317_L24, Mar 11/08, J. Schaafsma 1 Review of the Last Lecture are discussing shadow pricing in the context of cost-benefit analysis noted that shadow pricing may be needed because: 1. market prices do not capture the true opportunity cost of an input a) monopoly prices b) externalities 2. non-market goods (life and limb) we will look at three methods of shadow pricing (human capital method, revealed preference (WTP, WTA) contingent valuation (WTP, WTA) are part way through discussing the human capital method

317_L24, Mar 11/08, J. Schaafsma 2 Techniques for Shadow Pricing: The Human Capital Approach basic concept  a life cut short is a loss of output value of a human life (limb lost, physical function lost)= PV of stream of future earnings lost if life were ended now (or limb lost, or physical function lost) this method yields very specific results However, the method is: a) ethically indefensible b) inconsistent with standard theory of value. ///

317_L24, Mar 11/08, J. Schaafsma 3 The Human Capital Approach: Ethically Indefensible retired elderly  don’t produce  valueless very young  earnings twenty or more years into the future  very low PV  very low value women  generally earn less than men  female’s life worth less than a male’s life blacks  generally earn less than whites  a black’s life worth less than a white’s life wealthy and productive individuals valued more than the poor These are all ethically offensive conclusions ///

317_L24, Mar 11/08, J. Schaafsma 4 The Human Capital Approach: Theoretically Problematic two basic theoretical issues ignored by this method: 1.Can’t value all of a person’s contribution by the value society places on the last unit produced  ignores the consumer surplus (see diagram) - a simple non healthcare example: what is the value we place on our consumption of water? Can’t compute this by multiplying our consumption of water by the price of water! 2.Economic value is determined by the opportunity cost we are willing to incur to have the good or service  what are we willing to give up to have the good or service? ///

317_L24, Mar 11/08, J. Schaafsma 5 Techniques for Shadow Pricing: Revealed Preference revealed preference  infer value of life and limb implicit from data generated by real choices made by individuals two basic methods: 1. willingness to accept (WTA) 2. willingness to pay (WTP) will explain each method & critique each one. ///

317_L24, Mar 11/08, J. Schaafsma 6 Revealed Preference: Willingness to Accept Studies most frequent focus in RP WTA studies  labour market choices basic idea  in order to induce people to accept a job with a higher risk of death  need to pay a higher wage rate use wage and risk of death differentials across two jobs to compute shadow price for a human life (or for limb). ///

317_L24, Mar 11/08, J. Schaafsma 7 Willingness to Accept method Job AJob B Probability(Death) Annual income $50,000 $50,450 Assume: ceteris paribus for the two jobs!!! For job A: 1 death per 10,000 workers For Job B: 10 deaths per 10,000 workers Shadow price = (total risk premium for 10,000 workers)/extra deaths = (10,000x$450)/9 = $500,000 Alternatively, willing to accept increased risk of for $450/yr Thus implicit value of human life = $450/ = $500,000

317_L24, Mar 11/08, J. Schaafsma 8 Willingness to Accept Method: Critique 1.imperfect labour markets  discrimination, lack of mobility 2.Are risks correctly perceived (are workers fully informed)? 3.Wealth affects choices, the rich have more choices and can avoid risky jobs, the poor may be less able to do so (thus accept a lower risk premium). Wealth still affects value of human life indirectly through revealed preferences!! NB. WTA  no upper limit on “bribe” required to induce people to take risks. ///

317_L24, Mar 11/08, J. Schaafsma 9 Willingness to Pay Method (WTP) alternative revealed preference method for computing a shadow price => look at consumer behaviour to infer the value implicitly placed on a human life & limb by WTP to reduce risk of death e.g. how much are consumers willing to pay for safety devices such as smoke alarms, car safety options, etc implicit value = (cost of safety device(feature))/reduction in risk ///

317_L24, Mar 11/08, J. Schaafsma 10 WTP Method: Example smoke detector costs $40 assume prob(death/no detector) = assume prob(death/one detector) = assume prob(death/two detectors) = someone who buys one detector reveals an implicit value of life of at least $(40 – 0)/( – ) = $800,000, but less than: $(80 – 40)/( – ) = $2,000,000. WHY?  didn’t buy the second smoke alarm ///

317_L24, Mar 11/08, J. Schaafsma 11 WTP Method: Critique market price may understate the price the person is WTP for the first unit (consumer surplus) consumer surplus problem reduced if one could look at the margin e.g. buy 1 or 2 or 3 or 4 smoke alarms, prob of death  by ever smaller amounts as # of alarms installed in the house  then compute implicit value of human life from the marginal purchase, e.g. buy 2 but not 3 smoke alarms. However, there is still the problem of valuing life at the margin i.e., is it valid to value a life by looking at WTP for small reductions in risk => no => will undervalue the life Income still matters  low income person might only buy one smoke alarm, high income person might buy two!!

317_L24, Mar 11/08, J. Schaafsma 12 The Contingent Valuation Method the contingent valuation method is an alternative to the revealed preference method for generating shadow prices. CV method also has WTP and WTA variants CV studies: survey method  confront respondent with a hypothetical scenario (e.g.: a healthcare program that will reduce the risk of death by x%) ask the respondent to reflect on this contingency and then to state the maximum they are willing to pay for this good or service. NOTE: difference between this HYPOTHETICAL maximum WTP and market price = consumer surplus ///

317_L24, Mar 11/08, J. Schaafsma 13 Contingent Valuation Studies, Example: Ambulance Service current ambulance service  Prob(death en route) = (hypothetical) improved ambulance service  Prob(death en route) = (hypothetical) what is the maximum that you are willing to pay towards this service? If $15  implicit value placed on human life = $15/( – ) = $1,875,000

317_L24, Mar 11/08, J. Schaafsma 14 Contingent Valuation (CV) Studies: Problems must confront respondent with an easily understood scenario response is hypothetical  no actual payment CV studies could also use the WTA approach (for example, ask what the minimum compensation would need to be for the person to do without a safety feature currently in the work place). income/wealth still matter

317_L24, Mar 11/08, J. Schaafsma 15 RP and CV Value Statistical lives Revealed preference and contingent valuation methods focus on statistical lives; i.e. reductions in prob(death) ex ante, before life is actually in the balance, may implicitly place a value on own life of $x on a probabilistic basis ex post, if an accident does happen, and your life is at risk  will likely want to re-contract  place a higher value than $x on own life ///

317_L24, Mar 11/08, J. Schaafsma 16 RP and CV Ignore Externalities others around the person also place a value on that person’s life and limb  need to include this in the valuation public goods nature of human life  non-rivalry in consumption  given a fixed quantity of the good, “consumption” of the good by one person doesn’t reduce what is left for others.