Income and Substitution Effects Engel Curves and the Slutsky Equation

Demand and income If your income is initially X1, you buy A1 apples When your income rises to X2, you buy A2 apples. To make the obvious point, demand is a function of income X2 X1 I2 I1 A1 A2

How demand rises with income Lets plot the combinations of apples and income (X) from the previous graph. A2 A1 X1 X2

How demand rises with income Lets plot the combinations of apples and income (X) from the previous graph. Connecting all possible points, we get the Engel curve, giving demand as a function of income. A2 A1 X1 X2

The Shape of the Engel Curve The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve is a straight line, the income elasticity is 1.0 X

The Shape of the Engel Curve The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve has increasing slope the elasticity is greater than 1.0 X

The Shape of the Engel Curve The shape of the Engel Curve gives us the income elasticity of demand for the good If the Engel Curve has decreasing slope the elasticity is less than 1.0 X

The Shape of the Engel Curve Of course the Engel Curve need not be so well behaved This Engel Curve corresponds to a good that is both inferior and superior, depending on income X

Income and Substitution Effects We know that both price and income influence demand.

Income and Substitution Effects We know that both price and income influence demand. A price change means an income change.

Income and Substitution Effects We know that both price and income influence demand. A price change, means an income change. You are purchasing 10 apples at $1 each. If the price falls to 50¢, you effectively get $5 more income

Income and Substitution Effects Let’s draw the indifference curves between money and apples. $ Yo I1 A Yo/pA

Income and Substitution Effects Let’s draw the indifference curves between money and apples. Your income is Yo; Apples initially cost pa $ Yo I1 A Yo/pA

Income and Substitution Effects Let’s draw the indifference curves between money and apples. Your income is Yo; Apples initially cost pa You are are on indifference curve I1. $ Yo I1 A Yo/pA

Income and Substitution Effects Suppose the price of apples drops to p*a $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects Suppose the price of apples drops to p*a The budget line rotates out and you move to indifference curve I2. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects Suppose the price of apples drops to p*a The budget line rotates out and you move to indifference curve I2. Two things have occurred: a price cut and an increase in income. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects The substitution effect $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects The substitution effect To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects The substitution effect To isolate the effect of the lower price, imagine a budget line like the red line, reflecting the lower price but tangent to the old indifference curve. The move to the red point on I1 shows the substitution effect. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects The substitution effect is always negative Diminishing MRS guarantees it $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects The substitution effect is always negative The income effect Of course, income has gone up as well, and the movement from the red point to the green point reflects that. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects We effectively break the price change down into its two components. The substitution effect The income effect. $ Yo I2 I1 A Yo/p*A Yo/pA

Income and Substitution Effects We effectively break the price change down into its two components. The substitution effect The income effect. While the substitution effect is always negative, the income effect may or not be positive $ Yo I2 I1 A Yo/p*A Yo/pA

A Summary Table

The Slutsky Equation These effects are often summarized in the Slutsky equation

The Slutsky Equation These effects are often summarized in the Slutsky equation The substitution effect shows the change in demand from a movement along the indifference curve.

The Slutsky Equation These effects are often summarized in the Slutsky equation The income effect shows the change in demand from the effective increase in income.

An Application

An Application

An Application

An Application

An Application (Q/P) = 3/(-0.05) = - 60

An Application (Q/P) = - 60 Q(Q/I) = 50 (1) = 50

-60  (Q/P)U=Constant –50 An Application (Q/P) = - 60 Q(Q/I) = 50 -60  (Q/P)U=Constant –50

-60  (Q/P)U=Constant –50 An Application -60  (Q/P)U=Constant –50 (Q/P)U=Constant = -10

A Caution The version of the Slutsky equation we use is only an approximation.

A Caution The version of the Slutsky equation we use is only an approximation. We are assuming discrete changes in price and income; the correct equation assumes infinitesimal changes.

Why spend time on this topic? Giffin Goods

Why spend time on this topic? Giffin Goods The Demand for Leisure

Why spend time on this topic? Giffin Goods The Demand for Leisure As wage rates increase, the cost of an hour of leisure increases Demand goes up because the income effect dominates the substitution effect.

Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes .

Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes Changes in the price of one brand versus changes in the prices of all brands. .

Why spend time on this topic? Giffin Goods The Demand for Leisure Different Slopes Changes in the price of one brand versus changes in the prices of all brands. Heavily purchased goods versus lightly purchased goods.

A Final Point

A Final Point The slope of the Marshallian, or uncompensated demand function

A Final Point The slope of the Marshallian, or uncompensated demand function The slope of the Hicksian, or compensated demand function. ©2003 Charles W. Upton