Producer surplus and profit

The red and green areas are the same. The area between the MC- curve and
the price measures the producer surplus. The same applies to the rectangle
between the four red points.

The entire rectangle with price and quantity as corner points represents the revenue
(price x quantity). If you subtract the costs, i.e. the lower green/light green square
(average costs x quantity), the profit remains (upper red square). At the same
time, the total costs can be determined as the area under the marginal cost
curve^{1}
so that the profit represents the area between price and marginal costs. Thus, the
area of the upper red square is equal to the area between price and marginal cost
curve.

The following relations apply:

$$V\mathit{AC}\left(x\right)=\frac{C\left(x\right)-{C}_{\mathit{fix}}}{x}=\frac{{\int}_{0}^{x}\mathit{MC}\left(q\right)\mathit{dq}}{x}$$ |

and

$$\mathit{MC}\left(x\right)=\frac{d}{\mathit{dx}}C\left(x\right)=\frac{d}{\mathit{dx}}\left(K\left(x\right)-{C}_{\mathit{fix}}\right)=\frac{d}{\mathit{dx}}\left(x\cdot V\mathit{AC}\left(x\right)\right)$$ |

For technical reasons, the quantity control can only be moved up to point 5.3.

^{1}The marginal costs are the derivation of the cost curve. Thus, the cost curve can be
written as integral of the marginal cost curve and the costs can be represented as area under the
marginal cost curve.

(c) by Christian Bauer

Prof. Dr. Christian Bauer

Chair of monetary economics

Trier University

D-54296 Trier

Tel.: +49 (0)651/201-2743

E-mail: Bauer@uni-trier.de

URL: https://www.cbauer.de