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Lecture 13: Energy Efficiency
Economics
ENGY 604 - Prof. Winslow
Why do we care about energy
efficiency?
• Can be cheaper than new generation
• Can save money on transmission and
distribution
• Better for the environment than generation
• Helps us meet our GHG reduction goals
• Can create jobs
• Saves money for end users
Costs:
– Administration (programs or time)
– Equipment and ongoing maintenance
Existing programs in California
• Building Codes for
– Windows
– Insulation
– Heating and air conditioning (HVAC)
– Lighting
• Appliance Standards
– Kitchen appliances
– TV and some other electronics
– Water heaters
Terminology
• Energy Efficiency: energy services provided per unit of energy
input
• Energy Productivity: getting the most output for the least energy
input
– Aggregate energy productivity for economy: Gross Domestic
Product per unit of energy consumed – also called Energy Intensity
• Energy Conservation: a reduction in the total amount of energy
consumed
• Economic Efficiency: getting the most output for the least cost
– Energy efficiency does not always lead to economic efficiency (and
vice versa)
Allcott Greenstone 2012
https://www.eia.gov/todayinenergy/detail.php?id=27032
Predicted energy intensity improvement
7
0
1,000
2,000
3,000
4,000
5,000
6,000
7,000
8,000
1990 2015 2040
non-OECD
OECD
0
10
20
30
40
50
60
1990 2015 2040
0
1
2
3
4
5
6
7
8
9
10
1990 2015 2040
0
10
20
30
40
50
60
70
1990 2015 2040
Population
million people
Gross domestic product
per capita
thousand dollars
Carbon intensity
metric tons CO2 per billion Btu
Energy intensity
thousand Btu per dollar
US EIA www.eia.gov/ieo
What Leads to Energy Productivity
Improvements?
• Compositional changes in the economy toward less energy-
intensive industries
• Energy efficiency improvement
– Policies promoting energy efficiency
– High energy prices
• Adoption of more efficient equipment
• Energy-efficient innovation
• Economic forces that drive total factor productivity growth
• Energy prices induce factor substitution and technical change
Energy Efficiency is Cheapest Form of Energy
http://aceee.org/sites/default/files/publications/researchreports/u1402.pdf
Cost of Saved Energy (CSE) for
Utility Energy Efficiency Programs
http://aceee.org/sites/default/files/publications/researchreports/u1402.pdf
Energy Efficiency as a Win-Win
Opportunity
• Less money spent on energy
• Less environmental degradation
• McKinsey & Co. 2009 report, Unlocking Energy Efficiency
in the U.S. Economy:
– $1.2 trillion in energy cost savings
– 23% of projected demand savings
– 1.1 gigatons of GHG savings annually
• However, we are not obtaining the economically efficient
level of energy efficiency.
Source: McKinsey and Co. Impact of the financial crisis on carbon economics: Version 2.1 of the global greenhouse gas abatement cost curve
http://www.mckinsey.com/client_service/sustainability/latest_thinking/greenhouse_gas_abatement_cost_curves
Consumer Decision-making in
Energy Efficiency and Conservation
• We are not obtaining the economically efficient level of
energy efficiency.
• Why not?
• Energy efficiency choices require investment decision
making – trading off costs now for future savings
Isoquant
• The combinations of inputs (K, E) that
yield the producer the same level of
output.
• The shape of an isoquant reflects the
ease with which a producer can
substitute among inputs while
maintaining the same level of output.
Cost Minimization
Q = Isoquant
E
K
Point of Cost
Minimization
Slope of Isocost
=
Slope of Isoquant
Isocost line
Optimal Input Substitution
• A firm initially produces Q0
by employing the
combination of inputs
represented by point A at a
cost of C0.
• Suppose w0 falls to w1.
– The isocost curve rotates
counterclockwise; which
represents the same cost level
prior to the wage change.
– To produce the same level of
output, Q0, the firm will produce
on a lower isocost line (C1) at a
point B.
– The slope of the new isocost
line represents the lower wage
relative to the rental rate of
capital.
Q0
A
L
K
C0/w1C0/w0 C1/w1
B
Energy Efficiency Economics and Policy,
Gillingham et al. (2009)
Un-priced negative externalities could lead to under-priced energy –
budget line P0 vs P1 in figure (A).
Relative price changes Savings from tech improvements
Energy Efficiency Choices
• Higher initial investment
• Lower future costs
• Assessing future costs requires information
about:
– Future energy prices
– Energy savings with use
– Amount product will be used
– Life of the product
– Potential regulatory effect (carbon tax for
example)
– Discount rate
Minimizing Costs
• Individual wants to minimize private costs
• Society wants to minimize social costs
(externalities)
• Rational decision-making by individual
may not provide best social outcome
Elasticity of Demand
• Demand responsiveness to change in price of
energy (elasticity of demand) can determine if
decision making will be economically and energy
efficient.
• Long run and short run elasticities are different
due to purchase of energy using durables with
long life spans.
• Change in energy prices have found to influence
the adoption of energy saving equipment.
“Energy Efficiency Gap”
• The wedge between the cost-minimizing
level of energy efficiency and the level
actually realized
• We have not achieved the energy
efficiency improvements that engineering
and economic analyses suggest would be
economically efficient
Energy Efficiency Gap Causes
• Private decision-making regarding energy
efficiency may not be economically
efficient
– Information may be inadequate
– High consumer discount rates – studies found
ranges of 25 to 100%
– Behavioral “failures” – irrational behavior
• Can lead to systematic under-investment in energy
efficiency
Behavioral Failures
• Prospect Theory
• Welfare change from gains and losses is evaluated with respect
to a reference point, usually the status quo. Consumers are
more worried about losses than gains so their welfare change is
much greater from a loss than from an expected gain of the
same magnitude.
• Bounded rationality
• Consumers are rational, but face cognitive constraints in
processing information that lead to deviations from rationality in
certain circumstances
• Heuristic decision-making
• Consumers engage in decision strategies that differ in some
critical way from conventional utility maximization in order to
reduce the cognitive burden of decision-making.
Other Energy Efficiency Gap
Causes
• Hidden costs not accounted for by the analyst
– search costs
– reductions in other product attributes such as lighting
quality
• Lower energy savings than assumed by the
analyst
• Uncertain future energy savings
• The irreversibility of energy efficiency
investments and the associated option value of
waiting to invest later
Other Energy Efficiency Gap
Causes
• Split incentives – builder vs. buyer,
landlord vs. tenant
– Relevant to 25% or refrigerators, 66% of
water heaters, 48% space heaters (2006)
– Tenants with electricity included in their rent
use more energy
– Tenants will not pay more for apartments with
energy efficient equipment
Energy Market Failures
• Social cost not reflected in decision making because
energy prices don’t account for externalities
• Average cost pricing rather than MC pricing for electricity
– prices too high
• AC pricing rather than time of use pricing so prices are
too low or too high at times
• Lack of information about future operating costs
Allcott and Greenstone 2012
• What causes the energy efficiency gap?
• What are best policy options based on
these causes?
Two Classes of Market Failures Related to
Energy Efficiency
• Externalities
– Costs of externalities, in particular air emissions,
not included in energy conservation and
efficiency decision making.
• Investment inefficiencies
– Inadequate information provision (lack of
information about actual savings)
– Split incentives (landlord and renter for example)
– Lack of access to capital for investment in energy
efficient equipment, technologies.
Consumer Purchases
Energy Efficient Purchase Decision
Consumers will purchase the more efficient equipment
as long as the benefits are greater than the costs.
• p = price of energy
• m = how much the equipment is used by the individual
• (e0 – e1) = difference in energy use between the items
• ξ is unobserved benefits or costs
• ϒ (gamma) is weight consumer puts on energy cost
savings – this expresses the potential inefficiencies
Energy Efficient Purchase Decision with
Exernalities
Consumers will purchase the socially optimal option as
long as the benefits are greater than the costs.
• p = price of energy
• m = how much the equipment is used by the individual
• (e0 – e1) = difference in energy use between the items
• ξ is unobserved benefits or costs
• φ (phi) is the internalized externality (added to the
price of energy)
ϒ = how much consumer cares about
energy cost saving (investment inefficiencies)
φ = un-internalized externalities
Consumers on left side have high usage,
high energy cost, and low unobserved costs
Slope of demand curve (WTP) reflects level
of m (use), ξ (unobserved benefits and costs),
and p (price of energy)
High WTP
Lower WTP
Policy Responses
• If the problem is investment inefficiencies,
such that consumers will not spend more on
energy efficient equipment even if it will save
them money, the proper policy response is
subsidies on the equipment.
• If the problem is un-priced externalities, the
efficient policy response is a tax on energy to
reduce the use of the equipment as well as
encourage purchase of efficient equipment.
Market Failure Solutions
• Externalities solutions:
– Pigouvian taxes or equivalent program like cap-
and-trade
• Investment inefficiencies solutions:
– Information provision including Energy Star,
energy audits, product labeling
– Subsidies, tax credits, tax deductions, rebates,
loan subsides
– Regulations/ product standards
– Low-cost loans
Social welfare gain from a subsidy = abf
With addition of Pigouvian tax = adg
Cost of subsidy = hbjk
Information program could move demand
From D to D’. Compare the benefits to
the cost of the program.
Hard to Find Evidence of the Gap
Due to Consumer Behavior
• There might be unobserved reasons for energy choices
that do not seem efficient
• Engineering estimates of the gap usually only look at
upfront costs and then energy savings
• Surveys have found that, for many business that had
energy audits, investments were not taken due to
– lack of staff
– uncertainty about the new equipment
– risk of inconvenience to staff
– unaccounted opportunity costs
• Consumers may have high discount rates, not know how
much energy they use, nor trust the savings estimates
Example – Decision to Weatherize
Home
• uncertainty about savings
• work to find contractors
• fear of inferior work
• risk aversion
Example Following Model in Allcott and
Greenstone: Consumers can chose between
two air conditioner models that provide the
same level of cooling but one is more efficient
than the other
• e0 = 5kw
• e1 = 4kW
• m = 800 hours
• p = $.12/kWh
• ϒ = 1
• r = .05
• ξ = $50
• n (years) = 6
Q. What would the cost difference need to be so that the
consumer is indifferent?
Example Following Model in Allcott and
Greenstone
• e0 = 5kw
• e1 = 4kW
• m = 800 hours
• p = $.12/kWh
• ϒ = 1
• r = .05
• ξ = $50
• n (years) = 6
P = $.12 x 800 x 1kW) = $96
$96(1-1.05-6)/.05 - $50 = $487
So if the cost premium for the
energy efficient item is less than
$487, the consumer should buy it.
What if consumer doesn’t buy it and difference is
$300?
• e0 = 5kw
• e1 = 4kW
• m = 800 hours
• p = $.12/kWh
• ϒ = ???
• r = .05
• ξ = $50
• n (years) = 6
Maybe ξ is more than $50
Maybe ϒ < 1 so people value upfront
costs more than the stream of savings
What is the value of ϒ if c
is $300 and people are indifferent?
What if consumer doesn’t buy it and difference is
$300?
• e0 = 5kw
• e1 = 4kW
• m = 800 hours
• p = $.12/kWh
• ϒ = ???
• r = .05
• ξ = $50
• n (years) = 6
What is the value of ϒ if c
is $300 and people are indifferent?
$.12/kWh x 800h x 1kW = $96
(ϒ x $96)(1-1.05-6/.05) – 50 = 300
(ϒ x $96)5.0757 = 350
ϒ x $487.266 = 350
ϒ = 0.7183
So energy cost savings are de-valued by almost 30%
What is consumer doesn’t buy it and difference is
$300?
• e0 = 5kw
• e1 = 4kW
• m = ??? hours
• p = $.12/kWh
• ϒ = 1
• r = .05
• ξ = $50
• n (years) = 6
What if ϒ = 1, c = $300, but m < 800
so people are indifferent?
(m x .12)(1-1.05-6/.05) – 50 = 300
(m x .12)(5.0757) = 350
m = 350/0.61 = 574.63
So if m < 574 hours, people won’t buy
efficient version
What is consumer doesn’t buy it and difference is
$300?
The issue could also be that r >.05
for these consumers or they plan
to use it for fewer years.
Discounting Example Using Excel
You are buying an electric water heater. You can chose between
two model:
Regular (R)
• Capital cost: $500
• Power use: 4000watts (4kW)
• Hours per year: 1000
Efficient (E)
• Capital cost: $800
• Power use: 4000watts (4kW)
• Hours per year: 800
Base case:
• r = .05
• n = 10
• electricity price $0.10/kWh
Present Values
Annual cost for R = 4kW x 1000hr x 0.10 =
$400/year
PVR = $500 + $400(1-1.05-10)/.05 = $3,589
Annual cost for E = 4kW x 800hr x 0.10 =
$320/year
PVE = $800 + $320(1-1.05-10)/.05 = $3,271
Questions Related To Consumer
Behavior
Q. What r would leave PVs equal?
Q. What does n need to be so PVR = PVE?
Q. What does cost of energy need to be so
PVR = PVE?
Q. What difference in hours of use for PVR
= PVE?
Excel file
Regular Efficient Difference
Po 500 800 -300
annual cost 400 320 80
energy use 4 4
hours 1000 800 200
cost of energy 0.1
r 0.05
n 10
Q. What does r need to be for PVR = PVE? RATE
PV ($3,589) ($3,271) 0.23
Q. What does n need to be so PVR = PVE? NPER
4.256
Q. What does cost of energy need to be so PVR = PVE? PMT
$38.85 =$38.83/1460 $0.0266
Q. What difference in hours of use so PVR = PVE? = $38.85/.1 x 4 97.075
Consumers can chose between two air conditioners:
• Regular model that uses $15/month to operate ($180/year)
• Efficient model that uses $10/month to operate ($120/year)
• Each is expected to last for 6 years.
Q.1. What is the present value of the operating costs for each
given a discount rate of 5%.
Q. 2: If the price difference between two models is only $200, what
is the implied discount rate if a consumer is indifferent between
the two products?
Q.3. What number of year would the product need to last for the
PVs to be the same with r = .05 and price difference = $200?
ICE: Simple Energy Efficiency Investment Example
Energy Efficiency Investment Example:
PV operating costs
PV regular = $180(1-1.05-6)/.05 = $913.62
PV efficient = $120(1-1.05-6)/.05 = $609.08
FIN

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Energy Efficiency Economics

  • 1. Lecture 13: Energy Efficiency Economics ENGY 604 - Prof. Winslow
  • 2. Why do we care about energy efficiency? • Can be cheaper than new generation • Can save money on transmission and distribution • Better for the environment than generation • Helps us meet our GHG reduction goals • Can create jobs • Saves money for end users Costs: – Administration (programs or time) – Equipment and ongoing maintenance
  • 3. Existing programs in California • Building Codes for – Windows – Insulation – Heating and air conditioning (HVAC) – Lighting • Appliance Standards – Kitchen appliances – TV and some other electronics – Water heaters
  • 4. Terminology • Energy Efficiency: energy services provided per unit of energy input • Energy Productivity: getting the most output for the least energy input – Aggregate energy productivity for economy: Gross Domestic Product per unit of energy consumed – also called Energy Intensity • Energy Conservation: a reduction in the total amount of energy consumed • Economic Efficiency: getting the most output for the least cost – Energy efficiency does not always lead to economic efficiency (and vice versa)
  • 7. Predicted energy intensity improvement 7 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 1990 2015 2040 non-OECD OECD 0 10 20 30 40 50 60 1990 2015 2040 0 1 2 3 4 5 6 7 8 9 10 1990 2015 2040 0 10 20 30 40 50 60 70 1990 2015 2040 Population million people Gross domestic product per capita thousand dollars Carbon intensity metric tons CO2 per billion Btu Energy intensity thousand Btu per dollar US EIA www.eia.gov/ieo
  • 8. What Leads to Energy Productivity Improvements? • Compositional changes in the economy toward less energy- intensive industries • Energy efficiency improvement – Policies promoting energy efficiency – High energy prices • Adoption of more efficient equipment • Energy-efficient innovation • Economic forces that drive total factor productivity growth • Energy prices induce factor substitution and technical change
  • 9. Energy Efficiency is Cheapest Form of Energy http://aceee.org/sites/default/files/publications/researchreports/u1402.pdf
  • 10. Cost of Saved Energy (CSE) for Utility Energy Efficiency Programs http://aceee.org/sites/default/files/publications/researchreports/u1402.pdf
  • 11. Energy Efficiency as a Win-Win Opportunity • Less money spent on energy • Less environmental degradation • McKinsey & Co. 2009 report, Unlocking Energy Efficiency in the U.S. Economy: – $1.2 trillion in energy cost savings – 23% of projected demand savings – 1.1 gigatons of GHG savings annually • However, we are not obtaining the economically efficient level of energy efficiency.
  • 12. Source: McKinsey and Co. Impact of the financial crisis on carbon economics: Version 2.1 of the global greenhouse gas abatement cost curve http://www.mckinsey.com/client_service/sustainability/latest_thinking/greenhouse_gas_abatement_cost_curves
  • 13.
  • 14. Consumer Decision-making in Energy Efficiency and Conservation • We are not obtaining the economically efficient level of energy efficiency. • Why not? • Energy efficiency choices require investment decision making – trading off costs now for future savings
  • 15. Isoquant • The combinations of inputs (K, E) that yield the producer the same level of output. • The shape of an isoquant reflects the ease with which a producer can substitute among inputs while maintaining the same level of output.
  • 16. Cost Minimization Q = Isoquant E K Point of Cost Minimization Slope of Isocost = Slope of Isoquant Isocost line
  • 17. Optimal Input Substitution • A firm initially produces Q0 by employing the combination of inputs represented by point A at a cost of C0. • Suppose w0 falls to w1. – The isocost curve rotates counterclockwise; which represents the same cost level prior to the wage change. – To produce the same level of output, Q0, the firm will produce on a lower isocost line (C1) at a point B. – The slope of the new isocost line represents the lower wage relative to the rental rate of capital. Q0 A L K C0/w1C0/w0 C1/w1 B
  • 18. Energy Efficiency Economics and Policy, Gillingham et al. (2009) Un-priced negative externalities could lead to under-priced energy – budget line P0 vs P1 in figure (A). Relative price changes Savings from tech improvements
  • 19. Energy Efficiency Choices • Higher initial investment • Lower future costs • Assessing future costs requires information about: – Future energy prices – Energy savings with use – Amount product will be used – Life of the product – Potential regulatory effect (carbon tax for example) – Discount rate
  • 20. Minimizing Costs • Individual wants to minimize private costs • Society wants to minimize social costs (externalities) • Rational decision-making by individual may not provide best social outcome
  • 21. Elasticity of Demand • Demand responsiveness to change in price of energy (elasticity of demand) can determine if decision making will be economically and energy efficient. • Long run and short run elasticities are different due to purchase of energy using durables with long life spans. • Change in energy prices have found to influence the adoption of energy saving equipment.
  • 22.
  • 23. “Energy Efficiency Gap” • The wedge between the cost-minimizing level of energy efficiency and the level actually realized • We have not achieved the energy efficiency improvements that engineering and economic analyses suggest would be economically efficient
  • 24. Energy Efficiency Gap Causes • Private decision-making regarding energy efficiency may not be economically efficient – Information may be inadequate – High consumer discount rates – studies found ranges of 25 to 100% – Behavioral “failures” – irrational behavior • Can lead to systematic under-investment in energy efficiency
  • 25. Behavioral Failures • Prospect Theory • Welfare change from gains and losses is evaluated with respect to a reference point, usually the status quo. Consumers are more worried about losses than gains so their welfare change is much greater from a loss than from an expected gain of the same magnitude. • Bounded rationality • Consumers are rational, but face cognitive constraints in processing information that lead to deviations from rationality in certain circumstances • Heuristic decision-making • Consumers engage in decision strategies that differ in some critical way from conventional utility maximization in order to reduce the cognitive burden of decision-making.
  • 26. Other Energy Efficiency Gap Causes • Hidden costs not accounted for by the analyst – search costs – reductions in other product attributes such as lighting quality • Lower energy savings than assumed by the analyst • Uncertain future energy savings • The irreversibility of energy efficiency investments and the associated option value of waiting to invest later
  • 27. Other Energy Efficiency Gap Causes • Split incentives – builder vs. buyer, landlord vs. tenant – Relevant to 25% or refrigerators, 66% of water heaters, 48% space heaters (2006) – Tenants with electricity included in their rent use more energy – Tenants will not pay more for apartments with energy efficient equipment
  • 28. Energy Market Failures • Social cost not reflected in decision making because energy prices don’t account for externalities • Average cost pricing rather than MC pricing for electricity – prices too high • AC pricing rather than time of use pricing so prices are too low or too high at times • Lack of information about future operating costs
  • 29. Allcott and Greenstone 2012 • What causes the energy efficiency gap? • What are best policy options based on these causes?
  • 30. Two Classes of Market Failures Related to Energy Efficiency • Externalities – Costs of externalities, in particular air emissions, not included in energy conservation and efficiency decision making. • Investment inefficiencies – Inadequate information provision (lack of information about actual savings) – Split incentives (landlord and renter for example) – Lack of access to capital for investment in energy efficient equipment, technologies.
  • 32. Energy Efficient Purchase Decision Consumers will purchase the more efficient equipment as long as the benefits are greater than the costs. • p = price of energy • m = how much the equipment is used by the individual • (e0 – e1) = difference in energy use between the items • ξ is unobserved benefits or costs • ϒ (gamma) is weight consumer puts on energy cost savings – this expresses the potential inefficiencies
  • 33. Energy Efficient Purchase Decision with Exernalities Consumers will purchase the socially optimal option as long as the benefits are greater than the costs. • p = price of energy • m = how much the equipment is used by the individual • (e0 – e1) = difference in energy use between the items • ξ is unobserved benefits or costs • φ (phi) is the internalized externality (added to the price of energy)
  • 34. ϒ = how much consumer cares about energy cost saving (investment inefficiencies) φ = un-internalized externalities Consumers on left side have high usage, high energy cost, and low unobserved costs Slope of demand curve (WTP) reflects level of m (use), ξ (unobserved benefits and costs), and p (price of energy) High WTP Lower WTP
  • 35. Policy Responses • If the problem is investment inefficiencies, such that consumers will not spend more on energy efficient equipment even if it will save them money, the proper policy response is subsidies on the equipment. • If the problem is un-priced externalities, the efficient policy response is a tax on energy to reduce the use of the equipment as well as encourage purchase of efficient equipment.
  • 36. Market Failure Solutions • Externalities solutions: – Pigouvian taxes or equivalent program like cap- and-trade • Investment inefficiencies solutions: – Information provision including Energy Star, energy audits, product labeling – Subsidies, tax credits, tax deductions, rebates, loan subsides – Regulations/ product standards – Low-cost loans
  • 37. Social welfare gain from a subsidy = abf With addition of Pigouvian tax = adg Cost of subsidy = hbjk Information program could move demand From D to D’. Compare the benefits to the cost of the program.
  • 38. Hard to Find Evidence of the Gap Due to Consumer Behavior • There might be unobserved reasons for energy choices that do not seem efficient • Engineering estimates of the gap usually only look at upfront costs and then energy savings • Surveys have found that, for many business that had energy audits, investments were not taken due to – lack of staff – uncertainty about the new equipment – risk of inconvenience to staff – unaccounted opportunity costs • Consumers may have high discount rates, not know how much energy they use, nor trust the savings estimates
  • 39. Example – Decision to Weatherize Home • uncertainty about savings • work to find contractors • fear of inferior work • risk aversion
  • 40. Example Following Model in Allcott and Greenstone: Consumers can chose between two air conditioner models that provide the same level of cooling but one is more efficient than the other • e0 = 5kw • e1 = 4kW • m = 800 hours • p = $.12/kWh • ϒ = 1 • r = .05 • ξ = $50 • n (years) = 6 Q. What would the cost difference need to be so that the consumer is indifferent?
  • 41. Example Following Model in Allcott and Greenstone • e0 = 5kw • e1 = 4kW • m = 800 hours • p = $.12/kWh • ϒ = 1 • r = .05 • ξ = $50 • n (years) = 6 P = $.12 x 800 x 1kW) = $96 $96(1-1.05-6)/.05 - $50 = $487 So if the cost premium for the energy efficient item is less than $487, the consumer should buy it.
  • 42. What if consumer doesn’t buy it and difference is $300? • e0 = 5kw • e1 = 4kW • m = 800 hours • p = $.12/kWh • ϒ = ??? • r = .05 • ξ = $50 • n (years) = 6 Maybe ξ is more than $50 Maybe ϒ < 1 so people value upfront costs more than the stream of savings What is the value of ϒ if c is $300 and people are indifferent?
  • 43. What if consumer doesn’t buy it and difference is $300? • e0 = 5kw • e1 = 4kW • m = 800 hours • p = $.12/kWh • ϒ = ??? • r = .05 • ξ = $50 • n (years) = 6 What is the value of ϒ if c is $300 and people are indifferent? $.12/kWh x 800h x 1kW = $96 (ϒ x $96)(1-1.05-6/.05) – 50 = 300 (ϒ x $96)5.0757 = 350 ϒ x $487.266 = 350 ϒ = 0.7183 So energy cost savings are de-valued by almost 30%
  • 44. What is consumer doesn’t buy it and difference is $300? • e0 = 5kw • e1 = 4kW • m = ??? hours • p = $.12/kWh • ϒ = 1 • r = .05 • ξ = $50 • n (years) = 6 What if ϒ = 1, c = $300, but m < 800 so people are indifferent? (m x .12)(1-1.05-6/.05) – 50 = 300 (m x .12)(5.0757) = 350 m = 350/0.61 = 574.63 So if m < 574 hours, people won’t buy efficient version
  • 45. What is consumer doesn’t buy it and difference is $300? The issue could also be that r >.05 for these consumers or they plan to use it for fewer years.
  • 46. Discounting Example Using Excel You are buying an electric water heater. You can chose between two model: Regular (R) • Capital cost: $500 • Power use: 4000watts (4kW) • Hours per year: 1000 Efficient (E) • Capital cost: $800 • Power use: 4000watts (4kW) • Hours per year: 800 Base case: • r = .05 • n = 10 • electricity price $0.10/kWh
  • 47. Present Values Annual cost for R = 4kW x 1000hr x 0.10 = $400/year PVR = $500 + $400(1-1.05-10)/.05 = $3,589 Annual cost for E = 4kW x 800hr x 0.10 = $320/year PVE = $800 + $320(1-1.05-10)/.05 = $3,271
  • 48. Questions Related To Consumer Behavior Q. What r would leave PVs equal? Q. What does n need to be so PVR = PVE? Q. What does cost of energy need to be so PVR = PVE? Q. What difference in hours of use for PVR = PVE?
  • 49. Excel file Regular Efficient Difference Po 500 800 -300 annual cost 400 320 80 energy use 4 4 hours 1000 800 200 cost of energy 0.1 r 0.05 n 10 Q. What does r need to be for PVR = PVE? RATE PV ($3,589) ($3,271) 0.23 Q. What does n need to be so PVR = PVE? NPER 4.256 Q. What does cost of energy need to be so PVR = PVE? PMT $38.85 =$38.83/1460 $0.0266 Q. What difference in hours of use so PVR = PVE? = $38.85/.1 x 4 97.075
  • 50. Consumers can chose between two air conditioners: • Regular model that uses $15/month to operate ($180/year) • Efficient model that uses $10/month to operate ($120/year) • Each is expected to last for 6 years. Q.1. What is the present value of the operating costs for each given a discount rate of 5%. Q. 2: If the price difference between two models is only $200, what is the implied discount rate if a consumer is indifferent between the two products? Q.3. What number of year would the product need to last for the PVs to be the same with r = .05 and price difference = $200? ICE: Simple Energy Efficiency Investment Example
  • 51. Energy Efficiency Investment Example: PV operating costs PV regular = $180(1-1.05-6)/.05 = $913.62 PV efficient = $120(1-1.05-6)/.05 = $609.08
  • 52. FIN