Janet consumes two commodities x and y. Her utility function is min(x + 2y, y +

ID: 1098910 • Letter: J

Question

Janet consumes two commodities x and y. Her utility function is min(x + 2y, y + 2x). She

chooses to buy 10 units of good x and 20 units of good y. The price of good x is 1. Which of the

following is true? (Please show Work or explain; i already know the answer, just need to how to get there)

(a) Janet's income is 40.

(b) Janet's income is 50.

(d) Janet's income is 20.

(e) There is not enough information in the problem to determine her income because we are not told the

price of y.

To maximize the utility function,you need two equations
1.MUx/MUy=Px/Py
2. INcome=Px *X+Py * Y

U(x,y) = min (50, 40 ) = 40 hence for this choices
U (x,y) = 2x +Y

MUx = 2
MUy = 1

Px = 1

So Py = (1/2) = 1/2

Putting into second eqution.
Income = 1* 10 + 20*(1/2) = 20 [ d}

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