
a
Whether the given function exhibit constant returns to scale or not? It’s cost function and its nature of economies of scale and its importance.
a

Answer to Problem 7.8P
Function exhibits constant returns to scale.
Explanation of Solution
Given Information:
Cobb Douglas production function is:
Total Cost function derived from this production function is:
According to the situation given in the question
Yes, this function exhibits constant returns to scale. This is because the average Cost
Introduction:
Constant returns to scale means when input and outputs are increased in same proportion. It means when inputs to a given function are increased in certain proportion, with the same proportion, output is also increased.
b)
Role of q and its relation with production function and effect on shape of total cost curve.
b)

Answer to Problem 7.8P
‘q’ determines the nature of returns to scale.
Explanation of Solution
Given Information:
Cobb Douglas production function is:
Here, the exponent of
If the exponent
If
If
Introduction:
Total cost curve is a graphical representation showing cost incurred for producing output. It is sum of fixed cost and variable cost.
The cost function in its general form, i.e.
c)
Value of s and its relation with returns to scale.
c)

Answer to Problem 7.8P
It determines the nature of returns to scale
Explanation of Solution
Given Information:
Cobb Douglas production function is:
Here, the exponent of ‘s’ plays a very vital role. It determines the nature of returns to scale.
If the exponent
If
If
Introduction:
Returns to scale is a function of long run which determines impact of change in input to overall production process. It has three parts: Increasing returns to scale, Constant returns to scaleand Diminishing returns to scale.
d)
Impact of sizes of a and b on cost function
d)

Answer to Problem 7.8P
It determines the nature of returns to scale
Explanation of Solution
Given Information:
Cobb Douglas production function is:
Total cost curve is a graphical representation showing cost incurred for producing output. It is sum of fixed cost and variable cost.
Relative sizes of
Suppose
See that the slope of
Introduction:
Total cost curve is a graphical representation showing cost incurred for producing output. It is sum of fixed cost and variable cost.
e)
Reason for usefulness of given function and implication of coefficients.
e)

Answer to Problem 7.8P
Given function shows elasticity.
Explanation of Solution
Given Information:
Cobb Douglas production function is:
According to the situation given in the question,
This equation is very useful. Equations in this form help to find elasticity. For example,
This is nothing but the percentage change in
Introduction:
Elasticity is the numerical expression showing percentage change in a variable due to percentage change in another variable. It can be positive or negative.
f)
Findings of Translog Cost Function.
f)

Explanation of Solution
According to the situation given in the question
This type of function is called Trans log Cost Function. It is a very useful function and is mostly used in empirical research. See in Christenson and Greene paper on electric generation power references in table given in the text. Note that the entries in the table are an estimate of Cobb-Douglas production function.
Introduction:
Translog cost function is a system of equation in which firm’s cost behavior, output, revenue is estimated.
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