Unformatted text preview: ure out the consumer demands in equilibrium... XA = r + 3w = r + 3w 10PX 20(wr)1/2 X*A = 4 / 20 = 1 / 5 XB = 4r + 2w = 4r + 2w 10PX 20(wr)1/2 X*B = 6 / 20 = 3 / 10 So goods market demands are... X* = X*A + X*B = Y* = Y*A + Y*B = YA = r + 3w = r + 3w 10PY 20(wr)1/2 Y*A = 4 / 20 = 1 / 5 YB = 4r + 2w = 4r + 2w 10PY 20(wr)1/2 Y*B = 6 / 20 = 3 / 10 142 and just to check market clearing, this should be the market supply (i.e. amount produced by the producers) KX = r + w 4r KY = r + w 4r K=r+w 2r = = =1 LX = r + w = 4w LY = r + w = 4w L=r+w=1 2w (notice that this implies factor market clearing since factor endowments = 1 for each of L and K) QX = KX1/2LX1/2 QX = (1/2)1/2(1/2)1/2 QX = (notice goods market clearing, here!!!!) So all markets clear at the equilibrium price vector (PX, PY, r, w) = (2, 2, 1, 1) and the resulting demands for goods and factors are: (XA, YA) = (2/10 , 2/10) (KX, KY) = (1/2 , 1/2) (XB, YB) = (3/10 , 3/10) (LX, LY) = (1/2 , 1/2) QY = KY1/2LY1/2 QY = (1/2)1/2(1/2)1/2 QY = There are models where there is only one consumer in the production economy with two goods, two factors and one (representative) consumer. In such a case, there is no need to use the horizontal summation technique to sum over individual consumer demands to get the market demands for goods, since there is one consumer and their demands are the market demands in the goods market. The same applies to the aggregate supply of factors, since the one consumer is the owner of all the factor endowments of the economy. Otherwise, the model for one consumer, two factors, and two goods is very similar to the logical formulation of the model we just went through (two consumers, two factors, two goods production economy). ROBINSON CRUSOE ECONOMY Next time... 143 HOMEWORK 1. Find the equilibrium prices and quantities for the production economy with: UA = XA1/4YA3/4 UB = XB0.6YB0.4 QX = KX1/2LX1/2 QY = KY1/2LY1/2 and the following initial factor endowment distribution: Consumer A Consumer B Total Capital (K) KA = 1 KB = 1 KT = 2 Labour (L) LA = 1 LB = 2 LT = 3 144 ECON 301 L...
View Full Document
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