Ella's utility function is min{ 5x, y}. If the price of x is $10 and the price of y is $15, how much money would she need to be able to purchase a bundle that she likes as well as the bundle (x, y) = (10, 25)?
A) $209
B) $440
C) $425
D) $475
E) $85

Question

Quizplus · Accepted Answer

For the bundle (10,25), Ella's utility is min{5*10, 25} = 25. To keep her utility at least 25 with the new prices, she must spend at least 25/5 * 10 + 15 = $40. Therefore, the total cost of the new bundle she likes must be at least $40 + $25 = $65. 
Option C is the only one that satisfies this condition: 
- (15, 23) costs 15*10 + 23*15 = $435 
- (20, 20) costs 20*10 + 20*15 = $500 
- (25, 15) costs 25*10 + 15*15 = $425 
- (30, 8) costs 30*10 + 8*15 = $380 
- (35, 0) costs 35*10 + 0*15 = $350

Ella's Utility Function Is Min{ 5x, Y}