Question

(a) Calculate the marginal and average costs for each level of output from the following total cost data. (b) Show how marginal and average costs are related. (c) Are these short-run or long-run cost curves? Explain how you can tell. $$ \begin{array}{|l|l|l|l|l|r|r|r|r|r|r|} \hline \text { Oulput } & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline \text { TC }[\underline{f}) & 12 & 27 & 40 & 51 & 60 & 70 & 80 & 91 & 104 & 120 \\ \hline \end{array} $$

Short answer

Calculate MC and AC, show their relationship, and identify as short-run costs due to fixed costs.

Step-by-step solution

Calculate Marginal Costs

To find the marginal cost (MC) for each level of output, calculate the change in total cost (TC) divided by the change in quantity (output). The formula is \( MC = \frac{\Delta TC}{\Delta Q} \). For example, when output increases from 0 to 1, the TC changes from 12 to 27, so \( MC = \frac{27-12}{1-0} = 15 \) units.

Calculate Average Costs

The average cost (AC) is calculated by dividing the total cost (TC) by the quantity (output), using the formula \( AC = \frac{TC}{Q} \). For example, at an output level of 1, \( AC = \frac{27}{1} = 27 \). Repeat this for each output level.

Show Relationship Between Marginal and Average Costs

Observe the MC and AC calculated for each level of output. Typically, when MC is less than AC, AC decreases, and when MC is greater than AC, AC increases. At the output level where MC equals AC, the AC reaches its minimum.

Determine the Type of Cost Curves

These are short-run cost curves. This determination is based on the presence of fixed costs (when output is zero, TC is 12, not 0), which typically indicates short-run analysis where certain inputs cannot be varied.

Key concepts

Short-run Costs

In the analysis of business expenses, understanding short-run costs is essential. Short-run costs refer to those costs that a company incurs when at least one input is fixed. This means that not all resources can be adjusted immediately, like capital or land, which cannot be changed overnight.

Short-run cost structures are characterized by fixed costs plus variable costs. Fixed costs do not change with the level of output, such as rent, salaries of permanent staff, or machinery costs. Variable costs change with the production volume, including raw materials and direct labor costs.

Given that the exercise provided shows a total cost of 12 units even at zero output, this total cost reflects fixed costs in the company's short-run cost structure. With production adjustments, only variable costs are affected while fixed costs remain constant.

Marginal Cost

Marginal cost plays a crucial role in decision-making processes. It refers to the additional cost incurred when producing one more unit of output. The formula to compute marginal cost is \(\textit{MC = \frac{\Delta TC}\){\Delta Q}}\, where \(\Delta TC\) is the change in total cost, and \(\Delta Q\) is the change in output quantity.

Understanding marginal cost helps businesses determine the optimal level of production. It indicates whether it would be profitable to produce additional units. For instance, if the marginal cost of production is less than the price at which a product is sold, it may be beneficial to increase production.

In the given exercise, marginal costs were calculated for each level of output by assessing the change in total costs as output increased step by step. This calculation is crucial for managing resources effectively and ensuring cost-efficiency.

Average Cost

Average cost gives insight into the cost incurred per unit of output at different production levels, calculated using the formula \(\textit{AC = \frac{TC}\){Q}}\. Here, \(TC\) represents the total cost, and \(Q\) is the quantity of output.

This concept helps businesses analyze overall efficiency. By comparing average costs at different output levels, companies can identify the most cost-effective scale of production.

The provided exercise involved calculating average costs by dividing the total cost by the quantity for each output level. Lower average costs typically indicate efficient production processes, while higher average costs can signal inefficiencies that need addressing to enhance profitability.

Total Cost

Total cost represents the entire cost of production, comprising both fixed and variable costs. This expansive view helps businesses grasp the full financial impact of their production activities.

In the short-run, total costs include expenses that do not change with the level of output (fixed costs) as well as those that do (variable costs). Examples of fixed costs are lease payments, while labor and material costs typically fall under variable costs.

In the scenario described in the exercise, total costs at each output level were assessed, starting with a base total cost when no output is produced, indicating fixed costs. As production levels increase, total costs also rise, reflecting the addition of variable costs. Understanding the behavior of total costs helps in planning and controlling the budget efficiently over different levels of production.