Coursenotes_ECON301

r12 rw2 w12 px 2wr12 market for good x substituting

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Unformatted text preview: 3w = r + 3w 10PY 20(wr)1/2 YB = 4r + 2w = 4r + 2w 10PY 20(wr)1/2 and aggregate demand for good Y Y = r + 3w + 20(wr)1/2 Y = 5r + 5w 20(wr)1/2 Y=r+w 4(wr)1/2 4r + 2w 20(wr)1/2 X = X(r , w) On the supply side, producer X provides QX as the market supply of good X. At market equilibrium, the output supply of good X must equal the aggregate demand of good X. QX = X(r , w) = r + w 4(wr)1/2 MARKET FOR CAPITAL Substituting this output supply, QX, into the producer demands for capital, we get... KX = QX(w / r)1/2 KX = r + w 4(wr)1/2 KX = r + w 4r KY = QY(w / r)1/2 KY = r + w w1/2 4(wr)1/2 r1/2 KY = r + w 4r and aggregate demand for capital K=r+w 4r K=r+w 2r At capital market equilibrium, the Aggregate capital demand must match the aggregate capital supply. +r+w 4r w1/2 r1/2 Y = Y(r, w) On the supply side, producer Y provides QY as the market supply of good Y. At market equilibrium, the supply of good Y must equal the aggregate demand of good Y. QY = Y(r , w) = r + w 4(wr)1/2 MARKET FOR LABOUR Substituting this output supply, QY, into the producer demands for labour, we get... LX = QX(r / w)1/2 LX = r + w r1/2 1/2 4(wr) w1/2 LX = r + w 4w LY(r, w) = lY QY LY = r + w r1/2 4(wr)1/2 w1/2 LY = r + w 4w and aggregate demand for labour L=r+w +r+w 4w 4w L=r+w 2w At labour market equilibrium, the the aggregate labour demand must match the aggregate labour supply. 141 r+w 2r =1 r+w =1 2w If we solve for capital market equilibrium condition, we get the relationship between the price of labour and the price of capital. 2w = r + w w=r r/w=1 This is the equilibrium price solution that we need to figure out everything else. If we solve for capital market equilibrium condition, we get the following relationship between the price of labour and the price of capital. 2r = r + w r=w w/r=1 This is the equilibrium price solution that we need to figure out everything else. Let's figure out the rest of our equilibrium price vector... If we choose capital as the numeraire then r=1 r=w=1 PX = 2(wr)1/2 = 2r = 2 PY = 2(wr)1/2 = 2r = 2 Now let's fig...
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