Sam consumes Good X and Good Y. Her utility function is given by U(x, y) =5xy2.

a. Compute Sam's MRS(x, y) function. Show your work. You should find that MRS(x, y) = y/(2x).

b. Suppose PX= 3, PY= 2,I= 120. Find Sam's utility-maximizing quantities of x and y.

c. Suppose PY= 2 andI= 120, but that Pxis not specified. Instead, we are going to allow the Pxto vary.

(I.e., we are going to treat Pxas a variable, along with x and y.) Rewrite the two equations you used to solve the problem in part (b), but this time do not use 3 in place of Px. Instead, leave Pxin the two equations. You will have two equations in three unknowns, x, y and Px.

d. Find the equation for the price-consumption line as PXis allowed to vary. Since the price consumption line shows a relationship between x and y, one will need to eliminate Pxfrom the equations. Describe the significance of this result.

e. Find the equation for Sams demand function for x. Go back to the two equations in three unknowns in (c), but this time eliminate y from the system so that you are left with an equation relating x and Px(i.e., a demand equation). Write it with x on the left hand side of the equation, solving for x.

f. If PX= 1, according to your demand function, what quantity of X does Sam demand? Do the same for PX= 2, 4, 5, 8, 10, 20 and 40.

g. If the price of Good Y changes, will Sam'sdemand curve for Good X shift? Think about how you found this demand function.

h. If Sam's income changes, will Sam's demand curve for Good X shift? Think about how you found this demand function.

i. If Sam's preferences change, will Sam's demand curve for Good X shift? Think about how you found this demand function.