Coursenotes_ECON301

Kx kxr w qx lx lxr w qx constant returns to scale

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Unformatted text preview: KY = KY(r, w, QY) LY = LY(r, w, QY) Constant Returns to Scale The factor demands by producer Y are thus functions of factor and its output level QY. Since g(KY,LY) is a constant returns to scale production function, we can divide factor demands KY,LY by the total output level QY in order to get the factor demands on a per unit of output basis as follows: KY = kY(r, w) QY 132 LX = lX(r, w) QX KX and LX refer to the quantities of factors required by producer X to produce QX units of output. On the other hand, kX and lX refer to the quantities of factors required by producer X to produce 1 unit of output. Also, note that kX and lX are functions of factor prices (r,w) alone while KX and LX are functions of both factor prices and the total output QX. Marginal Cost We know that the marginal cost of good X is the cost of producing one more unit of the good using K and L. MCX = r kX + w lX and this is a function of only r and w. Perfect Competition Under perfect competition, producer X must satisfy the zero profit condition: PX = MCX (r,w) PX = PX (r,w) LY = lY(r, w) QY KY and LY refer to the quantities of factors required by producer Y to produce QY units of output. On the other hand, kY and lY refer to the quantities of factors required by producer Y to produce 1 unit of output. Also, note that kY , lY are functions of factor prices (r,w) alone while KY and LY are functions of both factor prices and the total output QY. Marginal Cost We know that the marginal cost of good Y is the cost of producing one more unit of the good using K and L. MCY = r kY + w lY and this is a function of only r and w. Perfect Competition Under perfect competition, producer Y must satisfy the zero profit condition: PY = MCY (r,w) PY = PY (r,w) Of course, we wouldn't go to all this trouble unless there was some significance to the fact that output prices PX and PY are functions of the factor prices (r,w) alone. The fact that the output prices PX and PY are functions of the factor prices (r,w) has a very important implication. 133 From now on, we only need to focus our attention on the factor prices (r,w) beca...
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