Coursenotes_ECON301

# E the price of the numeraire demand for good x demand

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Unformatted text preview: ility maximization problem: X = X(PX , PY) Y = Y(PX , PY) remain invariant to a change of all prices PX , PY. We describe this property by saying that the consumer demand functions are homogeneous of degree zero to prices. PURE EXCHANGE ECONOMY Now let's set up the logical structure of the pure exchange economy general equilibrium model (two consumers and two goods). As simple as it is, the pure exchange economy is an excellent introduction to various techniques and tools used in general equilibrium theory. This pure exchange economy focuses our attention on the consumption side of the economy while leaving the production side mysteriously unaccounted for. Basically, there are two consumers, A and B, making consumption and exchange decisions (barter) on two goods, X and Y. How do we get around this simplification? We assume that, since there is no production in the model, the consumers are endowed with some distribution of the two goods. This makes the supply side quite simple with the following endowment distribution: Consumer A Consumer B Total GOOD X XA XB X GOOD Y YA YB Y XA , YA denote the amounts of the goods originally owned by consumer A and XB , YB denote the amounts of the goods originally owned by consumer B. 95 The total (or market supply) of goods owned by both consumers are: X = XA + XB Y = YA + YB This endowment distribution completely specifies the supply side of the economy. There is no production of goods X, Y and the exogenously fixed amounts X and Y (of goods X and Y) are divided between consumers A and B. In other words, the supply curves are vertical for both goods, X and Y. PX &quot;SX&quot; PY &quot;SY&quot; X X Y Y Of course, the treatment of the demand side is more complex than that of the supply side. The consumers are equipped with individual utility functions, UA and UB, and endowments XA , YA , XB , YB. These consumers will make optimal decisions on demands XA , YA , XB , YB as follows: CONSUMER A decisions utility XA , YA UA = UA(XA,YA) CONSUMER B decisions utility XB , YB UB = UB(XB,YB) endowments XA , YA prices income PX , PY MA = PX XA + PY YA endowm...
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