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In an exchange economy, there are two goods, Quiches (Q) and Wine (W). Ken has preferences [tex]U= Q^2 W[/tex] and Barbie has preferences [tex]U= QW[/tex]. Ken has an endowment of 3 Quiches and 6 bottles of Wine, while Barbie has an endowment of 4 Quiches and 4 bottles of Wine. In the competitive equilibrium, how many Quiches and bottles of Wine would be exchanged?

A. Barbie gives Ken 2 Quiches and Ken gives Barbie 2 bottles of Wine.
B. Barbie gives Ken 1 Quiche and Ken gives Barbie 2 bottles of Wine.
C. Barbie gives Ken 2 bottles of Wine and Ken gives Barbie 1 Quiche.
D. Barbie gives Ken 1 bottle of Wine and Ken gives Barbie 2 Quiches.
E. None of the above.

Answer :

Final answer:

Determining the competitive equilibrium of goods traded between Ken and Barbie in an exchange economy requires equating their marginal rates of substitution and considering their respective endowments. Without additional price or trade willingness data, it is impossible to confirm the exact quantity of goods that would be exchanged between the two parties.

Explanation:

In an exchange economy with two goods, Quiches (Q) and Wine (W), we want to determine the competitive equilibrium in terms of how many Quiches and bottles of Wine would be exchanged between Ken and Barbie. Ken's utility function is U= Q²W, and he has an endowment of 3 Quiches and 6 bottles of Wine. Barbie's utility function is U= QW, with an endowment of 4 Quiches and 4 bottles of Wine.

To achieve a competitive equilibrium, we must equate the rate of substitution for both individuals, which implies that the marginal rate of substitution (MRS) for Ken must equal the MRS for Barbie, and trade must conserve the total endowment.

Ken's MRS (the rate at which he is willing to trade Wine for Quiches) is 2Q/W, and Barbie's MRS is Q/W. To find the equilibrium, we would solve the equation 2Q/W = Q/W, subject to the endowment constraints.

However, as this is a hypothetical situation that requires information not currently provided, we cannot determine the exact quantity of goods traded without additional data or assumptions about prices and the willingness of both parties to trade at those prices.

Considering the options given (A to E), without additional context or price information, it is not possible to confirm any of those trades as the definitive competitive equilibrium.

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