ZeePedia

MARGINAL UTILITY AND CONSUMER CHOICE:COST-OF-LIVING INDEXES

<< Note it is repeated:Consumer Preferences, Revealed Preferences
Review of Consumer Equilibrium:INDIVIDUAL DEMAND, An Inferior Good >>
img
Microeconomics ­ECO402
VU
Lesson 9
MARGINAL UTILITY AND CONSUMER CHOICE
Marginal utility
­ measures the additional satisfaction obtained from consuming one additional unit of a
good.
Marginal Utility: An Example
­ The marginal utility derived from increasing from 0 to 1 units of food might be 9
­ Increasing from 1 to 2 might be 7
­ Increasing from 2 to 3 might be 5
Observation: Marginal utility is diminishing
Diminishing Marginal Utility
­ The principle of diminishing marginal utility states that as more and more of a good is
consumed, consuming additional amounts will yield smaller and smaller additions to
utility.
Relationship of Total and Marginal Utility
Diminishing Marginal Utility: An Example
Quantity of good
Total utility
Marginal utility
consumed
0
0
1
4
4
2
7
3
3
9
2
4
10
1
5
10
0
Utility
TU
10
1
Total utility of
consuming a certain
2
amount is equal to
the sum of the
marginal utilities up
3
to the point
5
Total utility increases
at a decreasing rate
4
2
3
4
5
Quantity
0
1
41
img
Microeconomics ­ECO402
VU
Marginal Utility
The fact that total utility
increases at a decreasing
5
rate is shown by negative
4
slope of marginal utility
curve
3
2
1
MU
2
3
4
5
Quantity
0
1
Marginal Utility and
Consumer Choice
Marginal Utility and the Indifference Curve
­ If consumption moves along an indifference curve, the additional utility derived from an
increase in the consumption of one good, food (F), must balance the loss of utility from
the decrease in the consumption in the other good, clothing (C).
Formally:
0 = MUF (ΔF) + MUC (ΔC)
Rearranging:
- (ΔC/ ΔF) = MUF / MUC
Because:
- (  ΔC / ΔF ) = MRS of F for C
MRS = MUF/MUC
When consumers maximize satisfaction the:
MRS = PF/PC
Since the MRS is also equal to the ratio of the marginal utilities of consuming F and C, it
follows that:
MUF/MUC = PF/PC
Which gives the equation for utility maximization?
MU  F / PF = MU  C / PC
Total utility is maximized when the budget is allocated so that the marginal utility per dollar
of expenditure is the same for each good.
This is referred to as the equal marginal principle.
42
img
Microeconomics ­ECO402
VU
Gasoline Rationing
­ In 1974 and again in 1979, the government imposed price controls on gasoline.
­ This resulted in shortages and gasoline was rationed.
­ Non-price rationing is an alternative to market rationing.
­ Under one form everyone has an equal chance to purchase a rationed good.
­ Gasoline is rationed by long lines at the gas pumps.
Rationing hurts some by limiting the amount of gasoline they can buy.
This can be seen in the following model.
It applies to a woman with an annual income of $20,000.
Spending
on other
With a limit of
A
goods ($) 20,000
2,000 gallons,
D
the consumer moves
18,00
to a lower
C
indifference curve
15,00
(lower level of utility).
U
U
B
Gasoline
2,00 5,00
20,00
(gallons per year)
COST-OF-LIVING INDEXES
The CPI is calculated each year as the ratio of the cost of a typical bundle of consumer
goods and services today in comparison to the cost during a base period.
Example
­ Two sisters, Raheela and Sarah, have identical preferences.
­ Sarah began college in 1987 with a $500 discretionary budget.
­ In 1997, Raheela started college and her parents promised her a budget that was
equivalent in purchasing power.
Price of books
$20/book
$100/book
Number of books
15
6
Price of food
$2.00/lb
$2.20/lb
Pounds of food
100
300
Expenditure
$500
$1,260
·  Sarah' Expenditure
·
$500=100 lbs of food x $2.00/lb +15 books x $20/book
·
Raheela' Expenditure for Equal Utility
·
$1,260=300 lbs of food x $2.20/lb +6 books x $100/book
43
img
Microeconomics ­ECO402
VU
·
The ideal cost-of-living adjustment for Raheela is $760.
·
The ideal cost-of-living index is $1,260/$500 = 2.52 or 252.
·
This implies a 152% increase in the cost of living.
Books
(per
For Raheela to achieve
quarter)
the same level of utility
U1
25
as Sarah, with the higher
prices, her budget must
20
be sufficient to allow her
to consume the bundle
A
15
shown by point B.
10
B
5
l2
l1
Food
(lb./quarter)
0 50 100 200 250 300 350 400 450 500 550 600
The ideal cost of living index represents the cost of attaining a given level of utility at current
(1997) prices relative to the cost of attaining the same utility at base (1987) prices.
To do this on an economy-wide basis would entail large amounts of information.
Price indexes, like the CPI, use a fixed consumption bundle in the base period. Called a
Laspeyres price index.
The Laspeyres index tells us:
­ The amount of money at current year prices that an individual requires to purchase the
bundle of goods and services that was chosen in the base year divided by the cost of
purchasing the same bundle at base year prices.
Calculating Raheela's Laspeyres cost of living index
­ Setting the quantities of goods in 1997 equal to what were bought by her sister, but
setting their prices at their 1997 levels result in an expenditure of
$1,720 (100 x 2.20 + 15 x $100)
Her cost of living adjustment would now be $1,220.
The Laspeyres index is:
$1,720/$500 = 344.
This overstates the true cost-of-living increase.
Books
(per quarter)
Using the Laspeyres
index results in the
U1
25
budget line shifting
up from I2 to I3.
20
A
15
10
B
l3
5
l2
l1
Food
(lb./quarter)
0 50 100 200 250 300 350 400 450 500 550 600
44
img
Microeconomics ­ECO402
VU
What Do You Think?
­ Does the Laspeyres index always overstate the true cost-of-living index?
Yes!
­ The Laspeyres index assumes that consumers do not alter their consumption patterns
as prices change.
­ By increasing purchases of those items that have become relatively cheaper, and
decreasing purchases of the relatively more expensive items consumers can achieve
the same level of utility without having to consume the same bundle of goods.
The Paasche Index
­ Calculates the amount of money at current-year prices that an individual requires to
purchase a current bundle of goods and services divided by the cost of purchasing the
same bundle in the base year.
Comparing the Two Indexes
­ Suppose:
­ Two goods: Food (F) and Clothing (C)
Comparing the Two Indexes
­ Let:
·  P & P be current year prices
Ft
Ct
·  P & P  be base year prices
Fb
Cb
·  F & C be current year quantities
t
t
· F & C be base year quantities
b
b
­ Both indexes involve ratios that involve today's current year prices, PFt and PCt.
­ However, the Laspeyres index relies on base year consumption, Fb and Cb.
­ Whereas, the Paasche index relies on today's current consumption, Ft and Ct .
Then a comparison of the Laspeyres and Paasche indexes gives the following equations:
LI = --P-Ft-F-b----P-Ct-Cb----
- - - + - - ---
PFb Fb + PCb Cb
PI = --P---F--+---C----------
-  Ft -  t - P -t Ct
PFb Ft + PCb Ct
­ Sarah
(1990)
·  Cost of base-year bundle at current prices equals
$1,720 (100 lbs x $2.20/lb + 15 books x $100/book)
·  Cost of same bundle at base year prices is
$500 (100 lbs x $2.00/lb + 15 books x $20/book)
­
Sarah (1990)
$1, 720
LI =
= 344
$500
·  Cost of buying current year bundle at current year prices is
$1,260 (300 lbs x $2.20/lb + 6 books x $100/book)
45
img
Microeconomics ­ECO402
VU
·  Cost of the same bundle at base year prices is
$720 (300 lbs x $2/lb + 6 books x $20/book)
$1,260
PI =
= 175
$720
The Paasche index will understate the cost of living because it assumes that the individual
will buy the current year bundle in the base year.
46
Table of Contents:
  1. ECONOMICS:Themes of Microeconomics, Theories and Models
  2. Economics: Another Perspective, Factors of Production
  3. REAL VERSUS NOMINAL PRICES:SUPPLY AND DEMAND, The Demand Curve
  4. Changes in Market Equilibrium:Market for College Education
  5. Elasticities of supply and demand:The Demand for Gasoline
  6. Consumer Behavior:Consumer Preferences, Indifference curves
  7. CONSUMER PREFERENCES:Budget Constraints, Consumer Choice
  8. Note it is repeated:Consumer Preferences, Revealed Preferences
  9. MARGINAL UTILITY AND CONSUMER CHOICE:COST-OF-LIVING INDEXES
  10. Review of Consumer Equilibrium:INDIVIDUAL DEMAND, An Inferior Good
  11. Income & Substitution Effects:Determining the Market Demand Curve
  12. The Aggregate Demand For Wheat:NETWORK EXTERNALITIES
  13. Describing Risk:Unequal Probability Outcomes
  14. PREFERENCES TOWARD RISK:Risk Premium, Indifference Curve
  15. PREFERENCES TOWARD RISK:Reducing Risk, The Demand for Risky Assets
  16. The Technology of Production:Production Function for Food
  17. Production with Two Variable Inputs:Returns to Scale
  18. Measuring Cost: Which Costs Matter?:Cost in the Short Run
  19. A Firm’s Short-Run Costs ($):The Effect of Effluent Fees on Firms’ Input Choices
  20. Cost in the Long Run:Long-Run Cost with Economies & Diseconomies of Scale
  21. Production with Two Outputs--Economies of Scope:Cubic Cost Function
  22. Perfectly Competitive Markets:Choosing Output in Short Run
  23. A Competitive Firm Incurring Losses:Industry Supply in Short Run
  24. Elasticity of Market Supply:Producer Surplus for a Market
  25. Elasticity of Market Supply:Long-Run Competitive Equilibrium
  26. Elasticity of Market Supply:The Industry’s Long-Run Supply Curve
  27. Elasticity of Market Supply:Welfare loss if price is held below market-clearing level
  28. Price Supports:Supply Restrictions, Import Quotas and Tariffs
  29. The Sugar Quota:The Impact of a Tax or Subsidy, Subsidy
  30. Perfect Competition:Total, Marginal, and Average Revenue
  31. Perfect Competition:Effect of Excise Tax on Monopolist
  32. Monopoly:Elasticity of Demand and Price Markup, Sources of Monopoly Power
  33. The Social Costs of Monopoly Power:Price Regulation, Monopsony
  34. Monopsony Power:Pricing With Market Power, Capturing Consumer Surplus
  35. Monopsony Power:THE ECONOMICS OF COUPONS AND REBATES
  36. Airline Fares:Elasticities of Demand for Air Travel, The Two-Part Tariff
  37. Bundling:Consumption Decisions When Products are Bundled
  38. Bundling:Mixed Versus Pure Bundling, Effects of Advertising
  39. MONOPOLISTIC COMPETITION:Monopolistic Competition in the Market for Colas and Coffee
  40. OLIGOPOLY:Duopoly Example, Price Competition
  41. Competition Versus Collusion:The Prisoners’ Dilemma, Implications of the Prisoners
  42. COMPETITIVE FACTOR MARKETS:Marginal Revenue Product
  43. Competitive Factor Markets:The Demand for Jet Fuel
  44. Equilibrium in a Competitive Factor Market:Labor Market Equilibrium
  45. Factor Markets with Monopoly Power:Monopoly Power of Sellers of Labor