course: microeconomics text: varian’s intermediate microeconomics

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Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 1: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Course: Microeconomics Text: Varian’s Intermediate

Microeconomics

Page 2: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

In Chapter 6, we talk about how demand changes when price and income change individually.

In this chapter, we want to further analyze how the change in price changes the demand.

In particular, we decompose the change in quantity demanded due to price change into substitution effect and income effect.

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Page 3: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

What happens when a commodity’s price decreases? Substitution effect: the commodity is

relatively cheaper, so consumers use more of it, instead of other commodities, which are now relatively more expensive.

Income effect: the consumer’s budget of $m can purchase more than before, as if the consumer’s income rose, with consequent income effects on quantities demanded.

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Page 4: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

Original choice

Consumer’s budget is $m.

2p

m

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Page 5: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x1

Lower price for commodity 1pivots the constraint outwards.

Consumer’s budget is $y.x2

2p

m

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Page 6: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x1

Lower price for commodity 1pivots the constraint outwards.

Consumer’s budget is $m.x2

Now only $m’ are needed to buy the original bundle at the new prices, as if the consumer’s income has increased by $m -- $m’.

2p

m

2

'

p

m

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Page 7: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Slutsky asserted that if, at the new prices, If less income is needed to buy the

original bundle then “real income” is increased

If more income is needed to buy the original bundle then “real income” is decreased

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Page 8: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Changes to quantities demanded due to the change in relative prices, keeping income just enough to buy the original bundle, are the (pure) substitution effect of the price change.

Changes to quantities demanded due to the change in ‘real income’ are the income effect of the price change.

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Page 9: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Slutsky discovered that changes to demand from a price change are always the sum of a pure substitution effect and an income effect. n

isii xxx

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Page 10: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 11: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 12: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 13: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

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Page 14: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

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Page 15: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

Lower p1 makes good 1 relativelycheaper and causes a substitutionfrom good 2 to good 1.(x1’,x2’) (x1’’,x2’’) is the pure substitution effect.

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Page 16: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Substitution effect is always negatively related to the price change.

Note that the portion of the yellow compensated budget line below x’1 is inside the budget set of the original budget, thus these bundles should be less preferred than the original bundle.

As a result, the consumer must choose a point at or more than x’1 with the compensated budget, and as a result, the substitution effect is positive for a price decrease.

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Page 17: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

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Page 18: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

The income effect is (x1’’,x2’’) (x1’’’,x2’’’).

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Page 19: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

The change to demand due to lower p1 is the sum of the income and substitution effects, (x1’,x2’) (x1’’’,x2’’’).

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Page 20: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Most goods are normal (i.e. demand increases with income).

The substitution and income effects reinforce each other when a normal good’s own price changes.

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Page 21: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

Good 1 is normal becausehigher income increasesdemand, so the income and substitution effects reinforce each other.

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Page 22: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Since both the substitution and income effects increase demand when own-price falls, a normal good’s ordinary demand curve slopes down.

The Law of (Downward-Sloping) Demand therefore always applies to normal goods.

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Page 23: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Some goods are inferior (i.e. demand is reduced when income is higher.)

The substitution and income effects oppose each other when an inferior good’s own price changes.

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Page 24: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 25: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 26: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

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Page 27: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

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Page 28: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

The pure substitution effect is as fora normal good. But, ….

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Page 29: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

The pure substitution effect is as for a normal good. But, the income effect is in the opposite direction.

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Page 30: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’

(x1’’’,x2’’’)

The overall changes to demand arethe sums of the substitution and income effects.

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Page 31: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

In rare cases of extreme income-inferiority, the income effect may be larger than the substitution effect, causing quantity demanded to fall as own-price rises.

Such goods are Giffen goods.

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Page 32: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’

A decrease in p1 causes quantity demanded of good 1 to fall.

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Page 33: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x1’x1’’’

x2’’’

A decrease in p1 causes quantity demanded of good 1 to fall.

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Page 34: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

x2

x1

x2’

x2’’

x1’ x1’’x1’’’

x2’’’

Substitution effect

Income effect

A decrease in p1 causes quantity demanded of good 1 to fall.

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Page 35: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Giffen good can only result when the income effect of an inferior good is so strong that it dominates the substitution effect.

This may be possible for poor households where the low-quality necessity has taken up a large portion of expenditure.

This case is very rare, even if exists, so we have confidence that the Law of Demand almost always holds.

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Page 36: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

If we denote m’ as the income required to obtain the original bundle at the new prices, so thatm’=p’1 x1 + p2 x2 and m=p1 x1 + p2 x2 .

Thus the change in real income ism’– m = (p’1 – p1 ) x1

Or 11xpm

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Page 37: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

The substitution effect is

The Income effect is

Total Effect

),()','( 11111 mpxmpxx s

)','(),'( 11111 mpxmpxxn

ns xxmpxmpxx 1111111 ),(),'( 37

Page 38: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

In terms of derivative (or rate of change):

Which is known as the Slutsky Equation. (This is just a rough presentation. The

tools need for formal derivations is not covered in this class.)

)(

)(

11

1

1

1

1

11

1

1

1

1

1

1

1

1

1

1

xm

x

p

x

p

x

xm

x

p

x

p

x

p

m

m

x

p

x

p

x

s

s

s

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Page 39: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 40: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 41: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 42: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Slutsky’s method of decomposition is not the only reasonable way.

Hicks proposed another way of holding “real income” constant.

Instead of compensating him to be able to buy back the original bundle, Hicks method compensates the consumer to buy back a bundle that gives him the same utility as before.

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Page 43: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 44: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Hicks Substitution Effect is also negative, because of the convex preference. (It can also be shown by revealed preference.)

The nominal income required to maintain the utility constant is less than the one required to buy back the same bundle. It implies a larger income effect for a price decrease, but a smaller income effect for a price increase.

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Page 45: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

If government wants to impose tax to support public expenditure, or to ‘punish’ consumption of a good, say, due to pollution, various means can be used.

Here, given the revenue are the same in equilibrium, how do the effects of income tax and quantity tax on good 1 differ?(Note: Income and tax rates are regarded as given for consumers. The tax rate is adjusted so that at equilibrium the tax revenue is the same.)

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Page 46: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 47: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Income tax corresponds to an inward shift of budget line.

Quantity tax corresponds to an inward rotation of the budget line.

When the revenues are held the same for comparison, the budget line for the income tax must pass through the optimal point for quantity tax. (Note: The tax revenue is tx1

*, where x1*

is the optimal quantity under quantity tax.)

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Page 48: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

With the same tax revenue, the utility level attained is higher with income tax than with the quantity tax.

But quantity tax has a stronger effect in reducing the consumption of good 1 than income tax.

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Page 49: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Consider a similar case. Now a tax is imposed to reduce consumption of certain good, but at the same time, an equivalent amount is rebated (given back) to the consumer.

Again, consumer has to take the rebate and tax rate constant for his decision.

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Page 50: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

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Page 51: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

Note that the new consumption bundle must be on the original budget line, because in equilibrium, the tax amount and rebate are the same.

The consumer has become worse off after this quantity tax and rebate program.

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Page 52: Course: Microeconomics Text: Varian’s Intermediate Microeconomics

In this chapter, a decomposition of price effect on quality demand is introduced.

Substitution effect: effect of change of price holding ‘real income’ constant.

Income effect: effect of change in real income.

For normal goods, both effects are negative w.r.t. a price rise.

For inferior goods, sub. effect is negative, but income effect is positive w.r.t. a price rise.

Giffen goods can only be inferior goods with very strong income effect. 52