The Economics of Climate Change – C 175 The economics of climate change C 175 ‐ Christian Traeger 75 g Part 2: Efficiency, Public Goods, Externalities Externalities Suggested background reading for emerging questions: Suggested background reading for emerging questions: Kolstad, Charles D. (2000), “Environmental Economics”, Oxford University Press, New York New York. Varian, Hal R. (any edition...), “Intermediate Microeconomics – a modern approach”, W. W. Norton & Company, New York. pp , p y, Spring 09 – UC Berkeley – Traeger 2 Efficiency 1
The Economics of Climate Change – C 175 A Brief Micro Review: From Preferences to Efficiency Spring 09 – UC Berkeley – Traeger 2 Efficiency 2
The Economics of Climate Change – C 175 Preferences Preferences, Indifference Curves, Budget Constraints, and Choice (Blackboard) Spring 09 – UC Berkeley – Traeger 2 Efficiency 3
The Economics of Climate Change – C 175 Utility From (well behaved) preferences we can build “Mountains of Pleasure” (Blackboard? No, you have seen me drawing Antarctica and England…) Spring 09 – UC Berkeley – Traeger 2 Efficiency 4
The Economics of Climate Change – C 175 Spring 09 – UC Berkeley – Traeger 2 Efficiency 5
The Economics of Climate Change – C 175 Spring 09 – UC Berkeley – Traeger 2 Efficiency 6
The Economics of Climate Change – C 175 Utility Each bundle is associated with a utility level U(x,y) You can think of utility as a measure of pleasure, or happiness, or simply as representing preferences More utility = preferred Indifference curves are the topo lines or contour lines of the utility Indifference curves are the topo lines or contour lines of the utility mountain While of a lot of the analysis that we will do could be done right away with preferences, utility functions are a very convenient tool to make i h f ili f i i l k things easier Spring 09 – UC Berkeley – Traeger 2 Efficiency 7
The Economics of Climate Change – C 175 Utility Marginal utility (MU) of good x: Change in utility ( Δ U) associated with a small change in the amount of good x ( Δ x). (Note that good y is kept constant, MU depends on x ‐ level) (N t th t d i k t t t MU d d l l) ( , ) ( , ) U U x x y U x y Discrete change: MU x x x ( , ) ( , ) U U x x y U x y Infinitesimal change: lim MU 0 x x X x Change in utility caused by a change Δ x is then (approximately) Δ U = MU x Δ x Spring 09 – UC Berkeley – Traeger 2 Efficiency 8
The Economics of Climate Change – C 175 Utility More precisely marginal utility is itself a function of x and y: MU x = MU x (x,y) Frequently met assumption: Diminishing Marginal Utility : The pleasure of an additional unit of consumption of good x decreases the more of good x I consume. Spring 09 – UC Berkeley – Traeger 2 Efficiency 9
The Economics of Climate Change – C 175 Aside on Cardinal vs Ordinal Utility: An ordinal measure/ An ordinal utility function: – (only) ranks alternatives – the value means nothing in absolute terms – e.g. grades, finishing position in race A cardinal measure / A cardinal utility function: – Absolute measure allowing ranking and absolute comparison – e.g. tons of carbon, income For describing market outcomes we only need ordinal utility F d ibi k l d di l ili To aggregate utility over different individual we need cardinal utility (necessary for most normative comparisons of market outcomes) Spring 09 – UC Berkeley – Traeger 2 Efficiency 10
The Economics of Climate Change – C 175 Marginal Rate of Substitution Marginal rate of substitution (MRS) = Rate at which a consumer is just willing to substitute one good for the other = Rate at which the consumer is just on the margin of being willing to ‘pay’ some of good x in order to buy some more of good y = Slope of indiffierence curve = Slope of indiffierence curve (Note: Generally negative, what does that mean?) U Y Y MU MU p X Formally: X X MRS U X MU p Y Y Y This side is all about This side is all about Here he hits Here he hits the consumer the market Derive this from Δ U = MU x Δ x+ MU y Δ y=0 (meaning U is constant)! Spring 09 – UC Berkeley – Traeger 2 Efficiency 11
The Economics of Climate Change – C 175 Marginal Rate of Substitution Remark: While MU is a cardinal measure, MRS is an ordinal measure! MRS is an ordinal measure! Frequently made assumption: Diminishing marginal Diminishing marginal rate of substitution is responsible for max , A A A A A L U X Y M p X p Y X Y better bundles better bundles convex indifference curves ‘Different’ perspective on convex feasible bundles indifference curves: indifference curves: Averages are preferred Spring 09 – UC Berkeley – Traeger 2 Efficiency 12
The Economics of Climate Change – C 175 Efficiency in consumption: X vs Y For some Individual A: The necessary condition for Th di i f Individual utility utility maximizing maximisation: max , A A A A A L U X Y M p X p Y X Y better bundles Max U(X Y) Max U(X,Y) subject to: p x X+p y Y=M feasible bundles given prices and income M are given prices and income M are A U p A X A X MRS A U U p p Y A Y and yield the generally efficient choices X* and Y* Spring 09 – UC Berkeley – Traeger 2 Efficiency 13
The Economics of Climate Change – C 175 Pareto Efficiency ff O One of the most important economic concepts – named after the f th t i t t i t d ft th Italian economist Vilfredo Pareto (1848 ‐ 1923). Definition An allocation is Pareto optimal or Pareto efficient , if it is not possible to reallocate the resources of the economy in a way such that possible to reallocate the resources of the economy in a way such that at least one person is better off without making any other person worse off. An allocation is inefficient if it is possible to make one member of the A ll ti i i ffi i t if it i ibl t k b f th society better off without making any other member worse off. Such a movement is called Pareto improvement . Spring 09 – UC Berkeley – Traeger 2 Efficiency 14
The Economics of Climate Change – C 175 Efficiency in consumption: X vs Y Take a second consumer B Both consumers face same market prices and take them as given g Then efficiency requires A B U U p p A B X X X X A A B X MRS MRS A B U p U Y A B Y Y What about the efficiency of Wh t b t th ffi i f points a and b ? Edgeworth Box: Consumer A’s origin is the upper right corner and his utility i increases moving to the lower left i t th l l ft (blue indifference curve) Spring 09 – UC Berkeley – Traeger 2 Efficiency 15
The Economics of Climate Change – C 175 Efficiency in consumption: X vs Y Take a second consumer B Both consumers face same market prices and take them as given g Then efficiency requires A B U U p p A B X X X X A A B X MRS MRS A B U p U Y A B Y Y Point a not Pareto efficient; P i P ffi i point b is Pareto efficient Edgeworth Box: Consumer A’s origin is the upper right corner and his utility i increases moving to the lower left i t th l l ft (blue indifference curve) Spring 09 – UC Berkeley – Traeger 2 Efficiency 16
The Economics of Climate Change – C 175 Efficiency in consumption: X versus Y Note that there are infinitely many Pareto efficient ● allocations Which one will occur depends p ● on initial allocation of resources ● ● Spring 09 – UC Berkeley – Traeger 2 Efficiency 17
The Economics of Climate Change – C 175 Production (please review these slides in more detail at home) Firm i produces X and maximizes profits: max , X X X X p X K L p K p L i X i i i K i L i X ,L i X ) is the production function. Where X i (K i X and labor L i X . It uses the inputs capital K i Similarly some firms j produce Y and maximize: Similarly some firms j produce Y and maximize: max , Y Y Y Y p Y K L p K p L j Y j j j K j L j Spring 09 – UC Berkeley – Traeger 2 Efficiency 18
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