# Question - I've shown the working out I've done thus far.

• Mar 20th 2010, 11:01 PM
brumby_3
Question - I've shown the working out I've done thus far.
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)?
• Mar 20th 2010, 11:14 PM
Pulock2009
commerial mathematics???
Quote:

Originally Posted by 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)?

i donot understand a number of things here:1)Marginal utilities2)optimal basket3)substitution effects4)budget line
• Mar 20th 2010, 11:15 PM
brumby_3
It's for a microeconomics class - maths applied to economics.
Hi, I'm still hoping that someone will help me out,
thanks :)
• Mar 21st 2010, 03:40 AM
brumby_3
I've done b) again and this is what I've got:
With the new price,

90x + 10y = 32400
9x + y = 3240

and

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.