The Economics of Climate Change –C 175 The economics of climate change C 175 ‐ Christian Traeger Part 2: Efficiency, Public Goods, Externalities Suggested background reading for emerging questions: Kolstad, Charles D. (2000), “Environmental Economics”, Oxford University Press, New York. Varian, Hal R. (any edition...), “Intermediate Microeconomics –a modern approach”, W. W. Norton & Comppy,any, New York. 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 mountain While of a lot of the analysis that we will do could be done right away wihith preferences, utility fifunctions are a very convenient tool to make 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 (ΔU) associated with a small change in the amount of good x (Δx). (Not e that good y is ktkept constttant, MU dddepends on x‐ll)level) U U (x x, y) U (x, y) Discrete change: MU x x x U U (x x, y) U (x, y) Infinitesimal change: MU lim x X x0 x Change in utility caused by a change Δx is then (approximately) ΔU = MUx Δx 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: MUx = MUx (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 dibidescribing market outcomes we only need ordina l utility 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 (Note: Generally negative, what does that mean?) U Y MU p Formally: MRS X X X U X MUY pY Y This side is all about Here he hits the consumer the market Derive this from ΔU = MUx Δx+ MUy Δy=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! Frequently made assumption: Diminishing marginal rate of substitution A A A A A is responsible for max L U X ,Y M pX X pYY better bundles convex indifference curves ‘Different’ perspective on convex feasible indifference curves: bundles 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 condit ion for Individual utility utility maximizing maximisation: A A A A A max L U X ,Y M pX X pYY Max U(X,Y) better bundles subject to: px X+py Y=M feasible given prices and income M are bundles U A A A X pX MRS A U pY Y A 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 One of the most ittimportant economic concepts –named after the 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 at least one person is better off without making any other person worse off. An allocati on is iffiitinefficient if it is possible to make one member of the 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 Then efficiency requires U A U B A B A X pX X B MRS A B MRS U pY U Y A Y B What abtbout the effici ency of points a and b ? Edgeworth Box: Consumer A’s origin is the upper right corner and his utility increases moving to the lower lftleft (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 Then efficiency requires U A U B A B A X pX X B MRS A B MRS U pY U Y A Y B PiPoint a not Pareto effici ent; point b is Pareto efficient Edgeworth Box: Consumer A’s origin is the upper right corner and his utility increases moving to the lower lftleft (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 ● 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: X X X X max i pX X i Ki , Li pK Ki pL Li X X Where Xi (Ki ,Li ) is the production function. X X It uses the inputs capital Ki and labor Li . Similarly some firms j produce Y and maximize: Y Y Y Y max j pYYj K j , L j pK K j pL L j Spring 09 –UC Berkeley – Traeger 2 Efficiency 18 The Economics of Climate Change –C 175 A similar reasoning holds for production Marginal Rate of Technical Substitution (MRTS) or Technical Rate of Substitution = how much more of an input factor into production do we need if we give up a little bit of the other input factor while keeping the output constant Analogy: MRS Isoquant = set of all possible input combinations that are just sufficient to produce a given amount of the output Analogy: Indifference curve Marginal Rate of Transformation (MRT) = rate at which we can technically transform one output good into the other AlAnalogy: Also MRS (Note: we do not actually transform one output into the other, but switch inputs from one production to the other) Spring 09 –UC Berkeley – Traeger 2 Efficiency 19 The Economics of Climate Change –C 175 Efficiency in production: Capital K versus Labor L (inputs) All firms face the same factor prices and take them as given, say two X producers (first line) and two Y producer (second line) • Then efficiency requires: X1 X 2 K X p K X MRTS X 1 K 2 MRTS X 1 X X 2 1 pL 2 X X L1 L2 Y1 Y2 K Y p K Y MRTS Y 1 K 2 MRTS Y 1 Y Y 2 1 pL 2 Y Y L1 L2 • Point a not Pareto efficient; point b is Pareto efficient Spring 09 –UC Berkeley – Traeger 2 Efficiency 20 The Economics of Climate Change –C 175 Efficient product mix: output goods X versus Y ( a tough one…) Profit maximization: X X X X X max i pX X i Ki , Li pK Ki pL Li X X X Y i 0 p i p 0 i i K X X K X K p K X p K Y dX i i X i 1 X i i MRT Y X K pY i pY i dYi X X Y X i i Ki Ki X 0 pX X pL 0 Li Li Y Y Y Y Y max i pYYi Ki , Li pK Ki pL Li Y Y i 0 p i p 0 X Y K Y Y K Y K i i i i p LX p LY dX X i 1 X i i MRT Y Y Y X L i i pY i pY i dYi Y 0 pY Y pL 0 Y X Li Li Li Li Spring 09 –UC Berkeley – Traeger 2 Efficiency 21 The Economics of Climate Change –C 175 Efficiency in consumption and product mix Utility maximization: U A U B A B A X pX X B If not equal, then consumption mix MRS A B MRS U pY U should be changed.