Explain the production function satisfy the constant returns to scale
Answers
ᴘʀᴏᴅᴜᴄᴛɪᴏɴ ғᴜɴᴄᴛɪᴏɴ sᴀᴛɪsғʏ ᴛʜᴇ ᴄᴏɴsᴛᴀɴᴛ ʀᴇᴛᴜʀɴs ᴛᴏ sᴄᴀʟᴇ
Definition:
The rate of increase in output (production) relative to the associated increase in the inputs (the factors of production) in the long run
Explanation:
A production function f(K,L) has increasing returns to scale if for any s>1, f(sK,sL)>sf(K,L)
A production function f(K,L) has decreasing returns to scale if for any s>1, f(sK,sL)<sf(K,L)
A production function f(K,L) has constant returns to scale if for any s>1, f(sK,sL)=sf(K,L)
f(sK,sL)is the output of the production function being compared with sf(K,L)which is a form of ‘benchmark’.
For a Cobb Douglas production function:
General Equation:
f(K,L)=KαLβ
Adding s to determine the scale of returns,
f(sK,sL)=(sK)α(sL)β
f(sK,sL)=sα(K)αsβ(L)β
f(sK,sL)=sα+β(K)α(L)β
f(sK,sL)=sα+βf(K,L)
For an increasing returns to scale function, the following conditions have to be satisfied:
s>1 α+β>1
E.g Input increase by 5 times and output increases by 5x times (x>1).
For a constant returns to scale function, the following conditions have to be satisfied:
s>1 α+β=1
E.g Input increase by 5 times and output increases by 51 times.
For decreasing returns to scale function, the following conditions have to be satisfied:
s>1 α+β<1
E.g Input increase by 5 times and output increases by 5x times (x<1). (Output will be less than 5).
ʙᴇ ʏᴏᴜʀs..................^_^
