Lecture 1 Introduction to Micorarraysand Concepts of Molecular Biology

Lecture 1 Introduction to Micorarraysand Concepts of Molecular Biology

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  • cours magistral
Lecture 1 Introduction to Micorarrays and Concepts of Molecular Biology M. Saleet Jafri Program in Bioinformatics and Computational Biology George Mason University
  • prokaryotic cell
  • informational elements
  • molecular biology review
  • life shares
  • unicellular organisms
  • biological references
  • molecular biology
  • genomic dna
  • common origin
  • life

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Lecture 3: First and Second Theorems of Welfare Economics and Market Efficiency 1)For the moment we are going to forget that this class is about the environment and talk about basic welfare economics instead a)Start with definitions b)Move on to most powerful theorems of welfare economics c)Talk about the conditions for these theorems to hold 2)Definitions a)Welfare economicsis the systematic method of evaluating the economic implications of alternative resource allocations. Welfare analysis answers the following questions: i)Is a given resource allocation efficient? ii)Who gains and who loses under various allocations, and by how much? b)Competitive economy- an economy which consists of many small economic units - each with no market power - conditions for competitive economy – i)Q: What are the conditions for a competitive economy? ii)mobile resources, iii)many buyers and sellers, iv)traded good is homogenous, v)perfect information. c)Pareto improvement:A reallocation of resources such that some individuals are made better off while no individuals are made worse off. d)Pareto efficiency -We say we have satisfied Pareto efficiency when there are no opportunities for Pareto improvements i)We say allocation/arrangement X is Pareto superior to Y if all individuals are at least as happy with X as with Y, and at least one individual is happier. ii)Consider the case of three boys who will earn (5,5,7) if they do chore X together or (6,6,7) if they do chore Y together. the two tasks are equally onerous and the employer is indifferent between the two chore-payment arrangements. Then doing chore Y is Pareto superior.
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e)Kaldor-Hicks efficiency -We say X is Kaldor-Hicks superior to Y if there is a state that is accessible from X that is Pareto superior to Y. This allows for the theoretical possibility at least that everyone could be made better off by choosing X. i)What is a common application of the Kaldor-Hicks criterion? [Cost-benefit] ii)We are mostly going to be talking about the Pareto criterion today. 3)Role of trade in an economy - Edgeworth boxa)We have talked in V517 about i)Consumer and producer theory ii)Inputs and input prices iii)Have to ask, how do the right resources get to the right place? b)Consumption Economyi)Consider a very simple pure exchange economy: island economy - two individuals, two goods, no production (1)Call the individuals Gilligan and Skipper and the goods Coconuts and Fish. (2)There are C units of coconut and F units of fish that must be shared (3)Each individual has a utility function that expresses their relative satisfaction as a function of the amount of the two goods they consume. The utility functions are monotonic and selfish, (a)Monotonic - nonsatiation - more is better than less (b)Selfish - independence of utility from consumption of others (4)Must cover the entire range of consumption possibilities (5)Can express the utility function in graphical form, with indifference curves(a)The individual’s utility or welfare level is the same with any combination of goods that are on the same indifferent curve.
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(b)There is an decreasing marginal rate of substitution for either good (6)Gilligan’s indifference curve: FLIP IT OVER and it still means the same thing. In fact that is how we will represent Skipper’s indifference curve (a)We can map out the entire feasible distribution of goods by laying one on top of other (b)Any point in this coconut fish space represents a distribution of all resources among the two members of the economy. (c)Overlay the two sets of indifference curves to create a coconut-fish distribution space and consider an initial distribution D. This is called an Edgeworth Box. It is commonly used in microeconomics to illustrate simple trading priniciples.
(d)Gilligan consumesafish andbcoconuts, so Skipper consumes(F-a)fish and(C-b)coconuts. (e)There are an infinite number of initial distribution points, D
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(7)Now, suppose that we allow Skipper and Gilligan to trade, essentially reallocating resources from this initial distribution. (a)How do we know where they will end up? What criteria must be satisfied before they will stop trading? (b)We apply two criteria (i)Economic or allocative efficiency –Pareto Efficiency(ii)Some traders better off, none worse off; that is the outcome needs to bePareto Superiorto initial allocation (c)Pareto Efficiency:(i)Where are the Pareto efficient points in this coconut-fish space? Marginal rate of substitutionof fish for coconuts must be the same for both Skipper and Gilligan (ii)Defn: Number of units of coconuts that will give up for one unit of fish, while remaining on same indifference curve. Equal to (-1)(slope of indifference curve). (iii)The marginal rates of substitution are equal only where the indifference curves are tangent. (iv)How many tangents are there. Remember there are an infinite number of indifference curves in the coconut fish space, so there much be an infinite number of tangent points. But each of Gilligan’s curves are tangent to one and only one of Skipper’s curves. (v)Contract curve1.Def’ncontract curve: set of points where MRSG=MRSS
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2.It actually looks like a small subset of all possible allocations, but it is still an infinite number of points. Shown in green in this digram. (d)Pareto Superiority:(i)All points on the contract curve are Pareto Efficient or Optimal. Are all points on the contract curve Pareto Suprerior to the initial distribution point? No, they are not. (ii)Find a point on the contract curve that is not Pareto Superior. How do you know that it is not Pareto Superior? (iii)The set of points that are Pareto superior to D are called theLens. These are shown as the orange shaded area in the diagram above. They are the points (distributions of goods) at which both traders would be at least as well off, and one trader better off. Therefore, they also represent the points to which the traders would move voluntarily. (iv)TheCoreis the set of
points that are both Pareto superior and Pareto efficient; it is the locus of Pareto optimal points within the lens shaped area that is bounded by the indifference curves passing
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through the initial allocation D. 1.At any place on the core the MRS of two traders is the same, i.e. there are no more mutual gains from trade available. Where on the core they end up will depend upon the relative bargaining skills of the individual traders. 2.In a perfectly competitive economy, we get some outcome that distributes goods among consumers based on an equilibrium price system. 3.What is the relation between the theoretical market outcome based on prices and the core? 4)First Fundamental Theorem of Welfare Economicsa)Definitions: i)xis the allocation of goods to all traders in the economy - x is a matrix with two dimensions: quantity of good and amount allocated to each trader ii)pis a vector of prices for each good b)First Fundamental Theorem of Welfare Economics. If all traders have monotonic selfish utility functions, and if (x,p) is a competitive equilibrium, then x is in the core, and is therefore Pareto optimal as well. c)What this says is that the price system from a perfectly competitive economy, induces selfish individuals independently maximizing their private well-being, to bring the economy to a socially optimal state. Prices rise in response to excess demand, fall in response to excess supply - adjust on their own. d)Normatively, it says use the competitive mechanism - use the free market. e)Read excerpt from Kahn p11, Adam Smith on invisible hand. 5)Second Fundamental Theorem of Welfare Economicsa)Besides prices, what determines which of the many Pareto efficient points on the contract curve will result from the competitive equilibrium? [Initial allocation] i)Does the FFTWE say anything about the initial distribution or about equity? ii)Can the competitive equilibrium get you from a very uneven initial allocation to a more equitable final allocation? Not really, the theorem takes initial
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distribution as given. Uneven initial allocation => uneven competitive allocation. iii)What are some examples of uneven initial allocations? E.g. talent, capital, family etc. iv)Take awayWhy not just reallocate goods, move from one point to another? some of Skipper’s fish and give them to Gilligan v)The problem is that in a real economy there are large numbers of goods and consumers, not just two of each. vi)This madeE.g., of gasoline in 1979 - DOE reallocation of supplies by region. a mess of the distribution system and was inefficient. b)What would be an alternative mechanism? Simply reallocate one good - e.g., money. The price system can then facilitate exchange for Pareto efficient outcomes in the core. c)Definitions: i)yis any Pareto optimal allocation that assigns positive quantities of every good to every trader: yij> 0 for all I, j ii)m is the number of goods in the economy iii)n is the number of traders in the economy d)Second Fundamental Theorem of Welfare Economics.There exists a vector of bank balance transfers (T1, T2, ...,Tn) and a price vectorp= (p1, p2, ...,pm) such that y andpare a competitive equilibrium given the transfers. i)What does this say? (1)Choose an outcome that is economically efficient (i.e., it is on the contract curve). (2)You can get to that outcome by redistributing the initial allocation of resources and then simply relying upon the competitive mechanism. (3)C.f. western water supply – we know marginal cost pricing is superior to subsidized system - but we have always worried about the distributional effects it might have. If that is the case then simply redistribute the initial property rights.
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(4)So the SFTWE says that the competitive mechanism, with modifications, is even more robust than described by the FFTWE. 6)These two theorems taken together relieve the government of an enormous amount of work - no need to decide every consumption decision/opportunity for every consumer - just get the initial allocation close to an are you want, and you can let the market take over. a)Assumptions behind market efficiency i)What are the assumptions behind perfectly competitive markets (1)Costless entry and exit (2)Homogenous goods (3)Perfect info
(4)Many suppliers and buyers ii)In the FFTWE and SFTWE what were the assumptions? (1)Monotonic selfish utility functions - consumer sovereignty (2)That if you don’t like the initial distribution you can redistribute wealth. iii)Are there any other assumptions implicit in this (1)Goods are all owned - i.e., there are property rights in each important good – F&SFTWE apply to individual markets not whole economy (2)They are consumption goods - if you use it, I don’t (3)That I don’t steal your goods from you - No cheating (4)In the marginal cost supply function - full costs of production are reflected In the demand function full range of benefits is reflected (5)In fact, demand and supply functions are based on individual assessments of costs and benefits. Need to ask about the relation between social and private benefits. (6)No paternalism – we accept the consumer sovereignty
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