### 12.1 Costs

Enter here the variable and the fixed costs.
Variable costs:

Fix costs:

Costs are resource input expressed in monetary units. They can be divided into several categories.
Accounting Costs: actual expenditure and depreciation Opportunity costs, sunk costs, fixed and variable costs, marginal and average costs Fixed costs exist regardless of whether production takes place or not, e.g. rent, lease, basic wages. Variable costs depend on the quantity produced, e.g. raw materials, overtime. But attention: In the long run also fixed costs can become variable: E.g. additional rent of a building, dismissal of workers. The overall costs (total costs) are the sum of fixed costs and variable costs. In the above graph, different cost functions can be specified, with the fixed costs being variable separately.
Here, we illustrate the production costs, i.e. the costs in dependence of the produced quantity or indirectly of the resource input. The most important representation of the costs for economic considerations are the marginal costs MC, i.e. the costs of one additional unit. Formally, the marginal costs are the derivative of the cost curve. The following applies: With constant economies of scale: costs are linear in q, i.e. the marginal costs are constant. From decreasing economies of scale follow increasing marginal costs, and vice versa.
The marginal cost curve intersects the variable average costs (VAC) as well as the total average costs (TAC) in their minimum. The point of intersection between marginal and average costs is called operating optimum, since this represents the production quantity with the lowest unit costs. Proof:

 $\frac{d}{\mathit{dq}}V\mathit{DK}\left(q\right)=0⇔\frac{d}{\mathit{dq}}\frac{VK\left(q\right)}{q}=0⇔\frac{\mathit{GK}\left(q\right)}{q}-\frac{VK\left(q\right)}{{q}^{2}}=0⇔\mathit{GK}\left(q\right)=\frac{VK\left(q\right)}{q}=V\mathit{DK}\left(q\right)$

Characteristics of the cost function: Companies react to relative factor price changes. Therefore, costs increase disproportionately with rising factor prices. If, for example, the factor Work becomes 5% more expensive, then the enterprises will partially replace workers by machines. Thus, the total costs rise less than the portion of Work of the costs multiplied by 5% (see income- and substitution- effect for the consumption decision of households with price changes).

To be able to say something about the increase of costs in q with given factor prices, strong assumptions are necessary: If the production function is homothetic, i.e. the slope of the isoquants along a beam through the origin is constant, then changes in output do not trigger factor substitution. For each possible production quantity the optimal input ratio of the production factors is the same.

(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