How is the formula for constant returns to scale expressed?

The formula for constant returns to scale indicates that if all inputs in a production function are increased by the same proportion, the output will increase by that same proportion. This property can be mathematically expressed using the function notation for production.

When denoting inputs such as capital and labor in the production function represented by ( F(K, L) ), the expression ( zY = F(zK, zL) ) accurately captures the concept of constant returns to scale. Here, ( z ) is a scaling factor applied to both capital (K) and labor (L) inputs. As the factors of production are scaled up by ( z ), the output scales up accordingly by ( z ), hence maintaining the same proportionate relationship between inputs and output.

This characteristic is essential in macroeconomic models as it helps in understanding how economies respond to changes in inputs at a larger scale. In contrast, the other options do not represent the concept of constant returns to scale. For instance, ( Y = F(K, L) ) simply shows the relationship between output and inputs without indicating scaling behavior. Similarly, ( Y = C + I ) refers to the components of output in terms of consumption and investment, and ( M = P