A consumer's preferences over food (x) and other goods (y) are given by U(x,y) = xy.
With marginal utilities MUx = y and MUy = x. The consumer's income is $32,400.
a) Calculate the optimal basket when px = 40 and py = 10.
b) Calculate the income and substitution effects (in terms of changes in quantity of x demanded) of an increase in the price of food to px = 90.
c) Calculate the Compensating Variation of the price change.
So for a) Maximized when y/x=40/10, y=4x.
Budget line, 40x+10y=32,400,
b) If px=90, x=180. So %change in price=125%,%change in quantity=56%, elasticity of demand =56/125=0.448. The increase in price has the same effect as a decrease in income.
Have I done all that I need for b) and how do I do c)?
I've done b) again and this is what I've got:
With the new price,
90x + 10y = 32400
9x + y = 3240
9x = y
y still = 1620, but now x = 180. There has been no substitution effect. The reduced quantity demanded is totally due to income effect.
I still don't understand c), so please help out!