(Answered) For each of the following utility functionsa u xy 3x yb u

Economics

For each of the following utility functions:

a.) U (X,Y) = 3X + Y

b.) U (X,Y) = sqrt(XY)

c.) U (X,Y) = sqrt(X^2 + Y^2)

d.) U (X,Y) = ln(X) + ln(Y)

(i) Derive an equation for the marginal rate of substitution (MRS).

(ii) Calculate the MRS when the bundle is (X = 1 and Y =4) and the MRS when the bundle is (X = 4 andY = 1).

(iii) Based on your answers are preferences described by the utility function convex?

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