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Unformatted text preview: has the following data on utility function and endowment income: MRSB = YB XB MB = r KB + w LB = 0.8 r + 0.4 w Utility Maximization maximize UB = XB1/2YB1/2 subject to PX XB + PY YB = MB Consumer Equillibrium Analytically, the two conditions for consumer equilibrium must be satisfied: 251 MRSA = PX PY PX XA + PY YA = MA Solving these two equations for XA & YA we get the demands by consumer A. XA = M A 2PX XA = 0.2r + 0.6w 2PX Additional Step (notice ... but ignore for now) MRSB = PX PY PX XB + PY YB = MB Solving these two equations for XB & YB we get the demands by consumer B. XB = MB 2PX XB = 0.8r + 0.4w 2PX Since good X is our Public Good we need one extra step to find the individual consumer's willingness to pay for the public good. We can derive this from their individual demand functions as follows: XA = 0.2r + 0.6w 2PXA PXA = 0.2r + 0.6w 2 XA XB = 0.8r + 0.4w 2PXB PXB = 0.8r + 0.4 2 XB Now, remember that for public goods XA = XB = X so the above expressions become... PXA = 0.2r + 0.6w 2X PXB = 0.8r + 0.4 2X Now back to our original problem strategy. XA = r + 3w 10PX YA = M A 2PY YA = 0.2r + 0.6w 2PY YA = r + 3w 10PY 252 XB = 4r + 2w 10PX YB = MB 2PY YB = 0.8r + 0.4w 2PY YB = 4r + 2w 10PY PRODUCER OF GOOD X The producer of good X has the following MRTS: MRTSX = LX KX Cost Minimization minimize cost r KX + w LX subject to KX1/2LX1/2 = QX Producer Equilibrium Analytically, the two conditions for producer equilibrium must be satisfied: MRTSX = _r_ w KX1/2LX1/2 = QX Solving these two equations for KX & LX we get the demands by producer X. KX-1/2LX1/2 = _r_ w KX1/2LX1/2 LX = _r_ KX w KX = LXw r LX = KXr w sub KX into production function: QX = [LX(w / r)]1/2LX1/2 QX = LX(w / r)1/2 253 PRODUCER OF GOOD Y The producer of good Y has the following MRTS: MRTSY = LY KY Cost Minimization minimize cost r KY + w LY subject to KY1/2LY1/2 = QY Producer Equilibrium Analytically, the two conditions for producer equilibrium must be satisfied: MRTSY = _r_ w KY1/2LY1/2 =...
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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.
- Spring '10