If Bernice (whose utility function is min{x, y}, where x is her consumption of earrings and y is money left for other stuff) had an income of $19 and was paying a price of $5 for earrings when the price of earrings went up to $11, then the equivalent variation of the price change was

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To calculate the equivalent variation, we need to find out how much Bernice's income would have to change so that she is just as well off after the price increase as she was before the price increase.

Before the price increase, Bernice spent $5 on earrings and had $14 left for other stuff. Her utility was min(5, 14) = 5.

After the price increase, Bernice can only afford to buy (19/11) = 1.727 earrings (rounded to three decimal places). She will spend $11 on earrings and have $8 left for other stuff. Her utility will be min(1.727, 8) = 1.727.

To make Bernice just as well off as before, we need to find the income level that would give her a utility of 5 with the new price of earrings.

Utility = min(x, 19-11x/5) = 5

Case 1: x < 19-11x/5
x = 19-11x/5
x = 25/3

Case 2: x >= 19-11x/5
19-11x/5 = 5
x = 10/11

We choose Case 2 because Bernice cannot consume more than 1.727 earrings.

The equivalent variation is the difference between Bernice's initial income and the income she needs to have in the new situation to be just as well off:

EV = 19 - (10/11)($11) = $9.50.

If Bernice (Whose Utility Function Is Min{x, Y}, Where X