Math Project I

# Math Project I - Khuong Bui Giau La Math 218 Part A...

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Khuong Bui Giau La Math 218 # Part A: Production #Step 1: The Production Surface > P:=1000*((0.3)*x^(-0.7)+(0.7)*y^(-0.7))^(-10/7); := P 1000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 10 7 > with(plots): Warning, the name changecoords has been redefined > plot3d(P,x=0. .10,y=0. .10); #Step 2 : Marginal Productivity and Cross Elasticities > #First Order partials: > Px:=diff(P,x); := Px 300.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 x 1.7 > Py:=diff(P,y);

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:= Py 700.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 y 1.7 > # Evaluate Marginal Product for x=8, y=6 > eval(Px,[x=8,y=6]); 210.9003435 > eval(Py,[x=8,y=6]); 802.5090241 > # Capital Elasticity , Labor Elasticity > # Capital Elasticity for x=8,y=6 > eval(-(y/P)*Py,[x=8,y=6]); -0.7405204415 > #Labor Elasticity for x=8, y=6 > eval(-(x/P)*Px,[x=8,y=6]); -0.2594795585 #Step 3. Isoquant Analysis > contourplot(P,x=0. .10,y=0. .10); > # Critical Points > equations:={Px=0,Py=0};
:= equations , = 700.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 y 1.7 0 = 300.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 x 1.7 0 > Criticalpoints:=solve(equations); := Criticalpoints > # There is no Critical point > Pxx:=diff(Px,x); := Pxx - 153.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 24 7 x 3.4 510.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 x 2.7 > Pyy:=diff(Py,y); := Pyy - 833.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 24 7 y 3.4 1190.000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 17 7 y 2.7 > Pxy:=diff(diff(P,x),y); := Pxy 357.0000000 + 0.3 x 0.7 0.7 y 0.7 ( ) / 24 7 x 1.7 y 1.7 #Step 4 > # Use EVT to fine Maximum of production subject to x+y<=20, x>=0, y>=0 Objective value: 10511.6060591321840 x = 7.55828556812030428 y = 12.4417144318796975

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Math Project I - Khuong Bui Giau La Math 218 Part A...

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