Question

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3 X . His budget is $90 per period, the price of X is P_X=$2, and the price of Y is P_Y=$6.
1. Graph the indifference curve when U= 36
2. What is the Tamer’s MRS between goods X and Y at the bundle (X=8 and Y=2 )? What does the value of MRS means? (أحسب القيمة واكتب بالكلمات ماذا تعني القيمة)
3. How much good X and good Y should he buy to maximize his utility?

3 X

Answer 1

The utility function provided is as U(X,Y)= 3X

Therefore only good X matters to Tamer and his utility depends on its consumption.

As only good X matters therefore this indifference curve will be parallel to the x axis because of its utility function

U= 36 = 6X (3*2 where 2 is the price of the good)

X= 6 and y doesn't matters

So it can be said that such an indifference curve can't be graphed as it will be a parallel line to the x axis which is not possible for indifference curves as each point on it will have different significance but will lie on the same line which contradicts indifference curves properties as we know the utility or significance of each bundle is same on a curve

b) As any amount of y is not substituted for any amount of X therefore change in y/ change in x = 0.This means that the line is either parallel or co incides with the X axis.

c) Tamer can maximize his utility at 6X=90 where 90 is the total income with him and 2 is the price of good X

Therefore for X=15 tamer can hit his maximum utility with his income