General Equilibrium (weeks7-10)

General Equilibrium (weeks7-10) - Create theory of general...

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Unformatted text preview: Create theory of general equilibrium where there are multiple markets Prior chapters studied partial equilibria where prices of other goods were exogenous (e.g., w and r) But in markets, w and r are determined at same time as P version for Econ 100b, Winter 2011 1 Consider demand for apples and oranges Price of oranges affects demand for apples Price of apples affects demand for oranges In partial equilibrium, hold price of oranges fixed and calculate price of apples In general equilibrium, determine price of both apples and oranges version for Econ 100b, Winter 2011 2 Suppose for apples, QD = 10 – 2PA + PO Suppose for oranges, QD = 10 + PA - 2PO Supply only depends on own price: QS = 2PA QS = PO version for Econ 100b, Winter 2011 3 version for Econ 100b, Winter 2011 4 version for Econ 100b, Winter 2011 5 Suppose there is a $1 tax on apples. version for Econ 100b, Winter 2011 6 version for Econ 100b, Winter 2011 7 version for Econ 100b, Winter 2011 8 In an exchange economy, individuals own and trade goods No production or firms Simplification; introducing production isn’t a big headache. Consider an economy with two people: Jane and Denise Jane has 30 cords of firewood and 20 candy bars Denise has 20 cords of firewood and 60 candy bars Together, they have 50 cords of firewood and 80 candy bars Questions: What are the efficient allocations? Could a market achieve this efficient allocation? version for Econ 100b, Winter 2011 9 version for Econ 100b, Winter 2011 10 version for Econ 100b, Winter 2011 11 Utility Maximization: Each person maximizes her utility Convex Indifference curves Nonsatiation: Each person has strictly positive MU for each good No interdependence: Each person’s utility determined by own consumption version for Econ 100b, Winter 2011 12 Efficiency: Impossible to make one player strictly better off without making other strictly worse off Could of course make both worse off Where indifference curves are tangent version for Econ 100b, Winter 2011 13 version for Econ 100b, Winter 2011 14 version for Econ 100b, Winter 2011 15 version for Econ 100b, Winter 2011 16 version for Econ 100b, Winter 2011 17 version for Econ 100b, Winter 2011 18 Suppose there is 1 unit of x and 1 unit of y Person 1’s Utility: u1 = x y1Person 2’s Utility: u2 = x y1- version for Econ 100b, Winter 2011 α −α ∂ = ∂ ∂= ∂ ∂ ∂ ∂= ∂ 19 β− −β − If = , version for Econ 100b, Winter 2011 20 = −α β −β α + β−α = −β α β−α + −α β −α β = + −β α −α β − version for Econ 100b, Winter 2011 21 version for Econ 100b, Winter 2011 22 version for Econ 100b, Winter 2011 23 version for Econ 100b, Winter 2011 24 version for Econ 100b, Winter 2011 25 Recall that from consumer maximization: So, in a competitive eqm, condition for efficiency holds version for Econ 100b, Winter 2011 26 version for Econ 100b, Winter 2011 27 Suppose that A and B both have utility functions u(x,y) = x1/2y1/2, Let A’s endowment be (2,1) and B’s endowment be (1,2). Derive the competitive equilibrium prices. version for Econ 100b, Winter 2011 28 version for Econ 100b, Winter 2011 29 version for Econ 100b, Winter 2011 30 Any competitive equilibrium is Pareto efficient. Markets create opportunities for exchange that lead to efficiency Pareto efficiency: no one can be made strictly better off without making the other strictly worse off Weak criterion: Not sensitive to inequality version for Econ 100b, Winter 2011 31 version for Econ 100b, Winter 2011 32 Any competitive equilibrium is Pareto efficient. Markets create opportunities for exchange that lead to efficiency Pareto efficiency: no one can be made strictly better off without making the other strictly worse off Weak criterion: Not sensitive to inequality Conditions for this to apply not satisfied in practice. version for Econ 100b, Winter 2011 33 version for Econ 100b, Winter 2011 34 Any Pareto efficient equilibrium can be obtained by market competition, given appropriate endowments As such, can rely on markets if we re-arrange endowments Of course, re-arranging endowments can’t be done If one can re-arrange endowments, why have any market exchange? version for Econ 100b, Winter 2011 35 Any Pareto efficient equilibrium can be obtained by market competition, given appropriate endowments One may wonder whether Market allocations PE allocations. Result tells us that every Pareto efficient allocation is “stable.” version for Econ 100b, Winter 2011 36 Basic question: how should society rank alternatives? Utilitarianism Weighted Utilitarianism Rawlsian MaxMin version for Econ 100b, Winter 2011 37 Some natural criteria for “social welfare”: 1. (Unrestricted Domain) Social preferences should be complete and transitive 2. (Pareto Optimality) If everyone prefers a to b, society should prefer a to b 3. (Independence of Irrelevant Alternatives) The social assessment of a and b should depend only on individual preferences between a and b 4. (Non-Dictatorship) Social preferences should not reflect the preferences of any single individual. version for Econ 100b, Winter 2011 38 There exists no social welfare function that satisfies the preceding four criteria. version for Econ 100b, Winter 2011 39 Suppose there are 3 people – {1,2,3} 3 Alternatives {a,b,c} version for Econ 100b, Winter 2011 40 version for Econ 100b, Winter 2011 41 Two consumers A and B in a trade economy (with no production), have utility functions: U A = x A yA U B = x B yB and initial endowments of the goods: xA = 10 yA = 6 xB = 8 yB = 12 What is the contract curve? What is the core? version for Econ 100b, Winter 2011 42 xB = 8 Y = 18 yB = 12 yA = 6 xA = 10 X = 18 version for Econ 100b, Winter 2011 43 version for Econ 100b, Winter 2011 44 version for Econ 100b, Winter 2011 45 xB = 8 Contract curve Y = 18 yB = 12 yA = 6 xA = 10 X = 18 version for Econ 100b, Winter 2011 46 version for Econ 100b, Winter 2011 47 version for Econ 100b, Winter 2011 48 version for Econ 100b, Winter 2011 49 version for Econ 100b, Winter 2011 50 Thought of firms as producers, but firms are also consumers of services Purchase capital from a capital market Hire labor from a labor market Analysis similar to that of Chapters 7 and 8. Recall that Diminishing Marginal Product of Labor: Marginal product of labor decreases with L ∂MPL <0 ∂L version for Econ 100b, Winter 2011 51 Suppose capital is fixed at K Production function can be written as q = f(L,K) = q(L) Then profit function is: version for Econ 100b, Winter 2011 52 Labor’s marginal product tells you how much more of the output each additional unit of labor produces Labor’s marginal revenue product is how much more $$ each additional unit of labor yields Monetized version of marginal product Is the “Marginal utility” to a producer of hiring another unit of labor MRPL = ∂R(q ( L)) ∂L version for Econ 100b, Winter 2011 53 Taking derivative wrt L: version for Econ 100b, Winter 2011 54 version for Econ 100b, Winter 2011 55 version for Econ 100b, Winter 2011 56 Would intuitively expect dL/dw < 0: as w increases, L decreases as w decreases, L increases pMPL = w version for Econ 100b, Winter 2011 57 version for Econ 100b, Winter 2011 58 Would intuitively expect dL/dp > 0: as p increases, L increases as p decreases, L decreases pMPL = w version for Econ 100b, Winter 2011 59 version for Econ 100b, Winter 2011 60 q = ALaKb version for Econ 100b, Winter 2011 61 Now suppose that K and L are flexible version for Econ 100b, Winter 2011 62 version for Econ 100b, Winter 2011 63 version for Econ 100b, Winter 2011 64 Suppose f(L,K) = L1/3K1/3, p = 5, w = 2, r = 1. Usually would find C(q) using MRTS = - w/r Then set p = MC(q) Can use factor demand equations for easier method Have to check that MPL is decreasing in L and MPK is decreasing in K MaxL,K 5L1/3K1/3 – 2L-K version for Econ 100b, Winter 2011 65 version for Econ 100b, Winter 2011 66 Suppose f(L,K) = LK1/2, p = 1, w = 2, r = 1. Notice that MPL is not decreasing in L MaxL,K LK1/2 – 2L - K version for Econ 100b, Winter 2011 6 version for Econ 100b, Winter 2011 6 ...
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This note was uploaded on 11/30/2011 for the course ECON 311 taught by Professor Zambrano during the Fall '08 term at Cal Poly.

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