On the x-y-plane, a ray from the origin is a straight line passing through the origin. (Mathematically, it is given by the equation y=rx for some real number r.) A preference is said to be homothetic if, the MRS does not change as we move along each ray from the origin. In other words, along each ray from the origin, the in difference curves are parallel. See Figure 1 for an illustration. Mathematically, a preference is homothemtic if, for any number >0 and any bundle (x,y)MRS(x,y) = MRS(x,y).

(a) Consider a two-good world and suppose a consumer's preference is homothetic.Can either one of the two goods be an inferior good for this consumer? (Hint:Sketch an indifference curve diagram with an increase in income.)

(b) What is the income elasticity of Good X when preferences are homothetic? (Hint:How does the ratio between the two goods consumed change when there is an increase in income?)