Equations i iii and iv are definitions or transposed

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hour)/(\$/labour-hour), or a pure number. Equations (i), (iii) and (iv) are definitions or transposed definitions. In fact, since P L = MFC L for a perfect competitor in the input market, in this situation (iii) and (iv) are identical. Equations (vi) and (vii) are both derived from profit-maximization conditions. Equation (vi) simply involves dividing both sides of Equation (M.4.4) by MFC L , so that the left side is in (\$/labour-hour)/(\$/labour-hour) = a pure number, as is the right side. Equation (vii) reﬂects the fact that MRP L = MR x MP L , with MR = P X for a perfect competitor in the output market and MR < P X for a monopolist in the output market. M ATH M ODULE S olutions to Exercises 4

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4. (a) There are two (equivalent) ways of looking at this question, which concerns a perfect competitor in the input and output markets. We can solve it using the rela- tion MRP L = VMP L = P X x MP L = P L = MFC L , which gives us VMP L = P X MP L = 2.5 (40 – L) = 40 = P L , or VMP L = 100 – 2.5 L = 40 = P L . Here the units on the left side are in (\$/kg)(kg/labour-day) = \$/labour-day, as on the right side. We can also, however, set MP L = 40 – L = P L / P X = 40 /2.5 = 16 kg/labour-day, and solve for L = 40 –16 = 24 labour-days , as in the Figure below. Here the left side
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