I'm in need of some help with an Economics question.

A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle (8,1). she is also willing to trade in 1 unit of x for 2 units of y when she is consuming bundle (4,4). She is indifferent between these two bundles. assuming that the Utility function is Cobb-Douglas of the form U(x,y)=X^(alpha) Y^(beta), where alpha and Beta are positive constants, what is the utility function of the consumer?

Re: I'm in need of some help with an Economics question.

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**asantos007** A consumer is willing to trade 4 units of x for 1 unit of y when she is consuming bundle (8,1). she is also willing to trade in 1 unit of x for 2 units of y when she is consuming bundle (4,4). She is indifferent between these two bundles. assuming that the Utility function is Cobb-Douglas of the form U(x,y)=X^(alpha) Y^(beta), where alpha and Beta are positive constants, what is the utility function of the consumer?

If you start from (8, 1) and "trade 4 units of x for 1 unit of y", you get (8- 4, 1+1)= (4, 2) Saying that she is indifferent between those means that $\displaystyle (9^\alpha)(1^\beta)= (4^\alpha)(2^\beta)$. If you start from (4, 4) and "trade in 1 unit of x for 2 units of y", you get (4- 1, 4+ 2)= (3, 6). Saying she is indifferent between those means $\displaystyle (4^\alpha)(4^\beta)= (3^\alpha)(6^\beta)$. That gives you two equations to solve for the two unknown values $\displaystyle \alpha$ and $\displaystyle \beta$.

Re: I'm in need of some help with an Economics question.

Thank you so much! I can do the rest of the my problems now. =)