Suppose that Bobby has a utility function U(x,Y)=x^(alpha )Y^(1-alpha ) and an income of I. P_(x) and P_(Y) are the prices of x and Y respectively.
a. Set up Bobby's utility maximization problem subject to her budget constraint. Use the Lagrange multiplier method to solve for her Marshallian demand function , P_(Y).
b. Solve for (delta x)/(delta P_(x)) and her uncompensated own-price elasticity of demand e_(x,p_(x))
c. Solve for (delta x)/(delta I) and her income elasticity of demand e_(x,I).
Now solve for her Hicksian demand using the following steps:
d. Write down her total expenditure E(x,Y).
e. Set up her expenditure minimization problem subject to a constant level of utility /bar (U) using the Lagrange multiplier method.
f. Use the Lagrange multiplier method to solve for her Hicksian demand function , P_(x),P_(Y).
g. Solve for (delta x)/(delta P_(x))|_(U()/(b))|=ar (U) and her compensated own-price elasticity of demand tilde(e)_(tilde(x),p_(x)). Next, assume that alpha =0.25,I=$240,P_(x)=$12,P_(Y)=$15. Assume that x and Y are perfectly divisible goods.
h. Use the Marshallian demand function you found in part a. to solve for the quantities of x and Y she consumes.
i. Bobby has the opportunity to join a discount club that allows her to purchase any quantity of Y at $12 per unit, while P_(x) remains unchanged. The fee for joining the club is $60. Should she pay the fee and join the discount club? Support your answer by comparing the utilities from joining the club and not joining the club. please show your work, dont just give conceptually, we will thumbs down if you dont explain
1.Suppose that Bobby has a utility function UX,Y)=Xy1- and an income of I.Px and Py are the prices of X and Y respectively. a. Set up Bobby's utility maximization problem subject to her budget constraint.Use the Lagrange multiplier method to solve for her Marshallian demand function Xm = X(I, Px, PY).
Now solve for her Hicksian demand using the following steps d.Write down her total expenditure E(X,Y. e. Set up her expenditure minimization problem subject to a constant level of utility U using the Lagrange multiplier method. f. Use the Lagrange multiplier method to solve for her Hicksian demand function X = X(U, Px,Py). and her compensated own-price elasticity of demand ez,px: 8PxU=U Next, assume that a = 0.25, I = $240, Px =$12, Py = $15. Assume that X and Y are perfectly divisible goods. h. Use the Marshallian demand function you found in part a. to solve for the quantities of X and Y she consumes. i.Bobby has the opportunity to join a discount club that allows her to purchase any quantity of Y at $12 per unit,while Px remains unchanged.The fee for joining the club is $60. Should she pay the fee and join the discount club? Support your answer by comparing the utilities from joining the club and not joining the club.
