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Suppose u(x,y)=min(x,2y) and the price of X is 1, the price of Y is 1 and income is $12. If the price of X increases to 2, the income effect is supposed to be -1.
I keep getting zero for some reason. Gx(2,1,12)=4.8 and Gx(1,1,12)=8 while Hx(2,1,U)=4.8 and Hx(1,1,U)=8?
Why is it not zero? What am i doing wrong?
For perfect complements, the substitution effect is 0 so the income effect = total price effect. When price of x = \$1 then the quantity demanded of y = 12/3 = 4 units (and quantity demanded of x = 2*y = 8 units). When the price of x increases to \$2 then the quantity demanded of y falls to 12/5 = 2.4 units, so quantity demanded of x falls to 2*2.4=4.8 units of x. Thus, the total price effect is 4.8 - 8 = -3.2 which is the same as the income effect.
