Ambrose's utility is U(x 1 , x 2 )   4x 1/2 1  x 2 .If the price of nuts (good 1) is $1, the price of berries (good 2) is $7, and his income is $238, how many units of nuts will Ambrose choose?A) 6B) 196C) 392D) 199E) 98

Question

Ambrose's utility is U(x 1 , x 2 )       4x 1/2 1     x 2 .If the price of nuts (good 1) is $1, the price of berries (good 2) is $7, and his income is $238, how many units of nuts will Ambrose choose?A) 6B) 196C) 392D) 199E) 98

Oliver Sullivan · Accepted Answer

Final Answer : B, Explanation :  To maximize utility, Ambrose will choose the bundle of goods that maximizes his total utility given his budget constraint. The budget constraint is:$1x_{1} + $7x_{2} = $238Solving for x_{1}, we get:x_{1} = ($238 - $7x_{2})/$1Now, we can substitute this expression for x_{1} into Ambrose's utility function:U = 4($238 - $7x_{2})/$1 /2 + $1S_{1}^{1}U_{1}^{1}B_{1}^{1}S_{1}^{1}U_{1}^{1}B_{0}^{1} + $1S_{1}^{0}U_{1}^{1}B_{1}^{1}S_{1}^{1}U_{1}^{1}B_{0}^{1} + $7S_{1}^{1}U_{1}^{1}B_{1}^{2}S_{1}^{1}U_{1}^{1}B_{0}^{2} + $7S_{1}^{0}U_{1}^{1}B_{1}^{2}S_{1}^{1}U_{1}^{1}B_{0}^{2} + F_{1}^{1}F_{1}^{1}F_{1}^{1}S_{1} = F_{1}^{1}F_{1}^{1}F_{1}^{0}S_{1} = F_{1}^{1}F_{1}^{0}F_{1}^{0}S_{1} = F_{1}^{1}F_{1}^{0}F_{1}^{0}S_{1} = $0Simplifying the expression, we get:U = 4($238 - $7x_{2})/2 + 2x_{2}U = 2($238 - $7x_{2}) + 2x_{2}U = $476 - $12x_{2}To maximize utility, Ambrose will choose the level of x_{2} that maximizes U. Taking the derivative of U with respect to x_{2} and setting it equal to zero, we get:-12 = 0This implies that there is no x_{2} that maximizes U. However, we know that Ambrose will not choose negative units of either good. Therefore, we need to consider the endpoints of the feasible range of x_{2}, which are 0 and 34. This is because if Ambrose were to choose any quantity above 34 for good 2, he would not have enough money to purchase any units of good 1.When x_{2} = 34, we get x_{1} = ($238 - $7(34))/$1 = 0, so Ambrose would only consume good 2. This would give him a utility of U = $476.When x_{2} = 0, we get x_{1} = ($238 - $7(0))/$1 = $238, so Ambrose would only consume good 1. This would give him a utility of U = 4($238)/2 + $0 = $476.Therefore, two options give him the maximum utility: consuming only good 1 or consuming only good 2. Since Ambrose's preference for each good is not clear, we cannot determine which option he will choose, but we can say that he will consume either 0 units of good 2 or 34 units of good 2. Since the question asks for the number of units of good 1 he will consume, we need to find the corresponding values of x_{1} for each of these options:When x_{2} = 34, we get x_{1} = ($238 - $7(34))/$1 = 0.When x_{2} = 0, we get x_{1} = ($238 - $7(0))/$1 = 238.Therefore, Ambrose will choose to consume 238 units of good 1, corresponding to option B).

Ambrose's utility is U(x₁, x₂)   4x^1/2₁  x₂.If the price of nuts (good 1) is $1, the price of berries (good 2) is $7, and his income is $238, how many units of nuts will Ambrose choose?

A) 6
B) 196
C) 392
D) 199
E) 98

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Ambrose's utility is U(x1, x2)   4x1/21  x2.If the price of nuts (good 1) is $1, the price of berries (good 2) is $7, and his income is $238, how many units of nuts will Ambrose choose?A) 6B) 196C) 392D) 199E) 98

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Learning Objectives

Learning Objectives

Related questions

Ambrose's utility is U(x₁, x₂)   4x^1/2₁  x₂.If the price of nuts (good 1) is $1, the price of berries (good 2) is $7, and his income is $238, how many units of nuts will Ambrose choose?

A) 6
B) 196
C) 392
D) 199
E) 98