Economics 202: Intermediate Microeconomic Theory

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Economics 202 Intermediate Microeconomic Theory

• Any questions?

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Demand Elasticity

• We assume all D-curves have a downward-slope, but
  how steep one is depends on the commodity.
• A reduction in the Pmilk may lead to a small
  increase in purchases, but a ? in Pairline may
  lead to a big increase in purchases.
• Own-Price Elasticity of Demand ?X,Px ?QdX /
  ?PX
• Just how sensitive is qty demanded to a change in
  price?
• ? (?Q/Q)/(?P/P) (?Q/?P)(P/Q)
  (1/slope)(P/Q)
• ? (?Q/ ?P)(P/Q)
• If ? lt -1 we say D for that good is elastic gt
  -1 D is inelastic -1
  D is unit-elastic

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Demand Elasticity

• Find the elasticity of a D-curve Q a - bP.
• Properties of Price Elasticity of Demand when
  D-curve is linear
• it is different at every point along the
  D-curve approaching -? at vertical intercept, 0
  at horizontal intercept
• it is never positive (always negative, except one
  point)
• it is inversely related to the slope of the
  linear D-curve
• Two polar cases
• slope of D-curve is much easier to calculate, so
  why bother with elasticity at all?

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More Demand Elasticities

• Income elasticity of demand measures how
  responsive consumption of a good is to a change
  in income
• ?X,I Px,Py (?QdX/QdX)/(? I/I)
• If ?X,I gt 0, then the good is normal.
• Luxury good, ?X,I gt 1 (eat out 1.4 dentist
  1.42)
• Necessity, 1 gt ?X,I gt 0 (food bought for home
  0.5 physician 0.75)
• If ?X,I lt 0, then the good is inferior.

• Cross-price elasticity of demand measures how
  responsive consumption of good X is to a change
  in price of good Y.
• ?X,Py Px,I (? QdX/QdX)/(? PY/PY)
• If ?X,Py gt 0, then X and Y are substitutes.
• If ?X,Py lt 0, then X and Y are complements.
• Often used in anti-trust cases to measure how
  competitive a market may be. Are there
  substitutes?

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Point vs. Arc Elasticity

• Point Elasticity is what we just did
• ? (? Q/Q)/(? P/P) (?Q/ ?P)(P/Q)
• Arc elasticity is the same thing except we use
  the average of the two prices and quantities
  (mid-point method)
• ?arc (? Q/Qavg)/(? P/Pavg) (? Q/ ?
  P)(Pavg/Qavg)
• for point elasticity, when the changes are small,
  it doesnt make a big difference for our result
  which point we choose
• for arc elasticity, it would make a big
  difference if we chose 1 point, so we take the
  average
• example

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Elasticity

• Suppose that instead of a linear D-curve, Q a
  bP,
• we have Q 1,200/P as the demand for zip
  drives.
• This is a hyperbola. PQ 1,200 regardless of
  the price.
• Total Expenditure is constant!
• In general, if demand takes the form Q aPb (b lt
  0), the price elasticity of demand is constant
  and equal to b.
• No need to worry about specifying the point at
  which elasticity is measured.

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Elasticity and Total Revenue

• GGB toll 1, then 100,000 trips.
• If ? -2, what happens to trips when you
  ?toll by 10? Total revenue?
• When D is Price and Total expenditure move in
  
• elastic opposite directions
• inelastic the same direction
• unit-elastic TE doesnt change as P changes

D unit-elastic
P
D elastic
D inelastic
Q
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Estimates of some Elasticities

• Good or service Own-Price Elasticity of Demand
• Green peas -2.8
• Cars -1.5
• Electricity -1.2
• Beer -1.19
• Movies -0.87
• Foreign Air Travel -0.77
• Shoes -0.70
• Doctors services -0.60
• Water -0.40
• Theater, opera -0.18
• Determinants of Elasticity of Demand

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Using Elasticity

• Doctors, through the AMA, restrict the supply of
  physicians. How does this affect the incomes of
  doctors as a group?
• A labor union negotiates a higher wage. How does
  this affect the incomes of affected workers as a
  group?
• UNC decides to raise the price of football
  tickets. How is income from the sale of tickets
  affected?
• Airlines propose to raise fares by 10. Will the
  boost increase revenues?
• Davidson is considering raising tuition by 7.
  Will the increase in tuition raise revenues of
  the college?
• CATS is considering lowering bus fares. Will
  this decrease CATS total receipts?

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Utility Functions Attitudes toward Risk

• Total Utility curve plots the utility of
  different return levels
• The return is unknown beforehand and ? uncertain
• ProbReturn 2 0.5
• ProbReturn 8 0.5
• Expected return 2(.5) 8(.5) 5

Total Utility
U
300
Z
UE(r)225
EU(r)200

• Expected Utility is the average utility you can
  expect to get from different possible returns
• EU(r) 100(.5) 300(.5) 200

100
A
Return
2
8
E(r)5

• Utility from a certain return UE(r)
• Risk-aversion is when a person prefers a certain
  return to an uncertain return giving the same
  expected return
• UE(r) gt EU(r)

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Utility Functions Attitudes toward Risk

• Risk-aversion ? TU has positive, diminishing
  slope ? Diminishing Marginal Utility
• Risk-aversion is common
• Fire-Insurance
• UE(r) utility of 1,000 premium
• EU(r) average utility of
  (-100K.01) (0.99) -1,000
• Depends on the probabilities and amount of loss

UE(r)225
EU(r)200
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Utility Functions Attitudes toward Risk

• Risk-Neutrality ? TU has positive, constant slope
  ? constant marginal utility
• Investor is indifferent between the certain
  return and the risk of 2 or 8 return
• UE(r) EU(r)

UE(r)
EU(r)

• Risk-loving ? TU has positive, increasing slope ?
  increasing marginal utility
• Investor prefers the risk of 2 or 8 return
• UE(r) lt EU(r)
• Example could be 10 lottery tickets
• Utility from 0 for sure lt -50 return
• Decreases as stakes increase Vegas!

U
TU
Z
EU(r) gt
UE(r)
A
Return
2
8
E(r)5
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Methods to Minimize Risk

• (1) Insurance (fire, health, car, etc.)
• What is the max price a risk-averse person will
  pay?
• For an expected loss of 1,000, they will pay gt
  1,000 Why?
• They value 98,300 for sure the same as 99,000
  expected income ? 1,700 max
• Green line is expected utility line
• Will the insurance co. provide a policy?
• Pr(fire) .01 so 1 out of 100 will burn
• Minimum ins. co. will accept 1,000
• per homeowner since 1 will burn.
• Room for mutually beneficial exchange
• (2) Diversification (variety of risks)
• Stocks in different industries, start-ups

U
Total Utility
Z
U
Income
A
0
100K
98,300
99K
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Example Risk Preference Insurance

• In Japan, golfers who get a hole-in-one are
  expected to give gifts to relatives, fellow
  workers, and friends. These gifts can cost them
  the equivalent of thousands of dollars. The cost
  is so great that there actually exists a market
  for hole-in-one insurance. A Japanese golfer,
  who is an expected utility maximizer, has the
  following utility function, U(I) I½ where I is
  monthly income. Our golfer, who has a monthly
  income of 10,000, is quite accomplished and has
  a probability of making a hole-in-one equal to 1
  in 100. If our golfer does indeed ace a hole,
  the typical gift expenditure is 3600.
•  
• (a) Is the golfer risk-averse, risk-neutral, or
  risk-loving? Support your answer mathematically
  and explain.
• (b) Calculate the expected income and expected
  utility (indicate your units).

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Example Risk Preference Insurance

• (c) Compute the maximum premium that would be
  paid to fully insure against the expected costs
  of getting a hole-in-one.
• (d) If the golfers monthly income were only
  8,000, what would be the maximum he or she is
  willing to pay? Explain the relationship between
  income and the risk premium.