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Question: tangent line to an indifference curve

Question:tangent line to an indifference curve

MrMarc 3163 Maple
December 17 2009
0

I want to find a tagent lines to the below contourlines for a function  U := Q[a]^alpha*Q[b]^(1-alpha); given any

value of Q[a] and Q[b]. I know the slope of such a tagent lines but I dont know the intercept. How can I derive such an equation ?



alpha := .5; U := Q[a]^alpha*Q[b]^(1-alpha);

SlopeIndiff = eval(-(diff(U, Q[a]))/(diff(U, Q[b])), {Q[a] = 4, Q[b] = 4});

plot3d(U, Q[a] = 0 .. 10, Q[b] = 0 .. 10, axes = boxed, style = patchcontour, color = "Orchid", contours = 20, orientation = [-90, 0], title = "Indifference Curves", titlefont = [times, bold, 16]);
 
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