if Charlie's utility function were X 2 A X B , the price of apples were p A , the price of bananas were p B , and his income were m, then Charlie's demand for apples would beA) 0.67m/p A .B) 0.50p A m.C) m/(p A  p B ) .D) m/(2p A ) .E) 1.50p B m/p A .

Question

if Charlie's utility function were X  2 A  X B , the price of apples were p A , the price of bananas were p B , and his income were m, then Charlie's demand for apples would beA) 0.67m/p A .B) 0.50p A m.C) m/(p A     p B ) .D) m/(2p A ) .E) 1.50p B m/p A .

Prakshal Bhavesh Parekh · Accepted Answer

Final Answer : A, Explanation :  To find Charlie's optimal demand for apples, we need to maximize his utility subject to his budget constraint. This involves finding the quantity of apples that maximizes his utility given the prices of apples and bananas, and his income.We can do this by finding Charlie's marginal rate of substitution (MRS), which is the rate at which he is willing to trade bananas for apples while holding his utility constant. The MRS is given by the ratio of the marginal utility of bananas to the marginal utility of apples:MRS = MU(B) / MU(A)Using the utility function given above, we can find Charlie's marginal utilities:MU(A) =  2 MU(B) =  ASubstituting these into the MRS equation, we get:MRS =  A /  2 This tells us that Charlie is willing to trade off some amount of bananas (as determined by  A) for each additional unit of apples, as long as the ratio of prices p A  / p B  does not exceed the MRS.To find Charlie's optimal demand for apples, we need to set his MRS equal to the price ratio, and solve for the quantity of apples that maximizes his utility: A /  2   = p A  / p B Solving for the quantity of apples, we get: A / (p A  / p B ) =  2 Simplifying the equation, we get: A / p A  =  2  / p B The quantity of apples that maximizes Charlie's utility is the amount that satisfies this equation, given his income.Substituting m for the total amount of money Charlie has to spend on apples and bananas, we can solve for Charlie's demand for apples: A / p A  =  2  / p B Solving for  A, we get: A = ( 2  / p B ) * p A This simplifies to: A =  2  * (p A  / p B )Finally, we can express Charlie's demand for apples in terms of his income and the price of apples:A)  A =  2  * (p A  / p B )This tells us that Charlie's demand for apples is directly proportional to his income, and inversely proportional to the price of bananas relative to apples.

if Charlie's utility function were X ²_AX_B, the price of apples were p_A, the price of bananas were p_B, and his income were m, then Charlie's demand for apples would be

A) 0.67m/p_A.
B) 0.50p_Am.
C) m/(p_A  p_B) .
D) m/(2p_A) .
E) 1.50p_Bm/p_A.

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Learning Objectives

Related questions

if Charlie's utility function were X 2A XB, the price of apples were pA, the price of bananas were pB, and his income were m, then Charlie's demand for apples would beA) 0.67m/pA.B) 0.50pAm.C) m/(pA  pB) .D) m/(2pA) .E) 1.50pBm/pA.

Definitions

Learning Objectives

Learning Objectives

Related questions

if Charlie's utility function were X ²_AX_B, the price of apples were p_A, the price of bananas were p_B, and his income were m, then Charlie's demand for apples would be

A) 0.67m/p_A.
B) 0.50p_Am.
C) m/(p_A  p_B) .
D) m/(2p_A) .
E) 1.50p_Bm/p_A.