5. For each of the following utility functions, draw the three indierence curves

Question

5. For each of the following utility functions, draw the three indierence curves that correspond to the three stated utility levels, labeling each curve with the corresponding utility

level. Label any intercepts or kinks" in the line to fully identify the position of the curve.

(a) U(X; Y ) = minf3X; Y g; utility levels = 3; 6; 9

(b) U(X; Y ) = minf3X; 2Y g; utility levels = 6; 12; 18.

(c) U(X; Y ) = 5X + 2Y ; utility levels = 10; 15; 20.

6. For each of the following utility functions, derive MUX; MUY , and the MRS. Show your

steps.

(a) U(X; Y ) = X2Y

(b) U(X; Y ) = X(1/3) Y(2/3)

(c) U(X; Y ) = 4rootXY

(d) U(X; Y ) = XY + 3X + 2Y

Explanation / Answer

Let us take the utility function U= U(x , y). where U stands for utility and x and y are two goods.
Now this is a general form of the utility function. You will be given a specific function like U= 4(x+y) + 1/(x+y)
What you do is as follows:
Take U= 4.25 and find out the different sets values of x and y for which U=4.25. This sets of values give different points on the indifference curve with Utility equal to 4.25. You can see
if x= 1 and y= 3, U=4.25.
Again, if x= 2, y=2, U=4.25
Again if x= 3, y= 1, U =4.25.
Or, x =0, y=4, U=4.25
So, you plot the points (1,3),(2,2), (3,1), (0,4) and (4,0) and join them and you get one indifference curve.
To get another indifference curve with higher utility, you can set U=8.50 and find out the values combination of (x,Y) to get the points in the new indifference curve.

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