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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   . 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

1. At the utility U = 36 the indifference is as given below :

2) The MRS between X and Y is infinite at all the bundles including the bundle X = 8 & Y = 2 .

MRS or marginal rate of substitution means how much good Y do you need , if you give up one good X , so that your utility is still the same . As in this case because Y is neutral no amount of it will substitute giving up one unit of X.

3 ) Given the prices PX = 2 , PY= 6 and budget is 90 . and budget line will be 2X + 6Y = 90

To Maximize utility he has to consumer as much good X as possible and zero good Y which in this case is

X = 90/2 = 45

Utility will be U (X,Y) = 3X = 3 * 45 = 135

Below is the graphical solution to it

Rahul Sunny answered 1 year ago
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