By David F. Heathfield
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Extra info for An Introduction to Cost and Production Functions
After that, one additional unit of output demands proportionately more and more of inputs. This is the same as saying that factor productivity increases up to q = 4 and decreases thereafter or that the process exhibits increasing returns to scale in the interval D-4 (units of output) and decreasing returns to scale for output levels greater than four units. Transforming this to the isoquant map we might say that increasing returns to scale means that the isoquant map becomes more and more dense as output grows, while the opposite is true for decreasing returns.
But the combinations refer to the possibilities when we have a free choice of all inputs. This would be the case before we made the investment or in the long run when we can redesign the plant. 7 as the relevant description of the technical possibilities open to us. But assume that we have made the fundamental investment and that the factory is built. If we then analysed the technical possibilities in the short run , we would have to take various restrictions into account. The amount of capital invested would be fixed and not possible to increase.
1) Cost Functions and tire Theory of tire Firm where P is average revenue and is a function of q and and is a function of q. 3) but opq/oqP is the elasticity of the demand curve for the product, Ep and oe ' q/oq·e is the elasticity of costs with respect to output Ee. For constant returns to scale Ee = 0, for increasing returns to scale Ee < 0 and for decresing returns to scale Ee > O. For all normal demand curves 0 > Ep > - 1. 3) implies that average revenue (P) equals average cost (C) and hence is the condition for zero profits.