2. A Production Function relates the
maximum quantity of output (Q)
that can be produced from given
amounts of inputs (K,L)
Q= f(K,L)
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Created by M. Mahdi Mesbahi
3. Q= aK L
K=Capital
Q
L=Labor
Short Run: L
K=cte. K
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Created by M. Mahdi Mesbahi
4. 4.5
Q= aK L 4
3.5
3
K=Capital (xK )
2.5
2
L=Labor
Q
1.5
1
0.5
Short Run: 0
0 10 20 30
K=cte.
L
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Created by M. Mahdi Mesbahi
5. APL= K.3 L-.2
APL= Q/L Q= APL.L = K.3 L(-.2+1)
Q= K.3 L.8
MPL= Q/ L = d (K.3 L.8) = 0.8 K.3 L(.8-1)
dL
MPL = 0.8K.3 L-.2
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Created by M. Mahdi Mesbahi
6. Q= K.3 L.8
APL= K.3 L-.2 APL= K.3 L-.2
MPL = 0.8K.3 L-.2 MPL = 0.8(K.3 L-.2)
MPL = 0.8 APL
Page 6 of 9
Created by M. Mahdi Mesbahi
7. Q= K.3 L.8 APL maximum
when
APL= K.3 L-.2 APL = MPL
MPL = 0.8K.3 L-.2 APL = 0.8 APL
MPL = 0.8 APL APL = 0 K.3 L-.2=0
Page 7 of 9
L= ∞
Created by M. Mahdi Mesbahi
8. Q= K.3 L.8 APL maximum
when
APL= K.3 L-.2 APL = MPL
MPL = 0.8K.3 L-.2 APL = 0.8 APL Max
Max
MPL = 0.8 APL APL = 0 K.3 L-.2=0
Page 8 of 9
L= ∞
Created by M. Mahdi Mesbahi