At market equilibrium the supply of good y must equal

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Unformatted text preview: + KY(r, w) K = K(r , w) On the supply side, we have the aggregate capital endowment as determined by K = KA + KB At capital market equilibrium, the Aggregate capital demand must match the aggregate capital supply. K(r , w) = KA + KB = K MARKET FOR LABOUR On the demand side, we have the individual producer demands for labour LX(r, w) = lX QX LY(r, w) = lY QY and aggregate demand for labour L = LX(r, w) + LY(r, w) L = L(r, w) On the supply side, we have the aggregate labour endowment as determined by L = LA + LB At labour market equilibrium, the the aggregate labour demand must match the aggregate labour supply. L(r , w) = LA + LB = L We now have a system of two simultaneous factor market equilibrium equations in two unknown factor prices: K(r , w) = K L(r , w) = L (1) (2) which must be solved for the equilibrium factor prices (r*, w*). As we know, the equilibrium factor prices are defined as those factor prices which match demand and supply in each factor market. 135 K(r* , w*) = K L(r* , w*) = L Once (r*, w*) are known, we can further calculate equilibrium output prices PX, PY, and all remaining equilibrium quantities. Now we can reduce our problem even further by using our knowledge of Walras Law and the numeraire. RELATIVE PRICES If we specify a good or a factor (say, labour) as the numeraire then we can express all other prices in terms of the numeraire. PX = PX (r, w) PY = PY (r, w) r = ? (to be solved) w = 1 (chosen as numeraire) That is, we have reduced the number of unknown prices to solve from four prices (PX, PY, r, w) down to three prices (PX, PY, r) since we automatically have w = 1 from choosing labour as numeraire. WALRAS LAW If the markets for good X, good Y, & capital are all in equilibrium, then Walras Law ensures that the market for labour is also in equilibrium. X(r , w) = QX Y(r , w) = QY K(r , w) = K L(r , w) = L That is, we have reduced the number of market equilibrium conditions to solve from four markets (X, Y, K, L) to three markets (X, Y, K) since we automatically have the labour market in equilibrium fr...
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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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