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HOMOGENEOUS OF DEGREE N: A property of an equation the exists if independent variables are increased by a constant value, then the dependent variable is increased by the value raised to the power of n. The value of n can be greater than, less than, or equal to one. This property often surfaces in the analysis of production functions. If n = 1, then a doubling independent variables results in a doubling of the dependent variable and the production function has constant returns to scale. If n > 1, then a doubling independent variables results in more than a doubling of the dependent variable and the production function has increasing returns to scale. If n < 1, then a doubling independent variables results in less than a doubling of the dependent variable and the production function has decreasing returns to scale.

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LONG-RUN AVERAGE COST CURVE, DERIVATION

The long-run average cost curve is the envelope of an infinite number of short-run average total cost curves, with each short-run average total cost curve tangent to, or just touching, the long-run average cost curve at a single point corresponding to a single output quantity. The key to the derivation of the long-run average cost curve is that each short-run average total cost curve is constructed based on a given amount of the fixed input, usually capital. As such, when the quantity of the fixed input changes, the short-run average total cost curve shifts to a new location.

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