The economics of climate change C 175 Christian Traeger 75 g Part - PowerPoint PPT Presentation

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