By David F. Heathfield
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Additional info for An Introduction to Cost and Production Functions
The shape of the cost functions do of course depend on the underlying production function, and in particular, its scale properties. 5. At first we have a phase with increasing returns to scale and later on a phase with decreasing returns. 5 shows that this leads to a total cost curve with first a decreasing slope and then an increasing slope. 6 below. The marginal cost is simply the slope of the TC curve at any point (dTC jdq) and the AC is the slope of a line connecting any point on the TC curve to the origin (TC jq) .
As we move along the ray we may move from a range in which we experience increasing returns into a range in which returns are constant and thence into a range in which returns are decreasing. Assume now that we produce one unit (q = 1) with the amounts of labour and capital as indicated by A!. 5 we can see that the distance OA! A z . This means that we need not double inputs in order to double output. A z is greater than A zA 3 which means that increasing output from one to two units demands proportionately more inputs than increasing output from two to three units .
4. In this case the minimum cost is not zero but equal to the fixed cost. Thus the minimum isocost line equals fixed cost and lies on the v 1 axis between 0 and V2' This is because the firm can employ no labour but can employ any quantity of capital between zero and ih, for nothing more nor nothing less than fixed cost. A somewhat higher isocost line would permit some labour to be hired and this labour could be combined with any quantity of capital between 0 and V2' Thus this isocost line too is horizontal between the VI axis and P2' The firm would again wish to minimise costs for its given level of output and would hence choose that isocost line closest to the V2 axis and which touches the isoquant.