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By David F. Heathfield

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Relative factor prices determine the cost minimising point on the specified isoquant and hence determine how much capital and how much labour will be used in the production process. The firm's demand for factors of production is therefore a function of the rate of output and relative input prices. 12) It will be apparent from the isoquant-isocost diagram that factor demands are not affected by price level but only by price ratios . 12) are homogeneous of degree zero in prices. 12) are multiplicative separable in output and 42 An Introduction to Cost and Production Functions prices, that is doubling output will double the demand for all inputs if relative prices remain unchanged.

The marginal revenue of that unit must accordingly be lower than its price. For simplicity, we shall consider the case with a linear demand curve. 16) where ao, al are constants (ao > 0, al > 0). This is a straight line from the point ao on the P-axis to the point aolal on the q-axis. 16). -2 - oT R _ o(aoq - a l q2) - ao a,q MR - -- oq oq which is a straight line from the point Go on the P-axis to the point ao/2a, on the q-axis. 12. Profit maximisation implies the production of q* units, because at q*, MR = Me.

4 shows, that all the existing capital stock is utilised. This solution minimises labour input and, as a consequence, minimises the variable costs of production. 5 Cost Functions in the Long Run Long-run analysis implies that both factors are allowed to vary. 5). There will be one expansion path for each price ratio. For a homothetic production function the expansion paths are straight lines going through the origin (which means that factor proportions, VI /V2 remain unchanged unless input price ratios change).

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