Abe consumes Good X and Good Y. His utility function is given by U(x, y) = x - (3/y).

a.Compute Abe's MRS(x, y) function. Show your work. You should find that MRS(x, y) = 13(y2).

b.Suppose PX=144, PY= 48,I= 864. Find Abe's utility-maximizing quantities choice of x and y.

c.Suppose PY= 48 andI= 864, but that Pxis not specified. (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 144 in place of Px. Instead, leave Pxin the two

equations. You will have two equations and three unknowns, x, y and Px.

d.Find the equation for the price-consumption path as PXis allowed to vary. You will need to reduce your two equations in three unknows to one equation in two unknowns. Since the price consumption line shows a relationship between x and y, one will have to eliminate Pxfrom the equations. It will be easiest to make sense of it with x being a function of y (i.e. backwards).

e.Find the equation for Abe's 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= 144, according to your demand function, what quantity of X does he demand? Do the same for PX= 4, 9, 16, 36, 64 and 576 and draw a rough sketch of his demand curve.

g.If the price of Good Y changes, will Abe's demand curve for Good X shift? And how?

h.If Abe's income changes, will Abe's demand curve for Good X shift? And how?

i.If Abe's preferences change, will Abe's demand curve for Good X shift? How does the demand curve shift?