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Unformatted text preview: r 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!!!!) 257 QY = KY1/2LY1/2 QY = (1/2)1/2(1/2)1/2 QY = 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) However, if good X is our public good, then ... For public good X, we use vertical summation to obtain the market demand for good X from the two individual willingness to pays PX = PXA + PXB =r+w 2X Again we do an extra step to convert the market willingness to pay into the usual form of demand functions where quantities are expressed in terms of prices X=r+w 2PX Note that we just happen to have the same market demand for good X in this example for both "X as a private good" and "X as a public good"...this is not usually the case! Substituting the zero profit condition above so that the market demand for good X is expressed in terms of factor prices only... X=r+w 4(wr)1/2 Since good Y is private, the derivation of the market demand for good Y should be the same for both models Y=r+w 4(wr)1/2 Using these market demands for goods in the factor market equilibrium conditions kX X + kY Y = K lX X + lY Y = L 258 and solving for the equilibrium price (not any different from the 2 private good case above) the resultant price vector is as it was in the two good case. r=w=1 PX = PY = 2 r=w=1 PX = PY = 2 Solving for equilibrium quantities using the Public Good model... XA = 0.2r + 0.6w 2PXA PXA = 0.2r + 0.6w 2 XA XB = 0.8r + 0.4w 2PXB PXB = 0.8r + 0.4 2 XB Now, remember that for public goods XA = XB = X so the above expressions become... PXA = 0.2r + 0.6w 2X PXB = 0.8r + 0.4 2X And the prices that consumer A and consumer B are willing to pay for the same amount of public good X PXA = 0.2r + 0.6w 2X PXA = 0.2 + 0.6 1 PXB = 0.8r + 0.4w 2X PXB = 0.8 + 0.4 1 = 1.2 = 0.8 Solving equilibrium quantities using the equilibrium price vector (PXA, PXB, PX, PY, r, w) = (0.8, 1.2, 2, 2, 1, 1) we get... XA = 0.5 YA = 0.2 XB = 0.5 YB = 0.3 X = 0.5 Y = 0.5 And the capital and labour markets clear exactly as they did in the 2 Private good case. 259 ECON 301 LECTURE #15 EXT...
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- Spring '10