Discuss the demand functions-homothetic preferences

Discuss the demand functions-homothetic preferences

Microeconomics
Homothetic Preferences. The preferences represented by >= are homothetic if for any two bundles X and Y such that X >= Y, we have tX >= tY for all t > 0.

1) Show formally that if X is optimal in B(P,m), then tX is optimal in B(P,m).

Now assume that the utility functirepron that esents this preferences is given by: U(x1,x2) = x1^B * x2^1-B

2) Solve the consumer’s problem and deduce the demand functions.

3) Is G1 a normal or an inferior good? Explain.

4) Is G2 a normal or an inferior good? Explain.

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