Microeconomics: Income and Substitution Effects on Demand, Study notes of Construction

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INCOME AND

SUBSTITUTION EFFECTS

[See Chapter 5 and 6]

Two Demand Functions

• Marshallian demand xi ( p 1 ,…, pn , m ) describes

how consumption varies with prices and income.

• Obtained by maximizing utility subject to the budget constraint.
• Hicksian demand hi ( p 1 ,…, pn , u ) describes how

consumption varies with prices and utility.

• Obtained by minimizing expenditure subject to the utility constraint.

Changes in Income

• An increase in income shifts the budget

constraint out in a parallel fashion

• Since p 1 / p 2 does not change, the

optimal MRS will stay constant as the

worker moves to higher levels of utility.

Increase in Income

• If both x 1 and x 2 increase as income

rises, x 1 and x 2 are normal goods

Quantity of x 1

Quantity of x 2

C

U 3

B

U 2

A U 1

As income rises, the individual chooses to consume more x 1 and x 2

Changes in Income

• The change in consumption caused by a change

in income from m to m’ can be computed using

the Marshallian demands:

• If x 1 ( p 1 , p 2 , m ) is increasing in m, i.e. x 1 / m  0,

then good 1 is normal.

• If x 1 ( p 1 , p 2 , m ) is decreasing in m, i.e. x 1 / m < 0,

then good 1 is inferior.

 x 1  x 1 ( p 1 , p 2 , m ') x 1 ( p 1 , p 2 , m )

Engel Curves

• The Engel Curve plots demand for xi against

income, m.

Changes in a Good’s Price

• A change in the price of a good alters

the slope of the budget constraint

• When the price changes, two effects

come into play

• substitution effect
• income effect

• We separate these effects using the

Slutsky equation.

Changes in a Good’s Price

Quantity of x 1

Quantity of x 2

U 1

A

Suppose the consumer is maximizing utility at point A.

U 2

B

If p 1 falls, the consumer will maximize utility at point B.

Total increase in x 1

Changes in a Good’s Price

• The total change in x 1 caused by a

change in its price from p 1 to p 1 ' can be

computed using Marshallian demand:

 x 1  x 1 ( p 1 ', p 2 , m ) x 1 ( p 1 , p 2 , m )

Two Effects

• Suppose p 1 falls.

1. Substitution Effect

• The relative price of good 1 falls.
• Fixing utility, buy more x 1 (and less x 2 ).

2. Income Effect

• Purchasing power also increases.
• Agent can achieve higher utility.
• Will buy more/less of x 1 if normal/inferior.

Substitution Effect

• The substitution effect caused by a

change in price from p 1 to p 1 ' can be

computed using the Hicksian demand

function:

Sub. Effect  h 1 (^) ( p 1 ', p 2 , U ) h 1 ( p 1 , p 2 , U )

Income Effect

U 1

U 2

Quantity of x 1

Quantity of x 2

A

Now let’s keep the relative prices constant at the new level. We want to determine the change in consumption due to the shift to a higher curve

C

Income effect

B

The income effect is the movement from point C to point B

If x 1 is a normal good, the individual will buy more because “real” income increased

Increase in a Good 1’s Price

U 2

U 1

Quantity of x 1

Quantity of x 2

B

A

An increase in the price of good x 1 means that the budget constraint gets steeper

C

The substitution effect is the movement from point A to point C

Substitution effect Income effect

The income effect is the movement from point C to point B

Hicksian & Marshallian Demand

• Marshallian demand
  • Fix prices (p 1 ,p 2 ) and income m.
  • Induces utility u = v(p 1 ,p 2 ,m)
  • When we vary p 1 we can trace out Marshallian demand for good 1
• Hicksian demand (or compensated demand)
  • Fix prices (p 1 ,p 2 ) and utility u
  • By construction, h 1 (p 1 ,p 2 ,u)= x 1 (p 1 ,p 2 ,m)
  • When we vary p 1 we can trace out Hicksian demand for good 1.