Coursenotes_ECON301

# In this final step there is no difference between a

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Unformatted text preview: ect competition, we can express output prices in terms of factor prices PX = 2(wr)1/2 PY = 2(wr)1/2 246 PUBLIC 222 Solving a cost minimization problem faced by the producer of each good we have the following factor demand on a per unit of output basis: kX = kY = (w / r)1/2 lX = lY = (r / w)1/2 using the zero profit condition of perfect competition, we can express output prices in terms of factor prices PX = 2(wr)1/2 PY = 2(wr)1/2 Solving for individual demand functions from the usual constrained utility maximization problem XA = 0.2r + 0.6w 2PX XB = 0.8r + 0.4w 2PX Solving individual demand functions from the usual constrained utility maximization problem. XA = 0.2r + 0.6w 2PXA XB = 0.8r + 0.4w 2PXB For the public good model, we do one extra step to invert these individual demand functions so that prices are now expressed in terms of quantities PXA = 0.2r + 0.6w 2 XA PXB = 0.8r + 0.4w 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 + 0.4w 2X For private good X, we use horizontal summation to obtain the market demand for good X from the two individual demand functions X = XA + XB =r+w 2PX 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 247 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"... 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 Subbing 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 and solving for the equilibrium prices r=w=1 PX = PY = 2 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 and solving for the equilibrium prices r=w=1 PX = PY = 2 248 Solving for equilibrium quantities XA = 0.2 X...
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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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