In the short‐run production function, which one of the following is CORRECT?
Technology is assumed to be constant for a given production function relationship
Understanding the Short-Run Production Function
The short-run production function in economics describes the relationship between inputs (like labor and capital) and the maximum output a firm can produce within a specific time period where at least one input is fixed. Typically, capital is considered the fixed input in the short run, while labor is the variable input. This model helps us understand concepts like marginal product and diminishing returns.
Assumptions of the Short-Run Production Function
To simplify the analysis of how changing a variable input affects output, economists make certain assumptions about the other factors. A crucial assumption in standard short-run production function analysis concerns the state of technology. Let's look at the options provided and analyze which assumption is correct in this context.
Analyzing the Options
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Option 1: Technology is assumed to change as labour input changes
This is incorrect. In the standard short-run production function model, technology is not assumed to change just because the amount of labor used changes. Technology is usually considered a separate factor that shifts the entire production function, rather than being dependent on the level of labor input within a given function.
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Option 2: Technology is assumed to change as capital stock changes
This is incorrect. While changes in technology can sometimes be embodied in new capital equipment, the standard assumption for a given short-run production function relationship is that technology is constant. Changes in capital stock in the short run are generally not possible as capital is the fixed factor. Changes in capital stock over the long run might incorporate new technology, but the question refers specifically to the short-run production function.
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Option 3: Technology is assumed to change positively until diminishing returns set in
This is incorrect. Diminishing returns relate to the marginal product of a variable input decreasing as more of it is added, holding other inputs (including technology) constant. Technology is not assumed to change based on whether diminishing returns have set in or not. Technology is an underlying condition.
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Option 4: Technology is assumed to be constant for a given production function relationship
This is correct. For any specific short-run production function, the level of technology is assumed to be fixed. This allows economists to isolate the effect of changing the variable input (like labor) on output, holding the state of technology constant. A change in technology would lead to a new, different production function.
Key Assumption Regarding Technology
In the context of analyzing the short-run production function, where capital is fixed and labor is variable, the core assumption is that the technology used in the production process remains unchanged. This constant technology allows for the analysis of concepts like increasing, decreasing, and eventually diminishing marginal returns to the variable input (labor).
Conclusion
Based on the analysis of the options and the standard assumptions of the short-run production function, the correct statement is that technology is assumed to be constant for a given production function relationship.
| Input Type | Assumption in Short-Run |
|---|---|
| Capital | Fixed |
| Labor | Variable |
| Technology | Constant |
Revision Table: Short-Run Production Concepts
| Concept | Description |
|---|---|
| Production Function | Mathematical relationship between inputs and maximum output. |
| Short Run | Period where at least one input is fixed. |
| Fixed Input | An input whose quantity cannot be changed in the short run (e.g., capital). |
| Variable Input | An input whose quantity can be changed in the short run (e.g., labor). |
| Technology | The method or process used to transform inputs into outputs. Assumed constant in a given short-run function. |
| Diminishing Returns | Beyond a certain point, adding more of a variable input to a fixed input results in smaller increases in output. |
Additional Information: Long-Run vs. Short-Run Production
It's helpful to contrast the short-run assumptions with those of the long run. In the long run, all factors of production, including capital and technology, are considered variable. This means a firm can change its scale of operations, adopt new technologies, and adjust all inputs to find the most efficient production method. The assumption of constant technology is specifically characteristic of a *given* short-run production function, allowing focused analysis on the impact of variable inputs.
Changes in technology over time can shift the production function, meaning that with the same amount of inputs, a firm can produce more output. This represents technological progress, which is a key driver of economic growth in the long run, but it's held constant when analyzing the relationship between inputs and output in a specific short-run scenario.
Important Questions from Production Function - Teaching
If an estimated Cobb-Douglas production function is Q = 10 K 0.6 L0.8 , what type of returns to scale does this production function indicate?
Which of the following are NOT properties of Cobb‐Douglas production function?
A. Cobb‐Douglas production function is a homogeneous production function
B. Curves representing average and marginal productivity of inputs are not downward sloping
C. Marginal productivity of labour and capital in Cobb‐Douglas production function are functions of the capital‐labour ratio
D. Iso‐quants of Cobb‐Douglas production functions are positively sloped
Choose the correct answer from the options given below:
Given the production function Q = 10 L 0.8 K0.2 , the marginal product of labour (MP L) and capital (MP k) respectively are given by
A. MP L= 8(K/L) 0.2
B. MP L= 8(L/K) 0.2
C. MP K= 2(L/K) 0.8
D. MP K= 2(K/L) 0.2
Choose the correct answer
For the production function, Q = AL α Kβ
A. The coefficient A shows managerial efficiency
B. If α + β > 1, then the production function exhibits increasing returns to scale
C. Marginal rate of technical substitution of L for K is given by βk/αL
D. The marginal product of capital is given by βQ/K
Match List - I with List - II :
List – I
List – II
a
Product line
i
Total number of items under each product/brand in the line
b
Depth of product
ii
Number of products/brands the line
c
Width of product mix
iii
Group of closely related products
d
Length of product line
iv
Number of product lines
Choose the correct option from those given below:
