Coursenotes_ECON301

Utility maximization maximize uaxaya subject to px xa

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Unformatted text preview: r Equillibrium Analytically, the two conditions for consumer equilibrium must be satisfied: MRSB = PX PY PX XB + PY YB = MB Solving these two equations for XB & YB we get the demands by consumer B. XB = XB(PX, PY, MB) YB = YB(PX, PY, MB) Since the endowment income, MB, is a function of factor prices, r, w, we can eliminate MB and express the consumer demands in terms of prices (PX, PY, r, w) alone. XB = XB(PX, PY, r, w) YB = YB(PX, PY, r, w) Consumers A and B make their own optimal decisions on their quantities (XA and YA or XB and YB respectively), independent of the other consumer, yet they are linked to each other through market prices (PX, PY, r, w). The treatment of production is the key difference between the pure exchange economy and this production economy model. Each producer solves its own individual optimizing decision to get its demands for factors. PRODUCER OF GOOD X decisions KX , LX PRODUCER OF GOOD Y decisions K Y , LY production function QX = f(KX,LX) Assume CRS production function. 131 production function QY = g(KY,LY) Assume CRS production fnc. prices r,w prices r,w output level QX Cost Minimization minimize cost r KX + w LX subject to f(KX,LX) = QX Producer Equilibrium Analytically, the two conditions for producer equilibrium must be satisfied: MRTSX = _r_ w f(KX,LX) = QX Solving these two equations for KX & LX we get the demands by producer X. KX = KX(r, w, QX) LX = LX(r, w, QX) Constant Returns to Scale The factor demands by producer X are thus functions of factor prices and its prices output level QX. Since f(KX,LX) is a constant returns to scale production function, we can divide factor demands KX,LX by the total output level QX in order to get the factor demands on a per unit of output basis as follows: KX = kX(r, w) QX output level QY Cost Minimization minimize cost r KY + w LY subject to g(KY,LY) = QY Producer Equilibrium Analytically, the two conditions for producer equilibrium must be satisfied: MRTSY = _r_ w g(KY,LY) = QY Solving these two equations for KY & LY we get the demands by producer Y....
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.

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