Mid Term Question
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Service Industries Limited is a Pakistani multinational shoes and tyre manufacturer which is doing business with the name of “Servis” since 1941. Servis shoes is a shoe manufacturing company and Servis tyre is a tyre manufacturing company working under the Servis Industries Limited. Their factories are located in various cities of Pakistan i-e Gujrat, Muridke, Raiwind, etc. Servis group is operating through a network of more than 450 retail company stores nationwide. They supplies their products to over 2500 independent retailers in Pakistan. They also export shoes, tyres, rubber tubes etc to Europe, Middle East, and other Asian countries. Their famous shoe brands include Cheetah, Don Carlos, Liza, Calza, etc. Suppose Servis group is having the following cost function:
C = 0.0005Q2 + 6Q + 65000
Where, C = Cost of production
Q = Output (Number of products produced)
Their financial team has calculated output elasticity of cost at Q = 1000 and found it as 0.0979.
Being a student of mathematical economics, analyze the above case and observe the value of elasticity. Identify the type of returns to scale in which the Servis group is operating. Discuss the economic reasoning of the type of returns to scale.
To analyze the given case, let's first understand the concept of output elasticity of cost. Output elasticity of cost measures the responsiveness of production costs to changes in output. It indicates how much the cost of production changes when output increases by 1%. The formula for output elasticity of cost is given by:
Output Elasticity of Cost = (dC/dQ) * (Q/C)
Where:
dC/dQ represents the derivative of the cost function with respect to output (Q),
Q is the level of output (number of products produced), and
C is the cost of production.
Given the cost function:
C = 0.0005Q^2 + 6Q + 65000
To calculate the output elasticity of cost, we need to differentiate the cost function with respect to output (Q):
dC/dQ = 0.001Q + 6
Now, let's substitute the given values to calculate the output elasticity of cost at Q = 1000:
Output Elasticity of Cost = (0.001 * 1000 + 6) * (1000 / (0.0005 * 1000^2 + 6 * 1000 + 65000))
= (1 + 6) * (1000 / (0.5 + 6000 + 65000))
= 7 * (1000 / 71000)
≈ 0.0986
The calculated output elasticity of cost is approximately 0.0986, not 0.0979 as mentioned in the case. However, we'll use this value for further analysis.
Now, let's discuss the type of returns to scale based on the output elasticity of cost. Returns to scale refer to the change in output resulting from a proportional change in all inputs. It helps us understand how output changes when all inputs are increased or decreased simultaneously.
In this case, the output elasticity of cost is less than 1 (0.0986 < 1). When the output elasticity of cost is less than 1, it indicates that the cost of production increases at a slower rate than the increase in output. This suggests that Servis group is operating with decreasing returns to scale.
Decreasing returns to scale occur when an increase in inputs leads to a proportionately smaller increase in output. It implies that as the production scale expands, the cost of production per unit increases. The reasons behind decreasing returns to scale can include managerial inefficiencies, coordination problems, or limitations on available resources.
In the case of Servis group, the output elasticity of cost being less than 1 indicates that their cost of production is not increasing proportionately with the increase in output. This could be due to factors such as economies of scale, efficient production processes, or effective resource management. However, as the company continues to expand its production scale, it might face challenges in maintaining the same level of cost efficiency.
It's important to note that the value of output elasticity of cost is approximate and may vary depending on the actual calculations and data used.
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