The document discusses production functions and their relationships. It shows that a production function relates the maximum quantity of output (Q) that can be produced from given amounts of inputs (capital K and labor L). The production function is represented as Q=f(K,L). It then derives and graphs the equations for total product (Q), average product (APL), and marginal product (MPL) based on the Cobb-Douglas production function of Q=K^0.3 L^0.8. It finds that average product is maximized when average product equals marginal product.
VUCA Stands for Volatility, Uncertainty, Complexity and Ambiguity and often used to describe the new normal of today's business environment. The CPA Vision Project in 1998 identified many of these changes - this presentation talks about "now what"?
What changes to leadership and strategy have come from this VUCA world and what are accounting and finance leaders supposed to do. Collaboration combined with new skills is the answer.
We explore the application of optimal control techniques in agent-based macroeconomics. We specifically discussed the Ramsey-Cass-Koopman (savings), Barro (public finance), and Ellis-Fender (corruption) models. Model discussions lifted from Sala-i-Martin's lecture notes on economic growth. Some formulations were taken from lectures of Prof. Emmanuel de Dios and Prof. Rolando Danao of UP School of Economics. All errors mine.
The derivative of a composition of functions is the product of the derivatives of those functions. This rule is important because compositions are so powerful.
I collected this properties for each element from Internet and used excel to visualize properties and their relation to each others.
I also found in wikipedia some topics speak about similar relations.
for example you can see that atomic radius decreases as electrons increase that is because the electrical force increases between nuclear and electrons . . however for the same group radius increases as electron increases.
Atomic volume however has a minimum value for each period, you can see this clear starting from period 3.
Melting point and boiling points are reversely proportional with atomic volume.
Very amazing what Internet + Excel can make :)).
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
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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
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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
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L= ∞
Created by M. Mahdi Mesbahi