Coursenotes_ECON301

In other words the supply curves are vertical for

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Unformatted text preview: ents XB , YB prices income PX , PY MB = PX XB + PY YB Note that the endowment income, MA, is also a function of prices, PX , PY. Note that endowment income, MB, is also a function of prices, PX , PY. 96 Utility Maximization maximize UA(XA,YA) subject to PX XA + PY YA = MA Consumer Equilibrium Analytically, the two conditions for consumer equilibrium must be satisfied: MRSA = PX PY PX XA + PY YA = MA Solving these two equations for XA &amp; YA we get the demands by consumer A. XA = XA(PX, PY, MA) YA = YA(PX, PY, MA) Since the endowment income, MA, is also a function of prices, PX, PY, we can eliminate MA and express the consumer demands in terms of prices PX, PY, alone. XA = XA(PX, PY) YA = YA(PX, PY) Utility Maximization maximize UB(XB,YB) subject to PX XB + PY YB = MB Consumer 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 &amp; YB we get the demands by consumer B. XB = XB(PX, PY, MB) YB = YB(PX, PY, MB) Since the endowment income, MB, is also a function of prices, PX, PY, we can eliminate MB and express the consumer demands in terms of prices PX, PY, alone. XB = XB(PX, PY) YB = YB(PX, PY) 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). Now, on one hand we have the individual consumer demands XA, YA, XB, YB and on the other hand we have fixed quantities of goods supplied represented by the total endowment of the good in the economy, X , Y. Now, for equilibrium to occur, we need to put these hands together! 97 MARKET DEMAND FOR X On the demand side, using the horizontal summation technique, we obtain the aggregate demand function for good X. X = XA(PX, PY) + XB(PX, PY) = X(PX, PY) MARKET DEMAND FOR Y On the demand side, using the horizontal summation technique, we obtain the aggregate demand function for good Y. Y = YA(PX, PY) + YB(PX, PY) = Y(PX, PY) On the supply side, we already know that the market supply of good X is fixed at X. supply = X At market equilibrium, the aggregate de...
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