Valuation 6: Household Production Functions

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Valuation 6 Household Production Functions

• Revealed preference methods
• Defensive expenditures
• A simple travel cost model for price changes
• Travel cost with a random utility model
• Drawbacks

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Last two weeks we looked at

• The contingent valuation method and the design of
  a CV study
• its criticism
• many potential biases
• validity and reliability
• the part-whole/embedding problem
• An application to waterfowl
• Warm-glow and its effect on donations to public
  goods

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Revealed preference methods

• People make choices within markets prices paid
  and quantities purchased
• Derive values people place on environmental
  amenities and disamenities from purchase
  decisions
• Stated preference methods intended behaviour
  non-use values
• Four commonly used methods TCM, HPM, defensive
  expenditures and damage costs

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Revealed preference methods -2
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The Household Production Function Approach

• A household combines an environmental good/bad
  with market goods to produce and experience
  that directly provides utility
• To enjoy a national park people must visit the
  park and this costs money
• To defend against an environmental bad such as
  traffic noise money is spent on insulation
• The household production function (HPF) approach
  involves investigating changes in the consumption
  of commodities that are substitutes or
  complements for the environmental good of interest

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Defensive Expenditures

• A rational consumer buys self-protection up to
  the point where the marginal rate of substitution
  between purchase and potential harassment equals
  the price ratio
• Averting inputs include air filters, water
  purifiers, noise insulation and other defensive
  or self-protection inputs these are substitutes

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A Simple Model

• Noise pollution from a nearby road (higher Ps are
  worse)
• Level of quiet within the house (higher Q is
  better)
• Homeowner buys noise insulation D(Q,P) to achieve
  Q for a given P
• The homeowners problem to choose between X and Q
  is

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A Simple Model - 2

• Suppose the level of noise increases slightly
• consumer has to spend more to achieve same noise
  level
• If income increases
• The level of utility is the same
• Compensating surplus
• What happens if income is not adjusted?
• Lower level of utility
• Substitution effects Q drops
• Defensive expenditure lt true marginal WTP

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Travel Cost Model

• Widely used for recreation
• Natural areas seldom command a price in the
  market
• Basic premise time and travel cost expenses
  represent the price of access to the site
• WTP to visit the site
• Travel is a complement to recreation

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Travel Cost Model 2

• Application of TCM
• Reservoir management, water supply, wildlife,
  forests, outdoor recreation etc.
• History Harold Hotelling 1947
• Value of national parks
• Variations of the method
• Simple zonal travel cost approach
• Individual travel cost approach
• Random utility approach

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Zonal Travel Cost Approach

• Gives values of the site as a whole
• Based on number of visits from different
  distances
• Travel and time costs increase with distance
• Gives information on quantities and prices
• Construct a demand function of the site

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Steps

• Define a set of zones surrounding the site
• Collect number of visitors from each zone in a
  certain period
• Calculate visitation rates per population
• Calculate round-trip distance and travel time
• Estimate visitors per period and derive demand
  function

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An Example
Visits/1000 300 7.755 Travel Costs
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An Entrance Fee of 10 Euro
So now we have two points on our demand curve.
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Drawbacks

• Not data intensive, but a number of shortcomings
• Assumes that all residents in a zone are the same
• Individual data might be used instead
• More expensive
• Sample selection bias, only visitors are included

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Other problems

• Assumption that people respond to changes in
  travel costs the same way they would respond to
  changes in admission price
• Opportunity cost of time
• Single purpose trip
• Substitute sites
• Unable to look at most interesting policy
  questions changes in quality

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Quality Changes A Simple Model

• A single consumer and a single site
• The park has the quality q (higher qs are better)
• Consumer chooses between visit v and market goods
  x works for L hours at a wage w spends p0 for
  single trip
• The maximisation problem is

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Quality changes - 2

• What is the WTP for a small increase in quality?
• For a given price the demand increases
• Consumer would visit more often
• What is the marginal WTP
• Surplus gain from quality increase / change in
  quality

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Multiple Sites

• Consumer chooses among multiple sites
• The demand for one site is a function of the
  prices of the other sites as well as the
  qualities
• This is straightforward but empirical application
  is more complicated
• Random utility models (RUM)

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Multiple Sites - 2

• Visiting a site gives utility
• b is a parameter and e is an error term
  representing unknown factors
• We do not observe utility but consumer choice
• If consumer chooses site i over site j than ui gt
  uj
• Different values of b yield in different values
  of ui and uj
• From b we can compute the demand for trips to a
  site as a function of quality of the site and the
  price of a visit

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Random Utility Models

• Extremely flexible and account for individuals
  ability to substitute between sites
• Can estimate welfare changes associated with
• Quality changes at one/many sites
• Loss of one/many sites
• Creation of one/many new sites
• Main drawback estimate welfare changes
  associated with each trip
• Visitors might change their number of visits

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Sum up Alternative TCMs

• Zonal travel cost method trips to one site by
  classes of people
• Individual travel cost method trips to one site
  by individual people
• Random utility models trips to multiple sites
  by individual people