Chapter 4

CHAPTER 4

CONSUMER CHOICE

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Budget Constraint

Budget constraint

Set of baskets that a consumer can purchase with a limited amount of income

Budget line

Set of baskets that a consumer can purchase when spending all of his or her available income

Pxx + Pyy = I

Slope of budget line

How many units of y a consumer must forgo to obtain an additional unit of x

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Budget Constraint (cont.)

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Location of budget line shows what the income level is

Increase in income will shift the budget line to the right

More of each product becomes affordable

Slope remains unchanged

Decrease in income will shift the budget line to the left

Less of each product becomes affordable

Slope remains unchanged

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Increase in the price of x

Moves the intercept on x-axis toward the origin

Slope increases

Consumers purchasing power declines

Decrease in the price of x

Moves the intercept on x-axis away from the origin

Slope reduces

Consumers purchasing power increases

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Optimal Choice

Optimal choice

Optimal amount of each good to purchase

Maximise satisfaction (utility)

Live within budget constraint

Consumer chooses the basket that maximizes his satisfaction given the constraint that his budget

imposes

Consumer problem

max U(x,y)

subject to: Pxx + Pyy = I

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Optimal Choice (cont.)

Interior optimum

The optimal consumption basket is at a point where the indifference curve is just tangent to the

budget line

MUx / MUy = Px / Py

MUx / Px = MUy / Py The rate at which the consumer would be willing to

exchange X for Y is the same as the rate at which they

are exchanged in the marketplace

The extra utility per dollar spent on good x is equal to the extra utility per dollar spent on good y

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Utility maximisation

max Utility = U(x,y)

subject to: Pxx + Pyy = I

Exogenous: Px, Py, I; Endogenous: x, y, U

Expenditure minimisation

min expenditure = Pxx + Pyy

subject to: U(x,y) = U

Exogenous: Px, Py, U; Endogenous: x, y

Both are dual to one another

Lead to same utility and expenditure 13


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Corner points

A solution to the consumers optimal choice problem at which some good is not being

consumed at all

E.g. not all consumers purchase tobacco and alcohol

The optimal basket lies on an axis

Budget line is not tangent to an indifference curve at the optimal basket

MUx / MUy > Px / Py: Consume all the X and zero Y

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Coupons & Cash Subsidies

Composite good

A good that represents the collective expenditure on every other good except the commodity being

considered

Income subsidy

Increase in income shifts the budget line

Housing voucher

Budget line for consumer increases

Maximum amount spend on other goods still the same

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Coupons & Cash Subsidies (cont.)

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Coupons & Cash Subsidies (cont.)

24

Joining A Club

Club membership

Let consumer purchases goods and services at a discount

Need to pay a membership fee

E.g. joining a CD club

Able to buy more CDs due to price reduction

Buy less composite goods because have less income

New and old budget lines intersect indicates that consumer is no worse-off

Increase utility

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Joining A Club (cont.)

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Borrowing & Lending

Borrow

Able to spend more on the composite goods this year but decrease consumption next year

I1 + I2 / (1+r)

Lend

Able to spend more on the composite goods next year

Decrease consumption this year

I2 + I1 (1+r)

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Borrowing & Lending (cont.)

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Quantity Discounts

Discount

E.g. electricity

With discount consumer can purchase more electricity

The budget line become flatter after certain amount of consumption

Slope reduces

Consumer has a higher level of satisfaction

Higher indifference curve

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Quantity Discounts (cont.)

30

Revealed Preference

Can we infer preferences from purchasing behaviour?

Suppose that preferences are not known

Revealed preference

To analyse consumers ordinal ranking of baskets by observing how his or her choices of baskets

change as prices and income vary

Consumers choices of baskets reveal information about his preferences

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Revealed Preference (cont.)

If A is purchased, it must be preferred to all other affordable bundles

All baskets to the Northeast of A must be preferred to A

A C, C > B, A > B

A is strongly preferred to any basket on the segment EH because A > B

This gives us a narrower range over which indifference curve must lie

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At initial price

Basket 1 is more preferred than basket 2

Assuming:

Pxx1 + Pyy1 Pxx2 + Pyy2

At new price

Basket 2 is more preferred than basket 1

Assuming:

Pxx2 + Pyy2 Pxx1 + Pyy1

At new price, basket 2 cannot cost more than basket 1, otherwise basket 1 is chosen

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Chapter 4

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