PROVIDE EXPLANATION 2. Elmer’s utility function is U(x, y)  minx, 5y. If the price of...

PROVIDE EXPLANATION

2. Elmer’s utility function is U(x, y)  minx, 5y. If the price of x is $25, the price of y is $10, and Elmer
chooses to consume 5 units of y, what must Elmer’s income be?
a. $1,350
b. $175
c. $775
d. $675
e. There is not enough information to tell.

Solutions

Expert Solution

U(X,Y) = min(x, 5y)

price of x is $25, price of y is $10 and consume 5 units of y

Income = 25*x+10*y we know y =5

If U(x,y ) = min(ax,by) form than it's perfect compliment .

This function states that the value of the utility takes the minimum value of aX and bY. For example, if aX= 4 and bY is equal to 6, then U is equal to 4.The indifference curve for this type of utility function has an L-shaped. So it is difficult, if not impossible,to determine the MRS = MUx/MUy. Consequently, the common method in solving for the optimalbundle cannot be used here.However, this utility function provides the optimal ratio of good X and good Y for a given level of utility.This optimal ratio can be obtained by equating aX to bY. Or X/Y = b/a

Compare this with our utility function U(X,Y) = min(x, 5y) so a =1, b=5

X/Y =5/1

X/5 = 5/1 = 25 if y=5 is optimal consumption bundle

Income = 25x+5y = 25*25+5*10 = $675

Rahul Sunny answered 1 year ago

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