Ambrose has the utility function U(x₁, x₂)= 4x^1/2₁ + x₂.If Ambrose were initially consuming 9 units of nuts (good 1)and 21 units of berries (good 2), then what is the largest number of berries that he would be willing to give up in return for an additional 16 units of nuts? A)26 B)5 C)8 D)4 E)2

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To find the largest number of berries that Ambrose is willing to give up, we need to use the Marginal Rate of Substitution (MRS). MRS is the amount of one good a consumer is willing to give up in order to obtain an additional unit of another good while keeping the overall level of satisfaction constant. Mathematically, MRS is given by the slope of the indifference curve. The partial derivative of U with respect to x₁ gives the marginal utility of nuts, while the partial derivative of U with respect to x₂ gives the marginal utility of berries. So: MRS = (MU of Nuts) / (MU of Berries) = (2x^1/2₁) / 1 = 2x^1/2₁ At the initial consumption bundle of (9, 21), Ambrose's MRS is: MRS = 2(9)^(1/2)/(21)^(1/2) = 6/7 This means that he is willing to give up 6/7 units of berries for an additional unit of nuts, while staying equally satisfied. Now, we need to find the largest number of berries that Ambrose is willing to give up for an additional 16 units of nuts. This means that his new consumption bundle will be (25, y), where y is the number of berries he is willing to give up. To find y, we set up the following equation: MRS = (MU of Nuts) / (MU of Berries) = (2x^1/2₁) / 1 = 16/y Solving for y, we get: y = 26 So Ambrose is willing to give up 26 units of berries for an additional 16 units of nuts. Therefore, he would give up 26-21=5 units of berries.

Ambrose Has the Utility Function U(x1, X2)= 4x1/21 + X2

Ambrose Has the Utility Function U(x₁, X₂)= 4x^1/2₁ + X₂