© 2009 Pearson Education Canada 3/1 Chapter 3 Demand Theory

© 2009 Pearson Education Canada 3/2 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. p 1 x 1 + p 2 x 2 ≤ M

© 2009 Pearson Education Canada 3/3 Figure 3.1 Attainable consumption bundles

© 2009 Pearson Education Canada 3/4 Opportunity Cost, Real Income and Relative Prices  Rewriting the budget constraint by solving for X 2 gives: x 2 = M/p 2 – (p 1 /p 2 )x 1 Where: M/p 2 is real income P 1 /P 2 is the relative price The relative price shows that the opportunity cost of good 1 is P 1 /P 2 units of good 2. P 1 /P 2 is the absolute value of the slope of the budget line.

© 2009 Pearson Education Canada 3/5 Endowments Rather Than Money  Sometimes an endowment of goods is assumed rather than cash.  Sally owns apples x 1 0 and eggs x 2 0.  Her budget constraint is: p 1 x 1 + p 2 x 2 ≤ p 1 x p 2 x 2 0 p 1 x 1 + p 2 x 2 ≤ p 1 x p 2 x 2 0  Solving for x 2: x 2 = (p 1 x p 2 x 2 0) /p 2 – (p 1 /p 2 )/x 1 x 2 = (p 1 x p 2 x 2 0) /p 2 – (p 1 /p 2 )/x 1 As before, the budget constraint depends upon relative prices and real income (the endowment).

© 2009 Pearson Education Canada 3/6 Figure 3.2 The budget line with endowments

© 2009 Pearson Education Canada 3/7 The Choice Problem  The non-satiation assumption implies that utility maximizing consumption lies on the budget line.  The consumer choice problem is: maximize U(x 1, x 2 ) by choice of x 1 & x 2, subject to constraint p 1 x 1 + p 2 x 2 = M

© 2009 Pearson Education Canada 3/8 The Choice Problem  In principle we refer to the solution (x 1 *, x 2 * ) as endogenous variables, as these variables are determined within the model.  The actual values of X 1 * and X 2 * depend on the exogenous variables in the model, (p 1, p 2 and M) and on the specific form of the utility function.

© 2009 Pearson Education Canada 3/9 Figure 3.3 Non-satiation and the utility- maximizing consumption bundle

© 2009 Pearson Education Canada 3/10 Demand Functions X 1 * = D 1 (p 1, p 2, M) X 2 * = D 2 (p 1, p 2, M)  These demand function equations simply say that the choice of X 1 * and X 2 * depend upon the prices of all items in the consumption bundle and the budget devoted to that bundle.

© 2009 Pearson Education Canada 3/11 Anna’s optimal choice when both goods are perfect substitutes

© 2009 Pearson Education Canada 3/12 Graphic Analysis of Utility Maximization  Assume indifference curves are smooth and strictly convex.  Interior solutions are 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.

© 2009 Pearson Education Canada 3/13 Interior Solution  An interior solution is described by: 1. P 1 x 1 * + P 2 x 2 * Ξ M, the optimal bundle lies on the budget line. 2. MRS(X 1 *, X 2 * ) Ξ P 1 /P 2, the slope of the indifference curve equals the slope of the budget line at the optimal bundle.

© 2009 Pearson Education Canada 3/14 Figure 3.5 The utility-maximizing consumption bundle

© 2009 Pearson Education Canada 3/15 Figure 3.6 Essential goods

© 2009 Pearson Education Canada 3/16 Corner Solutions  A corner solution 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 X 2 axis, the budget line is steeper than the indifference curve, only good 2 will be purchased.

© 2009 Pearson Education Canada 3/17 Figure 3.7 Inessential goods

© 2009 Pearson Education Canada 3/18 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 3.8).

© 2009 Pearson Education Canada 3/19 Figure 3.8 Excise versus lump-sum taxes

© 2009 Pearson Education Canada 3/20 Figure 3.9 Cash transfer versus in-kind transfers

© 2009 Pearson Education Canada 3/21 Figure 3.10 Optimal consumption with endowments

© 2009 Pearson Education Canada 3/22 Figure 3.11 Normal and inferior goods

© 2009 Pearson Education Canada 3/23 Figure 3.12 Engel curves

© 2009 Pearson Education Canada 3/24 Figure 3.13 The consumption response to a change in the price of another good

© 2009 Pearson Education Canada 3/25 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 p 1 or p 2.  Note that when p 1 changes, M and p 2 are assumed to be constant. Likewise if p 2 were to change, M and p 1 are assumed to be constant.

© 2009 Pearson Education Canada 3/26 Figure 3.14 The price-consumption path and the demand function

© 2009 Pearson Education Canada 3/27 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.

© 2009 Pearson Education Canada 3/28 Figure 3.15 The need for a unit-free measure of responsiveness

© 2009 Pearson Education Canada 3/29 Own-Price Elasticity  Own-price elasticity ( E ll ) relates to how much the one good changes when its own price changes.  E ll = % change in x 1 / % change in P 1 OR

© 2009 Pearson Education Canada 3/30 Elasticity  If we allow changes in the exogenous variables to approach zero we obtain marginal or point elasticity.

© 2009 Pearson Education Canada 3/31 Elasticity  Arc elasticity measures discrete changes in x 1 when there is a discrete change in p 1,p 2 or M).  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.

© 2009 Pearson Education Canada 3/32 Income Elasticity  The income elasticity of demand is the elasticity of quantity consumed per capita with respect to income per capita.

© 2009 Pearson Education Canada 3/33 Income Elasticity Formula

© 2009 Pearson Education Canada 3/34 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 p 2.

© 2009 Pearson Education Canada 3/35 Cross Price Elasticity Formula