By David F. Heathfield
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Extra info for An Introduction to Cost and Production Functions
This alternative approach relies on the total, average and marginal product curves. Long Run In the long run when all inputs are variable we can show how total output grows as the level of inputs increases (in fixed proportion ). 9. / Total product curve Inputs As inputs increase from (0) to (a) output is increasing faster than inputs and hence there are increasing returns to scale. Between (a)and (b) the total product curve runs along a ray through the origin (0) (d) and hence a 10 per cent increase in inputs leads to a 10 per cent increase in output and is therefore a range ofconstant returns to scale.
4 33 Cost-minimising Choice of Technology in the Short Run The analysis in the preceding section can be regarded as the long-run choice of technology since both factors vary without any restrictions . Assume now that the fundamental investment has already been made and that we want to analyse the choice of technology in the short run. In the short run, capital represents a 'sunk cost' and the firm has to pay interest and mortgages even if the equipment is left idle. As a simplification, we shall assume that the ex post (the 'user') cost of capital is zero .
E. 0 2P/ oq2 = 0). 5) Thus for increasing returns to sale [(oC;oq) < 0] the second order condition for a maximum requires imperfect competition [(oP/oq) < 0] and for perfect competition [(oP/oq) = 0] it is necessary to have decreasing returns to scale [(oC;oq) > 0].