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# Cobb douglas production function

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### Cobb douglas production function

1. 1. M. Mahdi Mesbahi
2. 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)Page 2 of 9 Created by M. Mahdi Mesbahi
3. 3. Q= aK L K=Capital Q L=Labor Short Run: L K=cte. KPage 3 of 9 Created by M. Mahdi Mesbahi
4. 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. LPage 4 of 9 Created by M. Mahdi Mesbahi
5. 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-.2Page 5 of 9 Created by M. Mahdi Mesbahi
6. 6. Q= K.3 L.8APL= K.3 L-.2 APL= K.3 L-.2MPL = 0.8K.3 L-.2 MPL = 0.8(K.3 L-.2) MPL = 0.8 APLPage 6 of 9 Created by M. Mahdi Mesbahi
7. 7. Q= K.3 L.8 APL maximum whenAPL= K.3 L-.2 APL = MPLMPL = 0.8K.3 L-.2 APL = 0.8 APLMPL = 0.8 APL APL = 0 K.3 L-.2=0Page 7 of 9 L= ∞ Created by M. Mahdi Mesbahi
8. 8. Q= K.3 L.8 APL maximum whenAPL= K.3 L-.2 APL = MPLMPL = 0.8K.3 L-.2 APL = 0.8 APL Max MaxMPL = 0.8 APL APL = 0 K.3 L-.2=0Page 8 of 9 L= ∞ Created by M. Mahdi Mesbahi
9. 9. L Q=K0.3L0.8 APL=K0.3L-0.2 MPL=0.8K0.3L-0.2 0.000001 1.58489E-05 15.84893192 12.67914554Q= K.3 L.8 0.00001 0.0001 1E-04 0.000630957 6.309573445 10 5.047658756 8APL= K.3 L-.2 0 0.001 0.01 0.1 0.2 0.003981072 0.025118864 0.158489319 0.275945932 3.981071706 2.511886432 1.584893192 1.379729661 3.184857364 2.009509145 1.267914554 1.103783729 0.3 0.381677891 1.272259637 1.017807709 0.4 0.480449774 1.201124434 0.960899547MPL = 0.8K.3 L-.2 0.5 0.574349177 1.148698355 0.918958684 0.6 0.664539806 1.107566343 0.886053075 0.7 0.751758647 1.073940924 0.859152739 0.8 0.836511642 1.045639553 0.836511642 0.9 0.919166119 1.021295688 0.81703655 1 1 1 0.8 2 1.741101127 0.870550563 0.696440451 3 2.408224685 0.802741562 0.642193249 4 3.031433133 0.757858283 0.606286627 Short Run: 5 6 3.623898318 4.192962713 0.724779664 0.698827119 0.579823731 0.559061695 7 4.743276394 0.677610913 0.542088731 K=cte. 8 5.278031643 0.659753955 0.527803164 ∞ 9 5.799546135 0.644394015 0.515515212 10 6.309573445 0.630957344 0.504765876 20 10.98560543 0.549280272 0.439424217Page 9 of 9 30 15.19487052 0.506495684 0.405196547 Created by M. Mahdi Mesbahi
10. 10. 5 4.5 4 3.5 Q , APL , MPL 3 Q (xK0.3) 2.5 2 APL MPL 1.5 1 0.5 0 ∞ -1 0 1 2 3 4 5 6 LPage 10 of 9 Created by M. Mahdi Mesbahi
11. 11. Present like Professionals Created by: Mahdi Mesbahi mahdi.mesbahi@gmail.com