Question

In: Economics

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3...

Tamer derives utility from goods X and Y, according to the following utility function: U(X,Y)= 3 X square root of bold Y . His budget is $90 per period, the price of X is PX=$2, and the price of Y is PY=$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?

Solutions

Expert Solution

Budget = $90

PX = $2

PY = $6

Ans1.

Ans2.

1/2 value of MRS means that When Tameer has X=8 and Y=2; he is ready to give up half unit of Y for 1 extra X

Ans3.

How much should he buy to maximize utility?

Solution:

Budget = $90

PX = $2

PY = $6

Lets write the Lagrangian of the optimization Problem:

FONC's will be following:

Using FONCs

Using X=4Y into Budget Equation

Hence optimal X=30 and Y=5

Rahul Sunny answered 1 year ago
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