Suppose you are given the utility functionU1(qx,qy)=qx^(1/2)qy^(1/2)

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a) Show how the marginal rate of substitution is the same forU2(qx, qy)=(qx)^3(qy)^3

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b) What does this suggest about how economics utilizes preferences?

c) How does the marginal rate of substitution compare if the utility function isU3(qx,qy)=ln(qx)+ln(qy)

?Why would this be the case?Explain.