Question

Calculate a cost function from a production function and explain how economic costs differ from accounting costs.

Short answer

We know that production increases at higher isoquants. Thus, the cost function refers to the function that shows the linkage between the cost the firm had to bear to produce such isoquants.

Step-by-step solution

Calculating cost function from the production function

The cost function summarizes the production when factors are used for cost minimization. The cost function is the summation of fixed cost and variable cost which are in turn dependent on such production factors, such as capital(K) and labor (L).

Thus, the production function can be written as, $\mathrm{Q}=f(K,L)$.

Whereas, the cost function can be written as,

$$\begin{gathered} \mathrm{C}\left(Q\right)=\left({\mathrm{C}}_{\mathrm{K}}\times K\right)+\left({\mathrm{C}}_{\mathrm{L}}\times L\right) \\ =fixed\cos t+variable\cos t \end{gathered}$$

The following relation can be visualized through the table below:

K	L	Output	Fixed Cost	Variable Cost	Total Cost
2	1	5	$200	$50	$250
2	3	7	$200	$150	$ 350

If the cost of the capital is considered to be $\$100$and labor to be $\$50$, then the fixed cost becomes $\$200$for each capital and variable cost of $\$50$and $\$150$respectively.

Difference between Economic and Accounting Costs

Economic Cost represents those cost that is borne by the producer both in the short run and in the long run consisting of both fixed and variable that is assumed by the firm to reach the optimal output.

Whereas, accounting cost depicts the cost that includes the payments to labor and capital inputs directly. These accountings usually appear on the income statement.

Moreover, these resources can also be used to produce other goods which eventually includes the opportunities the firm had to face while production as well.