Question

U=U(X,Y)= 10X^0.9 * Y^0.1

the customer more likes X or Y? And what is the reason for your answer?

Thank you:)

(1) calculate the MUx and MUy
(2) the customer more likes x or y?
(3) what is MRSxy

Answer 1

U(X,Y)=10X^0.9*Y^0.1

Answer A)

MUx calculated as first-order differentiation of Utility function with respect to X, MUy calculated as first-order differentiation of Utility function with respect to Y.

MUx= dU/dX=10*d(X^0.9 * Y^0.1)/dX=10*Y^0.1*0.9*X^(-0.1)=9(Y/X)^0.1

MUy= dU/dX=10*d(X^0.9 * Y^0.1)/dX=10*X^0.9*0.1*Y^(-0.9)=(X/Y)^0.9

Answer B)

If we increase the consumption of good X from X=1 to X=2 keeping consumption of good Y constant at Y=1, then the increase in Utility will be 10(2^0.9-1) similarly if Y is increased from Y=1 to Y=2 keeping consumption of good X constant at X=1 then the increase in utility will be 10(2^0.1-1)

therefore we can see that, 10(2^0.9-1)>10(2^0.1-1). Increase in utility or satisfaction after consuming 1 unit of good X is higher than that of after consuming 1 unit of good Y.

Hence, customer more likes X over Y

Answer C)

MRSxy= MUx/MUy= 9(Y/X)^0.1/(X/Y)^0.9=9(Y/X)

By definition, the Marginal rate of substitution (MRS) is how much units of good Y one can forgo to consume an additional one unit of good X.