Supply function producer

Introduction:  The Marginal output rule and production rule are introduced in a setting where the price is fixed. Using this approach we find a supply function, which gives for each price the output quantity that maximizes profit.

  • The variable in this model is $y$, the output of the production process.
  • The parameter in this model is $p$, the price.
Furthermore, three functions are part of this model:
  • $R(y)$: the revenue function,
  • $C(y)$: the cost function,
  • $\pi(y)$: the profit function,
such that $\pi(y)=R(y)-C(y)$.

Supply function: The supply function of a producer with profit function $\pi (y) = py- C(y)$ is given by
y(p) =\left \{ \begin{array}{lll}

MC^{-1} (p) & \mbox{if} & p \geq \min AC(y),\\[1mm]
0               & \mbox{if} & p < \min AC(y).
\right .