[From Bill Powers (2002.11,16,1259 MST)]
Bill Williams (2002.11.13) --
Attached is an attempt at showing the Giffen surface. I've also greatly
simplified the algebra by saying
Qx*Px + Qy*Py = B (Budget equation, cost = amount obtained times price)
Qx + Qy = Q
(Total quantity obtained equal sums of x and y amounts obtained. If Q
represents calories needed, then Px is price per calorie of obtained from
x, and so on. If x is meat, then Px is price per calorie of meat. the
derivation is attached.
The figure is from MathCad 8, which I've had for a few years and don't use
much. The 3-D graph doesn't have any labels on the axes because I can't
figure out how to put them on. The vertical axis is total amount of Qy
obtained, the axis running left and right is budget (increasing to the
left), and the axis running in and out of the page is the price per calorie
of Qy. Qy is the "giffen good". The graph is "fogged" (a kind of shading)
to help bring out details.
Bill W., if you want to see the graph with different parameter values, let
me know what they are and I'll try.
Best,
Bill P.
GiffenSurface.bmp (99 Bytes)
GiffenAlgebra2.doc (100 Bytes)