Question

A computer company's cost function, which relates its average cost of production AC to its cumulative output in thousands of computers \(Q\) and its plant size in terms of thousands of computers produced per year \(q\) (within the production range of 10,000 to 50,000 computers), is given by \\[\mathrm{AC}=10-0.1 Q+0.3 q\\] a. Is there a learning-curve effect? b. Are there economies or diseconomies of scale? c. During its existence, the firm has produced a total of 40,000 computers and is producing 10,000 computers this year. Next year it plans to increase production to 12,000 computers. Will its average cost of production increase or decrease? Explain.

Short answer

a. Yes, there is a learning-curve effect. b. There are diseconomies of scale. c. The average cost of production will decrease next year.

Step-by-step solution

Determine the Learning-Curve Effect

A learning-curve effect exists if cumulative output (\(Q\)) has an influence on the average cost (\(\mathrm{AC}\)). From the cost function \(\mathrm{AC}=10-0.1Q+0.3q\), it can be seen that \(Q\) does influence the average cost. Therefore, there is a learning-curve effect.

Determine the Scale Economies

Economies of scale exist if an increase in plant size (\(q\)) decreases the average cost, while diseconomies of scale exist if an increase in \(q\) increases the average cost. From the cost function \(\mathrm{AC}=10-0.1Q+0.3q\), a positive coefficient on \(q\) indicates that as the plant size increases, average cost also increases. Therefore, there are diseconomies of scale.

Predict Change in Average Cost

Using the given cost equation \(\mathrm{AC}=10-0.1Q+0.3q\) and given that \(Q=40,000\) computers have been produced in total while 10,000 computers are being produced this year \(q=10\), the average cost this year is \(\mathrm{AC}=10-0.1(40)+0.3(10)=7\) . Next year, \(q\) will be 12 and \(Q\) will be 52 (\(40+10+2\)), the predicted average cost will be \(\mathrm{AC}=10-0.1(52)+0.3(12)=5.8\). Therefore, average cost of production will decrease next year.

Key concepts

Learning-Curve Effect

The learning-curve effect in microeconomics refers to the phenomenon where the average cost of production decreases as a firm accumulates experience in production over time. This can be attributed to improvements in efficiency and skill that occur naturally as workers and processes become more proficient with practice.
In our example, the company's cost function includes the term \(-0.1Q\), which shows that the cumulative output, \(Q\), directly impacts the average cost (AC). As more computers are produced, \(Q\) increases, leading to a reduction in AC. This negative coefficient on \(Q\) confirms that as production grows, the company becomes more efficient and experiences a learning-curve effect, reducing costs.
In practice, this implies that long-term production strategies are beneficial for firms aiming to cut costs through experience and learning.

Economies of Scale

Economies of scale occur when increasing production leads to a reduced average cost per unit. This typically happens when fixed costs are spread over a larger quantity of output, or when a company becomes more operationally efficient.
However, in the given cost function, we observe a positive coefficient on \(q\) (\(+0.3q\)), indicating that as the plant size grows, the average cost increases rather than decreases. This situation suggests that the company does not benefit from economies of scale in the current scenario. Instead, it experiences diseconomies of scale, where costs rise as production capacity increases. This is often due to factors such as increased complexity of operations or overutilization of resources. A firm might want to evaluate its production methods to understand the underlying causes.

Diseconomies of Scale

Diseconomies of scale represent the opposite of economies of scale, where an increase in production results in higher average costs. This can happen when a firm expands beyond its optimal capacity, leading to inefficiencies.
In our example, the \(+0.3q\) part of the cost function illustrates that as the plant size \(q\) increases, average costs also increase. This rise could stem from a variety of issues, such as management challenges, increased infrastructure maintenance, or communication overheads.
Identifying and addressing these inefficiencies is crucial for a firm experiencing diseconomies of scale, as it can hinder competitive advantage and profitability. Companies experiencing this should consider restructuring or optimizing operations to find a more cost-effective production level.

Average Cost Analysis

Average cost analysis evaluates how the average cost per unit of production behaves as output changes. It is vital for decision-making in both short and long-term business strategies.
For the given cost function, the average cost for the current year (when \(Q = 40,000\) and \(q = 10,000\)) is calculated as \(\mathrm{AC} = 10 - 0.1(40) + 0.3(10) = 7\). For the next year, with estimated \(Q = 52,000\) and \(q = 12,000\), it becomes \(\mathrm{AC} = 10 - 0.1(52) + 0.3(12) = 5.8\).
The decreasing trend from 7 to 5.8 suggests an overall reduction in average production costs, despite the firm's larger plant size next year. This could be due to the learning-curve effect outweighing the diseconomies of scale being experienced, showing the importance of understanding all contributing factors when analyzing costs.