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**brumby_3** **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,

40x+10(4x)=32,400

x=32,400/80=405,y=4(405)=1620.

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)?