – (p1/p2)x1

Where:Where: M/pM/p2 2 is real incomeis real income

PP11/P/P2 2 is the relative priceis the relative price

The relative price shows that theThe relative price shows that the

opportunity cost of good 1 is Popportunity cost of good 1 is P11/P/P2 2 units of units of

good 2. Pgood 2. P11/P/P22 is the absolute value of the slope of is the absolute value of the slope ofthe budget line.the budget line.


Endowments Rather Than MoneyEndowments Rather Than Money Sometimes an endowment of goods is Sometimes an endowment of goods is

assumed rather than cash.assumed rather than cash. Sally owns apples xSally owns apples x11

0 0 and eggs xand eggs x2200..

Her budget constraint is:Her budget constraint is:

pp11xx11 ++ pp22xx22 ≤ p ≤ p11xx110 + 0 + pp22xx22

00

Solving for Solving for xx2:2:

xx22 = (p = (p11xx110 + 0 + pp22xx22

0)0)/p/p2 2 – (p– (p11/p/p22)/x)/x11

As before, the budget constraint depends upon relative As before, the budget constraint depends upon relative

prices and real income (the endowment).prices and real income (the endowment).


Figure 3.2 The budget line with endowmentsFigure 3.2 The budget line with endowments


The Choice ProblemThe Choice Problem

The non-satiation assumption implies The non-satiation assumption implies that utility maximizing consumption that utility maximizing consumption lies on the budget line.lies on the budget line.

The consumer choice problem is:The consumer choice problem is:maximize U(xmaximize U(x11, x, x22) by choice of x) by choice of x1 1 & x& x22

subject to constraint psubject to constraint p11xx11 ++ pp22xx22 = M = M


Figure 3.3 Nonsatiation and the utility-Figure 3.3 Nonsatiation and the utility-maximizing consumption bundlemaximizing consumption bundle


Demand FunctionsDemand Functions

XX11* * = D= D11(p(p11,p,p22, M), M)

XX22* * = D= D22(p(p11,p,p22, M), M)

These equations simply say that the These equations simply say that the

choice of Xchoice of X11** and X and X22

* * depend upon the depend upon the prices of all items in the consumption prices of all items in the consumption bundle and the budget devoted to that bundle and the budget devoted to that bundle.bundle.


Graphic Analysis of Utility Graphic Analysis of Utility MaximizationMaximization

Assume indifference curves are Assume indifference curves are smooth and strictly convex.smooth and strictly convex.

Interior solution is where quantities Interior solution is where quantities of both goods are positive.of both goods are positive.

Corner solution is one where the Corner solution is one where the quantity of one good is positive and quantity of one good is positive and the quantity of the other is zero.the quantity of the other is zero.


Interior SolutionInterior Solution

An interior solution is described by:An interior solution is described by:

1.1. PP11xx11** ++ PP22xx22

** ΞΞ M, the optimal bundle M, the optimal bundle lies on the budget line.lies on the budget line.

2.2. MRS(XMRS(X11**, X, X22

**) ) ΞΞ P P11/P/P2 2 , the slope of , the slope of the indifference curve equals the the indifference curve equals the slope of the budget line at the slope of the budget line at the optimal bundle.optimal bundle.


Figure 3.4 The utility-maximizing Figure 3.4 The utility-maximizing consumption bundleconsumption bundle


Figure 3.5 Essential goodsFigure 3.5 Essential goods


Corner SolutionsCorner Solutions

A corner solutions graphically lies not A corner solutions graphically lies not in the interior between the two axis, in the interior between the two axis, but at a corner where the budget line but at a corner where the budget line intersects one of the two axes.intersects one of the two axes.

For example, if at the point where For example, if at the point where the budget line intersects the Xthe budget line intersects the X22 axis, axis, the budget line is steeper than the the budget line is steeper than the indifference curve, only good 2 will indifference curve, only good 2 will be purchased.be purchased.


Figure 3.6 Inessential goodsFigure 3.6 Inessential goods


Excise Tax Versus Lump-Sum TaxExcise Tax Versus Lump-Sum Tax

Given a choice between a lump sum Given a choice between a lump sum tax and an excise tax that raises the tax and an excise tax that raises the same revenue, the consumer will same revenue, the consumer will choose the lump sum tax (see Figure choose the lump sum tax (see Figure 3.7).3.7).


Figure 3.7 Excise versus lump-sum taxesFigure 3.7 Excise versus lump-sum taxes


Figure 3.8 Cash transfer versus Figure 3.8 Cash transfer versus in-kind transfersin-kind transfers


Figure 3.9 Optimal consumption Figure 3.9 Optimal consumption with endowmentswith endowments


Figure 3.10 Normal and inferior goodsFigure 3.10 Normal and inferior goods


Figure 3.11 Engel curvesFigure 3.11 Engel curves


Figure 3.12 The consumption response to a Figure 3.12 The consumption response to a

change in the price of another goodchange in the price of another good


Consumption Response to a Consumption Response to a Change in PriceChange in Price

The price-consumption path connects The price-consumption path connects the utility maximizing bundles that the utility maximizing bundles that arise from a change in the price of parise from a change in the price of p1 1

or por p2.2.

Note that when pNote that when p1 1 changes, M and pchanges, M and p2 2

are assumed to be constant. Likewise are assumed to be constant. Likewise if pif p2 2 were to change, M and pwere to change, M and p1 1 are are assumed to be constant.assumed to be constant.


Figure 3.13 The price-consumption Figure 3.13 The price-consumption path and the demand functionpath and the demand function


ElasticityElasticity

Elasticity is a measure of Elasticity is a measure of responsiveness of the quantity responsiveness of the quantity demanded for one good to a change demanded for one good to a change in one of the exogenous variables: in one of the exogenous variables: price or income.price or income.

Arc elasticity measures discrete Arc elasticity measures discrete changes in xchanges in x11 when there is a when there is a discrete change in pdiscrete change in p11,p,p22 or M). or M).


ElasticityElasticity By allowing changes in the By allowing changes in the

exogenous variables to approach exogenous variables to approach zero gives marginal or point zero gives marginal or point elasticity.elasticity.

Price elasticity of demand for a good Price elasticity of demand for a good is the elasticity of quantity consumed is the elasticity of quantity consumed per capita with respect to the price of per capita with respect to the price of the good.the good.


Price Elasticity FormulaPrice Elasticity Formula

)/)(/( 111111 xppxE


Income ElasticityIncome Elasticity

The income elasticity of demand is The income elasticity of demand is the elasticity of quantity consumed the elasticity of quantity consumed per capita with respect to income per per capita with respect to income per capita.capita.


Income Elasticity FormulaIncome Elasticity Formula

)/)(/( 111 xMMxE m


Cross Price ElasticityCross Price Elasticity

The cross price elasticity of demand The cross price elasticity of demand for good 1 with respect to the price for good 1 with respect to the price of good 2, is the elasticity of per of good 2, is the elasticity of per capita consumption of good 1 with capita consumption of good 1 with respect to prespect to p22. .


Cross Price Elasticity FormulaCross Price Elasticity Formula

)/)(/( 12211 xppxE m

Eaton Micro 6e Ch03

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