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 $15 and was paying a price of $8 for a pair of earrings, then if the price of earrings went up to $13, the equivalent variation of the price change would be
A)$5.36.
B)$8.33.
C)$16.67.
D)$2.68.
E)$6.85.

Question

Quizplus · Accepted Answer

To calculate the equivalent variation (EV), we need to find the amount of income Bernice would need at the old price of $8 to achieve the same level of utility as she can currently achieve with her $15 income at the new price of $13.

Using the formula for Bernice's utility function, we can set up the following equation:

min($8x, $15-$13x) = min($8y, $15-$13y)

where x is the quantity of earrings consumed at the old price and y is the quantity of earrings consumed at the new price.

To solve for y, we need to consider two cases:

Case 1: $8y < $15-$13y

In this case, Bernice spends all her available income on earrings and has nothing left for other stuff. We can solve for y as follows:

$8y = $15-$13y
$21y = $15
y = 15/21 = 0.71 pairs of earrings

Case 2: $8y > $15-$13y

In this case, Bernice spends all her available income on other stuff and does not buy any earrings. We can solve for y as follows:

$8y > $15-$13y
$21y > $15
y > 15/21 = 0.71 pairs of earrings

Therefore, Bernice's optimal choice of earrings at the new price of $13 is between 0 and 0.71 pairs. We can use the midpoint formula to estimate her optimal choice:

0.5(0 + 0.71) = 0.355 pairs of earrings

Using this quantity, we can calculate Bernice's utility at the new price:

min($13 * 0.355, $15 - $13 * 0.355) = min($4.62, $9.38) = $4.62

To find the EV, we need to find the amount of income Bernice would need at the old price of $8 to achieve the same utility of $4.62. We can set up the following equation:

min($8z, $15-$8z) = $4.62

Using the same approach as above, we get:

z = 1.25 pairs of earrings
min($10, $5) = $5

Therefore, the EV of the price change from $8 to $13 is $5 - $4.62 = $0.38 or approximately $5.36 in percentage terms ((0.38/15) * 100%). Therefore, the correct answer is A.

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