Consider a single consumer who has the utility function:

U(x1,x2)=x1x2 whose partial derivatives are:

U1(x1,x2)=x2

U2(x1,x2)=x1

Suppose that the prices of the two goods are (p1,p2)=(1,2) and that the income is m=5.

** Part a (5 marks)

Find the |MRS|, i.e. the absolute value of the slope of the indifference curve at (x1,x2)=(1,2). Check whether the point is on the budget line. At this point, does the consumer want to increase x1 by trading off x2 at the given market prices or not?

** Part b (5 marks)

Now suppose that (p1,p2,m) are unknown. Find the demand function of Good 1: i.e. x1 in terms of (p1,p2,m).

** Part c (5 marks)

Suppose that you want to study the effect of a (per-unit) consumption tax, which changes p1 to p1+t where t>0 is the tax. Show that whether the expenditure on x1 (including the tax) changes after the consumption tax, and by how much.