Constant returns to scale
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 (xi) 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 = ALαK1 − 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.