# Constant returns to scale

### From Conservapedia

A process displays **constant returns to scale** when increasing all inputs by a factor of *s* leads to an increase in output by the same factor. In economics, this is in terms of the production function of the process — for instance, that of a business, company, or economy as a whole. Mathematically, if the function is , where is a vector of inputs, constant returns to scale are characterized by , where *s* > 0.

A function displaying constant returns to scale is homogeneous of degree one, and by Euler's Theorem can be written as:

Since for a competitive market, the payment to each factor of production (*x*_{i}) is , this implies that that the total payments to all factors of production exhaust output (*F*), and the market has zero profit.

## Examples of functions displaying constant returns to scale

- Linear demand or supply:

- Cobb-Douglas production function with :
*Y*=*A**L*^{α}*K*^{1 − α}- The variables have the interpretation of Y as output, L as labour, K as capital, and A is multifactor productivity. In general, empirical studies have shown that the United States economy has approximately α = 0.33.