Hi Chegg experts! Please help me answer these questions in complete/step by step solution. Will uprate once answered ASAP. Thank you.
2.9 Utility, Utility, Utility (4 points) Consider a typical consumer whose preferences can be represented by a Constant Elasticity of Substitution (CES) utility function U(x1,x2)=(x1+x2)1/ where x1 represents the amount of good 1 consumed and x2 represents the amount of good 2 consumed. - Take the total differential of U(x1,xx) - Prove that the consumer is non-satiated. (Hint: Obtain the marginal utility of each good and prove that this is positive while stating the relevant domain). - Prove the phenomenon of diminishing marginal utility, that is, the additional utility per additional consumption will be lower for every additional consumption unit thereafter. - Prove that given the relevant domain, the consumer will never be "less" happy with an additional consumption of any good. - Demonstrate that Young's Theorem holds - Do the first five bullets but using the function U(x1,x2)=(x11)1(x22)2 where >0 is some subsistence parameter and 01 is some parameter. - Do the first five bullets but using the function U(x1,x2)=x1x21 where 01 is some parameter. 2.10 Rectangular Garden (2 points) Mr. Constantine wishes to mark out a rectangular flower bed using a wall of his house as one side of the rectangle. The other three sides are to be marked by wire netting, of which he has only 64ft. available. What are the length L and width W of the rectangle that would give him the largest possible planting area? Check to make sure that your answer gives you the largest, not the smallest area. 2.9 Utility, Utility, Utility (4 points) Consider a typical consumer whose preferences can be represented by a Constant Elasticity of Substitution (CES) utility function U(x1,x2)=(x1+x2)1/ where x1 represents the amount of good 1 consumed and x2 represents the amount of good 2 consumed. - Take the total differential of U(x1,xx) - Prove that the consumer is non-satiated. (Hint: Obtain the marginal utility of each good and prove that this is positive while stating the relevant domain). - Prove the phenomenon of diminishing marginal utility, that is, the additional utility per additional consumption will be lower for every additional consumption unit thereafter. - Prove that given the relevant domain, the consumer will never be "less" happy with an additional consumption of any good. - Demonstrate that Young's Theorem holds - Do the first five bullets but using the function U(x1,x2)=(x11)1(x22)2 where >0 is some subsistence parameter and 01 is some parameter. - Do the first five bullets but using the function U(x1,x2)=x1x21 where 01 is some parameter. 2.10 Rectangular Garden (2 points) Mr. Constantine wishes to mark out a rectangular flower bed using a wall of his house as one side of the rectangle. The other three sides are to be marked by wire netting, of which he has only 64ft. available. What are the length L and width W of the rectangle that would give him the largest possible planting area? Check to make sure that your answer gives you the largest, not the smallest area
