Ambrose has the utility function U(x 1 , x 2 )  4x 1/2 1  x 2 .If Ambrose were initially consuming 49 units of nuts (good 1) and 12 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 32 units of nuts?A) 9B) 21C) 8D) 4E) 2

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Ambrose has the utility function U(x 1 , x 2 )    4x 1/2 1     x 2 .If Ambrose were initially consuming 49 units of nuts (good 1) and 12 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 32 units of nuts?A) 9B) 21C) 8D) 4E) 2

Maria Robles · Accepted Answer

Final Answer : C, Explanation :  We need to find the Marginal Rate of Substitution (MRS) of nuts for berries, which is given by the partial derivative of the utility function with respect to berries (good 2) divided by the partial derivative of the utility function with respect to nuts (good 1).MRS = (∂U/∂x2)/(∂U/∂x1)Taking partial derivatives, we get:∂U/∂x2 = 4x 2 /  -  ∂U/∂x1 = 2x 1 1 / Therefore, MRS = (4x 2 /  -  )/(2x 1 1 / )At Ambrose's initial consumption bundle, x1 = 49 and x2 = 12. Substituting these values, we get:MRS = (4(12)/F1F1F1 -  )/(2(49)/F1F1F1) = 2/7This means that Ambrose is willing to give up 2 units of berries for every 7 units of nuts he gains, while keeping his utility constant.To find the largest number of berries that he would be willing to give up in return for an additional 32 units of nuts, we need to solve the following equation:(12 - y)/(49 + 32) = 2/7Solving for y, we get:y = 8Therefore, Ambrose is willing to give up 8 units of berries for an additional 32 units of nuts while keeping his utility constant. So, the answer is option C.

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