Short summary environmental economics
• All rational individuals want to maximize utility
• Utility function: describes the relationship between the consumption of a good/bundle and utility
• Producers maximize profit
• The environmental Kuznets Hypothesis attempts to explain the relationship between economic growth and human action
in the long run
• Aim of microeconomic theory: analyze people’s behaviour at the micro level (individual consumer and producer)
• What impacts consumer and producer choices? →L4+L5
• If y is utility and x is the consumption, f’(x) denotes the “marginal utility” for consuming one extra unit
• Script p.8: Refresher on mathematical Calculus
• Maximum consumption/Minimum consumption:
o if second-order derivation is negative →maximum
o if second-order derivation is positive-→minimum
• the total differential is the sum of partial derivatives of all independent variables
L3
• 5 key assumptions about properties of consumer’s preferences; definition of “good” and”bad” (see p.10 in script)
• Indifference curve=visualizing a preference ordering; all possible combinations of goods that generate the same utility
level
• A utility function represents all existing indifference curves
o U=x1*x2=imperfect substitutes
o U=x1*x2=perfect substitutes
o U=min{x1,x2}=perfect complements (shoe example)
• Exchange relationship between x1 and x2 at the margin = marginal rate of utility substitution (MRUS)
o The rate indicating how much x2 a consumer is willing to give up for an extra unit of x1 while keeping the overall
utility level constant=inverse ratio of marginal utilities of x1 and x2
o =the slope of the indifference curve in a particular point
o MRUS=-2 →at the margin a consumer is willing to exchange 2 units of x2 for 1 additional unit of x1
o →calculate total derivative of utility function
• Maximum value of utility function given a budget constraint (optimal consumption of goods) →Lagrange Method (p.15
in script)
o First, you solve for the two goods consumed in the optimum und then you insert those into the utility function, to
get the utility in the optimum
• Slope of the budget line=inverse price ratio
• Optimal consumption: MRUS=inverse price ratio
• FOC=First order conditions
L4
• If a firm keeps increasing an input, holding all other inpunts and technology constant, the corresponding increases in
output will become smaller eventually
• Isoquant=indifference curve (properties of isoquant see p.19 of script)
• MRTS=the rate at which a producer is willing to substitute k for an extra unit of l
o Derivate production function and set it equal to 0
o Optimal combination of input factors →Lagrange Method
• In short run: increase output only by increasing labor (capital is fix and cannot be varied)
• In long run: increase output by using more of both inputs
• Increasing economies of scale at low levels of output, decreasing economies of scale at high output levels
• Optimal output (given optimal use of input)=marginal revenue equals marginal costs
• Demand function=horizontally aggregating the demands of indivduals
o Shows the raltaionship between price and consumption amount of a good
• Profit maximizing production=marginal costs equal marginal benefits(revenue; p.23 script)
• Supply curve=marginal cost curve
o Horizontally aggregate each firms’ marginal cost curves
, L5 – market failure
• Consumer and producer surplus (see p.25/26 in script)
• The sum of producer and consumer surplus defines the social welfare at the competitive market equilibrium
• Market function conditions, e.g. all goods are private goods and no externalities exist; see p.26 →if one or more are
violated=market failure
• Pure private good/pure public good/common pool resource →p.27 script
• An externality occurs when the production or consumption decisions of one actor have an impact on the utility or profit
of another actor
o Positive vs negative externalities
• Consequences of market failure p. 28 script
• Pollution cause welfare losses to society (“hidden costs”)
o Social welfare in a competitive market, accounting for external costs
o Social welfare in the social optimum, after having internalised external costs
• Deadweight loss (DWL)=welfare difference between private optimum and social optimum
o It is a burden to society because the competitive market equates price with private marginal costs instead with social
marginal costs
• An efficient market equilibrium is assumed to maximize social welfare →sum of consumer and producer
L6 – market failure+Pollution control
• The social marginal benefit of a private good is the same as the marginal benefit to the individual who consumes that good
o The social demand of a private good(=social marginal benefit curve) = horizontal sum of the demand curves ovr all
individuals
o People’s marginal utility from consuming a public good is not known
→we cannot determine the optimal (efficient) consumption points for a public good at the individual level
→social demand curve=vertical sum of individual demands
→a supply curve can be constructed, but this is not sufficient to determine the market equilibrium for this good
• Non rivalry holds for public goods=all individuals can consume the same amount
• Optimal amount of a public good: sum of individuals MRUS=marginal costs od producers
• Flow pollution = residuals have short life-spans before they degrade into harmless forms
• Stock pollution = damages depend on the concentration of the pollutants; for the accumulation space and time may be
relevant
o E.g. Bioaccumulation
o The stock increase more over time, the higher the emission rate
o If production deceases, net benefits increase
• Analyzing stock pollution: p.34 in script
o Emissions per period=decay per period →”steady state”
o Constant production=constant pollution
• Socially optimal pollution level?
• Demage of pollution?
• Optimal abatement level?
L7 – Pollution control
• Markets ignore the true scarcities of natural resources and external costs of an (over)exploitation
o Internalize external effects a s possible solution →exploring the (marginal) willingness to pay of individuals (L6 social
demand curve)
• Difference between social and private costs/benefits!
o Maximization of social welfare: marginal social benefit=marginal social costs
• Marginal benefits of pollution = marginal damage costs of pollution
• Marginal abatement costs = marginal abatement benefits
• Costly to reduce pollution
• Production (causing pollution) generates producer surplus and consumer surplus
• Damages of pollution to society usually convex
• Benefits of pollution to society usually concave
• Discounting p.41 + 44 in script
o What does it cost you to wait for a payment?
o Value of payment at beginning of t=1?
o A Benefit (or Cost) in t years has a present value of B(orC)/(1+r)t
o 1/(1+r)t=discount factor →includes discount rate
• All rational individuals want to maximize utility
• Utility function: describes the relationship between the consumption of a good/bundle and utility
• Producers maximize profit
• The environmental Kuznets Hypothesis attempts to explain the relationship between economic growth and human action
in the long run
• Aim of microeconomic theory: analyze people’s behaviour at the micro level (individual consumer and producer)
• What impacts consumer and producer choices? →L4+L5
• If y is utility and x is the consumption, f’(x) denotes the “marginal utility” for consuming one extra unit
• Script p.8: Refresher on mathematical Calculus
• Maximum consumption/Minimum consumption:
o if second-order derivation is negative →maximum
o if second-order derivation is positive-→minimum
• the total differential is the sum of partial derivatives of all independent variables
L3
• 5 key assumptions about properties of consumer’s preferences; definition of “good” and”bad” (see p.10 in script)
• Indifference curve=visualizing a preference ordering; all possible combinations of goods that generate the same utility
level
• A utility function represents all existing indifference curves
o U=x1*x2=imperfect substitutes
o U=x1*x2=perfect substitutes
o U=min{x1,x2}=perfect complements (shoe example)
• Exchange relationship between x1 and x2 at the margin = marginal rate of utility substitution (MRUS)
o The rate indicating how much x2 a consumer is willing to give up for an extra unit of x1 while keeping the overall
utility level constant=inverse ratio of marginal utilities of x1 and x2
o =the slope of the indifference curve in a particular point
o MRUS=-2 →at the margin a consumer is willing to exchange 2 units of x2 for 1 additional unit of x1
o →calculate total derivative of utility function
• Maximum value of utility function given a budget constraint (optimal consumption of goods) →Lagrange Method (p.15
in script)
o First, you solve for the two goods consumed in the optimum und then you insert those into the utility function, to
get the utility in the optimum
• Slope of the budget line=inverse price ratio
• Optimal consumption: MRUS=inverse price ratio
• FOC=First order conditions
L4
• If a firm keeps increasing an input, holding all other inpunts and technology constant, the corresponding increases in
output will become smaller eventually
• Isoquant=indifference curve (properties of isoquant see p.19 of script)
• MRTS=the rate at which a producer is willing to substitute k for an extra unit of l
o Derivate production function and set it equal to 0
o Optimal combination of input factors →Lagrange Method
• In short run: increase output only by increasing labor (capital is fix and cannot be varied)
• In long run: increase output by using more of both inputs
• Increasing economies of scale at low levels of output, decreasing economies of scale at high output levels
• Optimal output (given optimal use of input)=marginal revenue equals marginal costs
• Demand function=horizontally aggregating the demands of indivduals
o Shows the raltaionship between price and consumption amount of a good
• Profit maximizing production=marginal costs equal marginal benefits(revenue; p.23 script)
• Supply curve=marginal cost curve
o Horizontally aggregate each firms’ marginal cost curves
, L5 – market failure
• Consumer and producer surplus (see p.25/26 in script)
• The sum of producer and consumer surplus defines the social welfare at the competitive market equilibrium
• Market function conditions, e.g. all goods are private goods and no externalities exist; see p.26 →if one or more are
violated=market failure
• Pure private good/pure public good/common pool resource →p.27 script
• An externality occurs when the production or consumption decisions of one actor have an impact on the utility or profit
of another actor
o Positive vs negative externalities
• Consequences of market failure p. 28 script
• Pollution cause welfare losses to society (“hidden costs”)
o Social welfare in a competitive market, accounting for external costs
o Social welfare in the social optimum, after having internalised external costs
• Deadweight loss (DWL)=welfare difference between private optimum and social optimum
o It is a burden to society because the competitive market equates price with private marginal costs instead with social
marginal costs
• An efficient market equilibrium is assumed to maximize social welfare →sum of consumer and producer
L6 – market failure+Pollution control
• The social marginal benefit of a private good is the same as the marginal benefit to the individual who consumes that good
o The social demand of a private good(=social marginal benefit curve) = horizontal sum of the demand curves ovr all
individuals
o People’s marginal utility from consuming a public good is not known
→we cannot determine the optimal (efficient) consumption points for a public good at the individual level
→social demand curve=vertical sum of individual demands
→a supply curve can be constructed, but this is not sufficient to determine the market equilibrium for this good
• Non rivalry holds for public goods=all individuals can consume the same amount
• Optimal amount of a public good: sum of individuals MRUS=marginal costs od producers
• Flow pollution = residuals have short life-spans before they degrade into harmless forms
• Stock pollution = damages depend on the concentration of the pollutants; for the accumulation space and time may be
relevant
o E.g. Bioaccumulation
o The stock increase more over time, the higher the emission rate
o If production deceases, net benefits increase
• Analyzing stock pollution: p.34 in script
o Emissions per period=decay per period →”steady state”
o Constant production=constant pollution
• Socially optimal pollution level?
• Demage of pollution?
• Optimal abatement level?
L7 – Pollution control
• Markets ignore the true scarcities of natural resources and external costs of an (over)exploitation
o Internalize external effects a s possible solution →exploring the (marginal) willingness to pay of individuals (L6 social
demand curve)
• Difference between social and private costs/benefits!
o Maximization of social welfare: marginal social benefit=marginal social costs
• Marginal benefits of pollution = marginal damage costs of pollution
• Marginal abatement costs = marginal abatement benefits
• Costly to reduce pollution
• Production (causing pollution) generates producer surplus and consumer surplus
• Damages of pollution to society usually convex
• Benefits of pollution to society usually concave
• Discounting p.41 + 44 in script
o What does it cost you to wait for a payment?
o Value of payment at beginning of t=1?
o A Benefit (or Cost) in t years has a present value of B(orC)/(1+r)t
o 1/(1+r)t=discount factor →includes discount rate
