Measuring Well Being

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Measuring Well Being

• Lecture 6

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Todays Lecture

• Consumer Price Index -- Measuring gains and
  losses in Real Income
• Other Price Indexes
• Consumer Surplus

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Todays Lecture Brought to by
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Nominal and Real Income

• Nominal Income How many dollars you have in
  your pocket to spend. You can directly measure
  this concept.
• Real Income Your level of well being that cant
  directly measured. We dont have an utilometer
  so we have to resort to indirect measures gauge
  changes in well being.

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Change in Income

• Assume that your nominal income increases by 50
  when the prices of all goods remained unchanged.
• How much has your well being increased?
• A common sense approach would indicate that you
  are 50 better off -- your nominal and real
  income has risen by 50.
• But should we ignore diminishing marginal utility
  of income?

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Changes in Prices

• We will assume that the price of food is 2 per
  unit and the price of clothing is 4. Let us
  assume that Jill has 100 to spend on these two
  goods. Jill purchases 20 units of clothing and
  10 units of food.
• Now the price of food rises to 4 and the price
  of clothing rises 8. Assuming that Jills
  nominal income remains at 100, wouldnt we say
  her real income has fallen? But by how much?
• If Jills income had rose to 200, her budget
  constraint would be the same as before and she
  could consume 10 units of food and 20 units of
  clothing (4(10)8(20)200).
• Jill would need 200 to maintain her real
  income and consequently if her nominal rose
  above 200 she would be better off, otherwise she
  would be worse off.

Initial Conditions PoF2 , PoC 4, Mo 100
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Price Index

• In the base period Jills nominal income was 100
  (Mo) . We adopt this period as our base for
  comparison consequently, we will say Jills real
  income in this period was also 100.
• In the current time period, Jill would need 200
  to maintain her real income she enjoyed in the
  base period. Since we have ignored changes in
  nominal income in making this calculation, we
  could construct a price index reflecting the
  percentage change in income needed to compensate
  Jill for the change in prices

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Constant or Current Dollars

• (Current Dollars) We can use this price index to
  bring the past level of real income into the
  present. For example, Jills level of real
  income in the base period was 100 multiplying by
  the price index we would say her old real income
  in current dollars is 200 PI x 100 2 x
  100. Comparing Jills current nominal income
  (MT) to her old real income in current dollars
  (prices) would indicate whether she was better or
  worse off and by how much.
• MT 250 Better off by 100(250-200)/200 25
• MT 200 Equally well off
• MT 150 Worse off by 100(150-200)/200 25
• (Constant Dollars) Alternatively, we could
  convert her current nominal income into base
  period dollars by deflating her current nominal
  income by the price index (MT/PI). Comparing
  this deflated amount to base period income yields
  the same comparison if we would have done it on a
  current dollars basis.
• MT 250 Better off by 100(125-100)/100 25
• MT 200 Equally well off
• MT 150 Worse off by 100(75-100)/100 25

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Price Change

• This situation was quite easy because relative
  prices did not change.
• What if relative prices do change? In the next
  situation we will assume that only the price of
  food changes -- doubles like the previous
  example.
• To hold real income constant with changing
  relative prices is impossible without knowledge
  of the indifference curves so will hold the
  consumption bundle constant as prices changes and
  compute the change in nominal income needed to
  purchase a base periods consumption bundle.

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Change in Food Price Only

• Now let us assume that only the price of food
  rises to 4 while the price of clothing and
  nominal income remains the same.
• How much income does Jill need to purchase her
  old bundle of goods? In other words, what
  nominal income is consistent with the blue budget
  constraint?
• 4(10) 4(20) 120
• The price index (PIT) would equal 1.20 for this
  scenario.
• If Jills current nominal income exceed 120, she
  would deemed to be better off, equal to 120 then
  equally well off, and less than 120 she would be
  deemed to be worse off.

Initial Conditions PoF2 , PoC 4, Mo 100
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Measurement Methodology

• In a base period, collect data on the prices
  (Poi) and quantities (Qoi) of individuals and
  consequently
• Collect data on prices in later time period (Pti)
  and compute the level of nominal income needed to
  purchase old quantities (Qoi)
• Construct the Price Index -- Consumer Price Index
  (CPI) in period t

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CPI Overstates Needed Compensation

• To construct the CPI, we held the quantities of
  food and clothing constant at some base period
  and then computed the needed income at current
  prices would be needed to buy the old bundle of
  goods. This is depicted by the black budget
  constraint representing the base period and the
  blue represents the new set of prices and the
  needed income to purchase the old bundle.
• If Jill had the blue budget constraint, wouldnt
  she be better off than she was in the base
  period?
• This calculation represents an overstatement of
  the needed compensation to restore Jill to her
  base period real income and hence the CPI tends
  to overstate inflation when prices are rising.

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Falling Price of Food

• Now let us assume the price of food drops to 1
  while the price of clothing remains at 4.
• To purchase the old bundle, Jill would need
• 1(10)4(20) 90
• Consequently the Price index would equal
• PI 90/100 .9
• But if Jill had 90 wouldnt she be better off
  than in the base period? YES
• Consequently the CPI understates the reduction in
  needed income when prices are falling. If we
  could hold real income constant, the reduction
  would be larger. The CPI is too high.

Clothing
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Food
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Alternative Price Index

• When the price of food and clothing are both 4,
  Jill spends 4(8) 4(30) 152 (her current
  nominal income).
• We could ask, how much income would Jill need to
  purchase the new bundle at the old set of prices?
  Income consistent with green budget constraint.
• 2(8) 4(30) 136
• In terms of a price index, this would equal
• 152/136 1.118
• If we inflate her old income, her real income in
  current dollars would be 112 100x1.118, since
  her current income is more she is better off,
  Her real income rose by 36

Clothing
30
8
Food
We could deflate, her current income by the price
index (152/1.118) and Jills real income in
constant dollars is 136 or 36 more.
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Problem?

• The alternative price index equaled
• 152/136 1.118.
• This was based upon comparing Jills current
  nominal income to the income she would need at
  the old prices to purchase the new bundle (136
  in the denominator).
• But is the 136 an overstatement of the needed
  income to maintain Jills current well being
  (real income)?
• Yes. Consequently this price index under states
  the impact of inflation. The opposite problem
  found with the CPI.

Clothing
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Food
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Summary of Price Indexes

• Laspeyres (CPI) Problem Overstates the impact of
  price inflation
• Paasche (GDP Deflator) Problem Understates the
  impact of price inflation

Too Big
Too Big
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Further Reading

• At What Price Conceptualizing and Measuring Cost
  of Living and Price Indexes
• (2002)
• A report by a NRC Panel (Branch of the National
  Academy of Science) published by the National
  Academy Press

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Why do these problems happen?

• Problems with the two price indexes occur because
  we are not holding real income constant but
  consumption bundles.
• What we are ignoring is that when relative prices
  change, individuals will change their consumption
  patterns even if real income is held constant
  (revenge of Slutsky).
• To measure real income effects, we would want to
  account for the substitution effect on
  consumption choices made by individuals and only
  consider the pure income effects.

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Increase in the Price of Food

• The demand function depicts the relationship
  between the price of food and the quantity of
  food desired.
• Now assume the price of food rises, the quantity
  of food will decline because of a real income and
  substitution effect.
• The Laspeyres Index (CPI) would compute the
  needed change in income to compensate the
  individual to equal
• (P1-Po) Fo
• Which exceeds the loss in consumer surplus
• (P1-Po) F1 (P1-Po)(Fo-F1)/2

Paying More for Less
Price
Consuming Less
P1
Po
F0
F1
Food
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Too Small?

• This demand curve (Marshallian) holds nominal
  income constant -- not real income. Hence the
  reduction in food consumption reflects both
  income and substitution effects but we want to
  account for the substitution effect not the
  combined income and substitution effect.
• Hicks devised the notion of a Hicksian demand
  that shows the relation between the price of the
  good and quantity demanded holding real income
  constant.
• Consumer Surplus measure under states the impact
  of price increases.

Price
P1
Po
F0
F1
Food
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Decrease in the Price of Food

• Now assume the price of food falls, the quantity
  of food will rise because of a real income and
  substitution effect.
• The Laspeyres Index (CPI) would compute reduction
  in spending on food
• (Po-P1) Fo
• Which is less than the gain in consumer surplus
• (Po-P1) Fo (Po-P1)(F1-Fo)/2

Price
Paying Less
Consuming More
Po
P1
F1
Fo
Food
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Too Big?

• If we hold real income constant and not nominal
  income, the increase in consumption is
  overstated.
• Consequently the consumer surplus using the
  Marshallian demand curve is too big and
  overstates the gain to the consumer.

Price
Po
P1
F1
Fo
Food
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For Next Lecture

• Complete Risk Survey and bring to class on
  Wednesday
• Read
• Chapter 5 pages 173 to 181
• Chapter 14 pages 511 to 517
• Questions
• If we tax the interest income from savings will
  individuals save less?
• If we tax individuals earned income, will they
  work less?