Question

Suppose that a consumer is at a bundle, (x_0,y₀), such that Ux/px > Uy/py. Assume a well-behaved utility function.
(a) Represent this situation graphically, in the commodity space (hint: you will have an indifference curve, a budget line, and the point (x₀,y₀)).
(b) What change in consumption will this consumer need to make so that Ux/ px = Uy/py and why.

Answer 1

(a)

Consider the following Consider the consumption bundle (x0 , y0)

The Budget line is given by: xPx + yPy = M, where Px and Py are the respective price per unit of good x and y

and M is the total outlay

Assume that the consumption bundle (x0 , y0) is on the budget line that means, x0px + y0Py = M and that at this consumption bundle Ux/px > Uy/py holds.

This situation is represented by:

(b)

Thus, the consumer should increase the consumption of good x and decrease the consumption of good y such that eventually, consumer attains Ux/ Px = Uy/Py

As the consumer increases the consumption of good x, the marginal utility would fall. Given Px, the ratio Ux/ px will fall

Similarly, as the consumer decreases the consumption of good y, the marginal utility would rise. Given Py, the ratio Uy/Py would rise and eventually a point is reached at which the consumer would attains Ux/ Px = Uy/Py