Suppose that an individual has a Utility function represented by a CES function. The utility function of the individual is given as: U(x,y) = x1/2 + y1/2 c. Is the demand more elastic or inelastic than a Cobb-Douglas Utility function? Use the Slutsky matrix to illustrate.

Frank's utility function for WWE wrestling event tickets (x,) and NASCAR race tickets (2) is of the following Cobb - Douglas form: U(x,, ) = x 1 2 0.25 0.75 x 2 his income is Y, the price of WWE tickets is p₁, and the price of NASCAR tickets is p₂. a. Mathematically derive his 1 demand functions for x, and x2. No graphs! You are not required to use Lagrangian Function, you can just use the demand formulas for the Cobb - Douglas utility function (Chapter 5, fourth slide). b. Using your answers from part (a), find the demand functions for x and x2, and mathematically prove that they have the proper negative slope.

Hugo likes computers (C) and video games (G) and has the following utility: U (C,G) = ln C + G(a) Suppose the price of each computer is pC = 1, the price of each game is pG = 1, and Hugo has income I = 20. Find the Marshallian demand for C and G.(b) Find Hugo’s indirect utility at the above price and income.(c) Suppose the government imposes a tax of 1 dollar on video games. What happens to Hugo’s consump- tion of each good and his indirect utility? How much money does the government raise?(d) Suppose the government instead imposes a lump sum tax that is equal to the amount of revenue from thepreviousproblem. SonowyouhavepC =1,pG =1,I=20−τ,whereτ istheamountofrevenue from part c). What happens to Hugo’s optimal consumption and his indirect utility? How does his indirect utility compare to the previous case of a tax on video games?

(b) U(x, y) = min [ax, y]