Ambrose's utility function is = 4x^1/2₁ + x₂.If the price of nuts (good 1)is $1, the price of berries (good 2)is $10, and his income is $460, how many units of berries will Ambrose choose? A)401 B)5 C)6 D)12 E)9

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Quizplus · Accepted Answer

To maximize Ambrose's utility, we need to find the combination of nuts and berries that will give maximum satisfaction within his budget constraint. Using the given utility function, we can find the marginal utility of berries as: MU2= F1F1F1S1/2 x^1/2₁ F1F1F1S1F1F1F10 MU2=$1/2 x (1/2√10)(10)^(-1/2)(460-4(1)+10(0)+1(11))+(1/2)(10)(460-4(1)+0(0)+1(12)) = $2.5 Similarly, the marginal utility of nuts can be found as: MU1= F1F1F1S1/2 x^1/2₁ F1F1F1S1F1F1F10 MU1=$1/2 x (1/2√10)(10)^(-1/2)(460-4(0)+10(1))+(1/2)(10)(460-4(0)+0(1)) = $10 Since the price of berries is much higher than the price of nuts, Ambrose will consume fewer berries and more nuts to maximize his utility. To find the optimal combination, we need to equate the marginal utility per dollar spent on each good: MU1/P1=MU2/P2 $10/$1=$2.5/$10 Solving for S1 gives us: S1 = 6 So, Ambrose will choose 6 units of berries and 23 units of nuts, which will cost $460 and maximize his utility. Therefore, the best choice is option C.

Ambrose's Utility Function Is = 4x1/21 + X2

Ambrose's Utility Function Is = 4x^1/2₁ + X₂