E market equilibrium so how do we go from individual

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Unformatted text preview: s along the horizontal axis. P DB DA Aggregate Demand Curve PX X X A X B X +X A B For example, suppose that we have two consumers, A and B, with the following individual demands for good X: XA = XA(PX, PY, MA) XB = XB(PX, PY, MB) These individual demand functions could have been derived from the usual utility maximization problem with given market prices, PX, PY, and individual incomes MA and MB as follows: CONSUMER A Utility Maximization problem: Maximize UA(XA, YA) Subject to: PXXA + PYYA = MA CONSUMER B Utility Maximization problem: Maximize UB(XB, YB) Subject to: PXXB + PYYB = MB 82 Consumer equilibrium condition: MRSA = PX PY PXXA + PYYA = MA Individual demand functions: XA = XA(PX, PY, MA) YA = YA(PX, PY, MA) Consumer equilibrium condition: MRSB = PX PY PXXB + PYYB = MB Individual demand functions: XB = XB(PX, PY, MB) YB = YB(PX, PY, MB) Now the aggregate demand can be constructed from these two individual demands by the technique of horizontal summation which basically adds the quantities demanded by both A and B as follows: X = XA(PX, PY, MA) + XB(PX, PY, MB) X = X(PX, PY, MA, MB) Note that while each individual demand is a function of incomes MA and MB separately, the aggregate demand is a function of both MA and MB jointly. We just said that general equilibrium theory studies the interdependence among the three basic components of the economy (consumer equilibrium, producer equilibrium, and market equilibrium). We showed how we go from individual levels to aggregate levels using aggregation or horizontal summation. Remember that we said this process is called horizontal summation because we fix the common independent variable at some level on the vertical axis and then add all of the individual dependent variables along the horizontal axis. 83 P DB DA Aggregate Demand Curve PX X X A X B X +X A B For example, suppose that we have two consumers, Ross and Rachel, with the following individual demands for good X and good Y XRoss = XRoss(PX, PY, MRoss) = MRoss / (2 PX) YRoss = YRoss(PX, PY, MRoss) = MRoss / (2 PY)...
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