Ambrose's brother Augustine has an income of $52 and a utility function U(x₁, x₂) = 18x^1/2₁ + x₂.The price of good 1(nuts) is $3 and the price of good 2(berries) is $1.How many units of berries will Augustine demand?

A) 25
B) 9
C) 50
D) 15
E) There is not enough information to determine the answer.

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Tushar Naidu · Accepted Answer

Final Answer : A, Explanation :  Augustine's marginal utility of income is 18x -1/2 1 . Setting this equal to the price of good 1, we get 18x -1/2 1  = 3. Solving for x 1 , we get x 1  = 9. Substituting this into the utility function, we get U(9, x 2 ) = 18(9) 1/2  + x 2  = 54 + x 2 . Setting this equal to Augustine's income, we get 54 + x 2  = 52. Solving for x 2 , we get x 2  = -2. This is not a valid solution, since Augustine cannot consume a negative amount of berries. Therefore, Augustine will demand 0 units of berries.

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