Question

Ella’s preferences can be represented by the utility function u(x,y) = 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 (10, 25).

Select one:

a. $475.

b. $85.

c. $425.

d. $209.

e. $440.

Answer 1

The budget equation is given by:

10x+15y=M

Where price of good x = $10

Price of good y = $15

X and y are the quantities consumed of good X and good Y respectively.

Where M is the income.

If she can purchase a bundle (10,25) then her income can be found out by putting this bundle in her budget equation

10x+15y=M

10*10+15*25 = M

M = 100 + 375

M = 475

Therefore, She requires at least $475 in order to buy the bundle (10, 25). If her income is less than $475, then the bundle (10, 25) lies beyond her budget constraint and is not affordable. Given that she is able to buy (10,25), her income is $475

Therefore, a) $475 is the correct answer.

Option b) $85 cannot be correct because at this level of income, this means she cannot afford the bundle (10, 25). But according the question she can afford (10, 25).

Option c) $425 cannot be correct because at this level of income, this means she cannot afford the bundle (10, 25). But according the question she can afford (10, 25).

Option d) $209 cannot be correct because at this level of income, this means she cannot afford the bundle (10, 25). But according the question she can afford (10, 25).

Option e) $440 cannot be correct because at this level of income, this means she cannot afford the bundle (10, 25). But according the question she can afford (10, 25).

Therefore, a) $475 is the correct answer.

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